Colin Broholm  Incommensurate Neutron Resonance in YbRh2Si2
Blogged by Piers Coleman

Colin gives the overview. He says that they've discovered a mesoscopic spin resonance and they'd love feedback on this new result about to appear in PRL.   He begins with a review o V2O3.  Its one of the classic examples of a Mott system.  There is a doping tuned transition from a spin density wave (SDW) into an antiferromagnetic (AF) Mott insulator (AFI). In this system, one can understand the helical spin density wave using RPA, which has a susceptibility that peaks at the observed Q vector.

Colin reviews neutron scattering and the RPA description  chi(q) = (chi0^-1(q)-J(q))^-1. In V2O3, they have not yet been able to use pressure to drive the Tc of V2O3 to zero.  Another approach is to use a heavy fermion system, governed by much lower energy scales.  He shows the tetragonal structure, and the afm phase below 70mK that is suppressed by a field. The standard understanding of this system, is as a result of the interplay of RKKY interactions with the Kondo ineteraction. Increasing J causes the magnetism to melt, into a heavy fermi liquid. Shows the figure from Schroeder et al (2003). Is the transition an SDW, or do we go from a local moment AFM into a state where the 4f electron is delocalized.  This would involve a metal insulator transition at the magnetic transition.  This is in contrast to V2O3, where an SDW separates the AFI from the metal.

Colin reviews the hall jump at the QCP measured by Friedemann, Paschen et al (PNAS, 2010). He shows that with Iridium/Co doping, one can split the localizing transition from the magnetic transition. This type of treatment does not explain why the localization and magnetization transition coincide without doping.

Q: How are the lines measured?
A: Not my data, but there are various thermodynamic anomalies that are followed to map out the phase diagram.

YRS is a problem for neutrons. Rh absorbs neutrons.  Crystals are small.  So combine 200 5x5 mm^2 crystals. Absorption of neutrons causes heating, which limits physics at the moment to T>0.1K.
Trying hard to go down to lower T, but not there yet - so the quantum critical region has not yet been accessed.

There are 4 crystal field doublets measured by neutrons.  The lowest excitation is at 80mK, so the ground-state doublet is pretty well isolated. The GS doublet is a mix of 3/2 and -5/2. The system is quite anisotropic, and has most of its Curie response in the easy plane. (20 x smaller in c-axis).

Now neutrons see an incommensurate feature around (002), with some incommensuration in the HH2 direction, at H~ +- 0.14 reciprocal lattice units (rlu). The incommensurate feature survives down to 0.1K, with a correlation length of about 3.6 (a+b). With a energy of about 0.1 meV.  The band structure would give 0.7,0.7,0 - not quite the right wavevector, but he speculates that there might be an indication of the origin of the incommesurate wave vector.

Q: would this have the 80mV crystal field split off
Mike Norman - even the dft differs.  One needs a renormalized band structure calculation.
Silke Paschen - this may have been done by Gertrude Zwicknagl.

So - since one can't look at low enough temperatures, try applying a  field to see the effect.  On heating, the detailed incommensurate structure merges into a ferromagnetic peak.  Now one can follow this as a function of field. This reminds one of MnSi (manganese silicide, which has similar behavior. )  The spectrum broadens with temperature. The width of the spectrum broadens with temperature. Quite unusual says Colin. (Blogger, but seen in CeCu6-xAu_x).

 Gamma = C T

Leads to omega/T scaling, he says. And indeed it is! Get a scaling exponent of alpha = 1.

chi'' (E,T) = 1/T^alpha f(E/T)

This is not deep into the qcp regime, but certainly consistent with the linear resistivity regime and specific heat.

Q: From the blogger - does this exponent also appear in the uniform susceptibilty, a la Schroeder et al?
A: It must do - if it fails, there would be something inconsistent with our experiment! But we should check it.

He shows how the intensity scales, as expected with M^2. Now back down in temperature, what is the effect of field? The signal shifts to finite energy - about 0.35 meV. By applying a field, the excitation is still there.  This he says, would tend to favor an SDW picture. (blogger - but E/T scaling?)

The neutron scattering is able to see the ESR mode - one extracts the same g factor of 3.86 (neutron)
vs gperp = 3.56 in ESR.   This is one of the first time that an ESR resonance has been seen in neutron scattering - it has been moved by field up into the regime where it can be seen by neutrons.

He points out that a similar FM spin resonance is seen in MnSi, but what is distinct in this case, the excitation has a dispersive form. Is a similar propagating mode seen here.

NO! There isn't!  Its a "spot" in energy momentum space, out at 1meV, with a width of 0.04 in qspace and 0.05meV  in energy.  How should we interpret this localized excitation?  It should be regarded as a completely collective precession of all of the f-electron spins.  A spatially extended spin density - a "mesoscopic spin resonance" . The size that we can extract from the peak is associated with the resonance -

Makes the analogy with the spins that develop as an edge state in Haldane spin chains. In that case, there is an extended spin=1/2 excitation.  Here, the correlation length is about

xi ~ 6(2) Angstroms

This is similar to a Kondo length scale

xi ~ v_F/TK ~ 15A.

Using the gamma in a field to get vF.

Q: in the spin chain example - does it exist for only one frequency?
A: change field, the resonance moves along.

Many conclusions (below).

• Main result - FM scritical regime for T> 1K.  
• Lower Incommensurate critical flus at Q= (q,q,0) q=0.14
• SDW instability may arise from nesting of hole fermi surfaces
• B suppresses SDW favoiring FM polarized metal
• Mesoscopic spin precession indicates Kondo screened 4f spin degree of freedom
• SDW correlations persist at lower energies in magnetized Kondo lattice state.

Q: from Andrey C.  Do you still see E/T scaling at lower temperatures?  Can you still do it below 1K?
A: can't answer this yet - I feel we need to go to lower T.  Our resolution is such that to answer this, with our resolution, will require the next generation of experiments.

Q: from Mike Norman. If you look at the AC susceptibility in LiHoFl - it also shows lifting up - one has large ferromagnetic clusters. I think you have to use a similar idea here.
A: Blogger missed it - seemed to agree.

Q:  fluctuating moment - how big is it?
A:  4 mu_B^2 - really large. Now the size of the ordered moment - can't say yet. 0.01 would be very small - has to be a way of accounting for why its so small, yet with such a large fluctuating moment.

Q: is there a change in the width of the esr type line with field?
A: no.

Q: There seems to be a double peak at o.1meV in your data 15K?
A: doesn't look healthy to me. When we went to higher fields - moved to higher energy - see commensurate peak at the esr energy and incomensurate peak sustained at lower energies (0.5meV).

Kedar Damle; Fractional spin textures and their interactions in a classical spin liquid

Kedar started by introducing the physics of frustrated magnets.
He introduced antiferromagnetic interactions between magnetic ions
and mentioned that the determination of exchange coupling J is not
always easy, but sometime may be measured by going into an order
phase (for example, by applying a magnetic field) as in Yb2Ti2O7.
Antiferromagnetic Ising interactions between magnetic ions in
triangular lattice is, for example, frustrated. This leads to macroscopic
degeneracy of classical ground states, leading to paramagnetic
liquid-like correlations with no magnetic order down to very
low temperature.

Then he turned to the question of impurities in real materials
and emphasized that these can be used to probe intrinsic properties
of the bulk system. For example, the local probe like NMR can measure
spin polarization histogram of local susceptibility at various distances
from impurity. This polarization histogram knows about the response of
the system to the impurity.

Kedar mentioned an example of the Haldane chain.
At the end of the open chain, we generate S=1/2 spins and this is
the characterics of topological order in the Haldane phase.
This was demonstrated in Y-NMR studies of the effect of
non-magnetic Mg^{2+} impurities in S=1 (Ni^{2+) chain) in
Y2BaNiO5. The data can be favorably compared to QMC simulation.
So the correlations encoded in intricate charge/spon textures
can be seed by impurities and picked up by the NMR local probe.

Now his main subject: SCGO

He is interested in non-magnetic Ga impurities in pyrochlore
slab magnet SCGO. This is an insulating magnet of
Cr^{3+}, S=3/2 system
The structure consists of Kagome bilayers with up and down pointing
tetrahedra - separated by Cr-Cr isolated spin pairs.
The idealized SrCr9Ga3O19 is not realizable and there is always
some disorder or impurities, so one may get about 5% Ga impurities
in isolated spin pairs and in Kagome bilayer

In experiments, the macroscopic susceptibility suggests
the Curie-Weiss temperature of \theta_CW = 500-600 K and there is
no sign of magnetic order down to T_f = 3-5K. There is some kind of freezing
or spin glassy behavior at T < T_f and the nature of phase for T < T_g not clear.

NMR measurements suggest that there is a broad, apparently symmetric,
Ga NMR line with broadening \Delat H = x/T for not-too-small x.
This may suggest short range oscillating spin density near defects
orphan spins.

Now turn to theoretical considerations.

The classical energy at T=0 can be minimized by making the spin sum
in each simplex or cluster to be zero.
Keadar demonstrated that, in the case of single Ga on any simplex,
there is no problem with simplex satisfaction, namely zero or minimum
spin sum in each simplex. On the other hand, for two Ga in one triangle,
one generates, <S_z_tot> = S/2 ! (at T=0, h/J->0). That is, one generates
half-orphan spins.

There is a way to formulate this using the so-called artificial electro-dynamics
using the mapping of
E_{\alpha}_i = S_i ^{\alpha} e_i, where E is an artificial electric field.
Then the simplex satisfaction condition becomes div E = 0 at T=0.
In this language, one defective simplex would correspond to
\div E^{\alpha}_triangle = S_{alpha}.
This leads to the T=0 Gauss law and 1/r decay of the spin-spin
correlation at T=0 for induced spin textures.

According to Moessner-Berlinsky's old work, defective tetrahedra/triangles
give Curie tail and no other simplex would give the Curie tail.
But what about correlation (long range) between simplifies ?
Also what about  the entropic effect at non-zero temperatures ?

Kedar looked at the large-N vector model which can describe classical
magnet with N-componet vector with the fixed length. Then he considers
the free energy, where he introduces phenomenological stiffness
parameters to write the entropy associated with the spins in Kagome
and apical simplices. Then he looked at the effective lone spin model
at the defective triangle and compute the spin polarization as a function
of magnetic field and temperature; it predicts the form of S B(hS/2T).
He tested the predictions of the effective theory of this lone spin
by doing Monte Carlo simulation.
He found the impurity susceptibility to be
\chi_omp = (S/2)^2 / 3T. That is it indeed shows the behavior of
fractional S/2 !
He also found that single defect does not lead to the Curie term, but
pairs of vacancies should lead to the Curie term. He also showed
the absence of three-body and higher order contributions.

Discussion on theory vs experiment followed.
Kedar found that \Delta H = A(x)/T = x /T captured correctly.
What is not captured in theory was discrepancy between the concentration
of impurities used to fit the susceptibility.
One interesting question:
are randomly positioned orphan spins interacting with each other ?

There were also some questions from the audience.

Q: Is there a possibility of charge density wave due to impurities explaining
the experiments ?
A: how to imagine it shows 1/r spin texture and Curie response etc

Q: does power decay necessarily mean the existence of fractional spin ?
A: while the theory presented here for pyrochlore lattice is pretty general,
there might be other situations that were not explored here.

Q: Why is the impurity concentration "x" in theory larger than experiment ?
A: There may be clustering or pair correlations between impurities in experiment.

Theory of magnetic structures in layered iridates; band or Mott
by Hae-Young Kee (Toronto Univ.)
blogged by Ryotaro Arita

Hae-Young starts with the periodic table, where she notes that the spin-orbit coupling of 5d elements is stronger  than that of 3d or 4d elements. In this talk, she will focus on the so-called Ruddelsden-Propper series of Ir oxides.

Then she moves to the crystal structure of Sr_{n+1}Ir_{n}O_{3n+1}. Here, she mentions that Sr2IrO4
is iso-structural to the mother compound of high T_c cuprate, La2CuO4 or Sr2RuO4. She shows the transport (resistivity as a function of temperature) data which indicates that the system is insulating for n=1 and 2, but bad metallic for n=∞. As for the magnetic property, she mentions that the ground state of Sr214 is canted AF.

Now her main subject is the "origin of magnetism and metal-insulator transition".

To address this question, she start with the level diagram. Here we see that the combination of crystal field splitting and strong spin-orbit coupling forms J_eff=1/2 and 3/2 band. Since the number of d electrons in each Ir atom is five, the J_eff=1/2 band is half-filling. If we follow the band theory, the system is a metal. On the other hand, if the electron correlation is strong enough, then the system should become a Mott insulator, like La2CuO4.

From the X-ray absorption spectra for Sr2IrO4, (by looking at the ratio between L3 and L2), we can say that the spin-orbit coupling is indeed strong, and the low-energy states around the Fermi level are formed by J_eff=1/2 states. The optical conductivity tells us that the system is an insulator, so that experimentally, it is suggested that Sr2IrO4 is a spin-orbit driven Mott insulator.

Given this situation, she raises the following two questions:
(1) For Sr214 and Sr327: Are they spin-orbit band or Mott insulator ?
(2) For SrIrO3: Is it semimetal and topological insulator?
She is going to answer these questions by means of a microscopic calculation.

First, she explains the detail of the effective model for Sr214. The perovskite octahedra in the unit cell have distortion and rotation, so that the unit cell contains 4 Ir layers, each layer has 4 Ir atoms. Considering this complexity, the one-body part of the Hamiltonian was derived by the Slater-Koster approach. The band dispersion of Sr2IrO4 is shown, which captures the essential feature of the ab initio calculations. Next she discusses what happens if the Hubbard U is introduced. She shows a phase diagram, where Uc (the critical U for metal-insulator transition) is about 1, but U for Sr2IrO4 is about 1.8. She comments that the magnetic pattern of the antiferromagnetic phase is canted AF (in the plane).

On the other hand, for n=2, she emphasizes that bilayer hopping is as strong as that of in-plane, and the band dispersion of the one-body part of the effective Hamiltonian already has a gap around the Fermi level. This is in high contrast with Sr214, and Sr327 has a possibility of being a band insulator. Indeed, according to her phase diagram,  Uc sits on the border between spin-orbit band insulator and AF insulator, so that she concludes that Sr3IrO7 is not a Mott insulator. This is the answer to the first question.

She also demonstrates that the magnetic pattern of Sr214 (canted AF) and Sr327 (collinear AF) can be understood in terms of the effective spin model (derived by the 1/U expansion for the multi-orbital Hubbard model). The spin model contains the Heisenberg isotropic exchange, DM, anisotropic exchange terms.

Q: How large is the spin dependent hopping ?
A: It depends on the distortion in the crystal structure.

Then she moves to the second question on SrIrO3. If we look at the crystal structure, we find that it has Pbnm lattice symmetry, i.e., there are rotation and tilting of the perovskite octahedra in the unit cell. To describe this complexity, she needs to introduce 3 Pauli matrices in the effective model.

She shows the result of LDA+SOC+U. Around U point in the Brillouin zone, the four J_eff=1/2 bands form two interpenetrated pairs of cones. These cones form two Dirac-like points and a circular line node at the Fermi energy. The density of states around the Fermi level is very small, and we need large Hubbard U to make the system a magnetic insulator. She shows a phase diagram against SOC and U, for which she emphasizes that SOC stabilizes the semimetal phase.

Lastly she proposes that if we make a superlattice of Sr2IrRhO6, then we will have phase transitions between nodal semimetal -> strong topological insulator -> band insulator.

Q: Z2 topological invariant calculated ?
A: Yes, by looking at the parity of wave functions

Q: Why Sr214 is not SC but Sr2RuO4 is SC?
A: SO is large for Sr214, while Sr2RuO4 has weaker SOC

Michael Norman (Argonne National Laboratory, USA)

Arcs versus Pockets - To d-wave or not to d-wave, that is the question

Blogged by Andrey Chubukov and  Aharon Kapitulnik

Arcs vs. Pockets


Shakespearean title: Arcs versus Pockets - To d-wave or not to d-wave, that is the question.

Mike appears, tall, slender, but... with more gray hair than last year.

Cannonical phase diagram of cuprates. Undoped state any AFM insulator.
All theories depend on what is going on in the pseudogap phase.  Shows a list of "What is the pseudogap."

Doping a Mott insuator - x vs. 1+x

- Slater approach - AFM causes small pockets around (\pi/2,\pi/2)

- Strong coupling proposal by PWA, uniform RVB. As doping goes to zero, no structure of ordered AFM. - 1987.
However, possibly a stable state is a flux-phase state - PA Lee. Gets a Dirac-like spectrum. At finite filling, pockets.

More recently, YRZ theory, umklapp RVB. GF has zeroes along AFM zone boundary. Pockets are displaced towards \Gamma points. Arc + suppressed intensity in the back side.

Andrey-  Mike says that the  straightforward way to track the FS is to analyze quantum oscillations.  He discusses early experiments at Los Alamos which show  small FS.  But these experiments  were questioned and argued to be possibly a noise effect.   He argues that failure of that experiment forced people to look at ARPES for the information about the FS.  He continue with the  arc story and its interplay with the pseudogap.  Mike  discusses the question, first asked by Shen et al,  whether the arc is real or a part of the pocket.  Mike shows data by Kanigel it al who found that the length of the arc apparently scales linearly with T.  This lead to a suggestion that the arc may a finite T effect of broadening of the spectrum of a d-wave SC.  Mike then discusses recent, higher quality data from Dessau group.  In more underdoped systems, there is still some evidence for d-wave like gaps.

Need to understand normal state - perform quantum oscillations: specific heat and transport. This probes Periods of extremal orbits. With Fourier Transform of QO, obtain the frequencies - map out Fermi surface.

 - Old data on optimally doped, 1992, saw a small Fermi surface - called noise effect - not believed.

 - ARPES took over. mapping of Fermi surface (occupied states.) Measure Energy Distribution Curves and Momentum distribution curves.
ARPES observed d-wave like dispersion, Large Fermi surface. Above T*, observe a large Fermi surface with no coherent QP. Between Tc and T*, arcs were observed.

Now Mike discusses: First - Arcs scenario, then Pockets scenario.

  

All transport scale as T/T*, and also ARPES arcs scale as T/T*. Maybe the normal phase is similar to the superconducting phase.

- New data by Dan Dessau. He constructed an angle resolved DOS. Arc length as a function of temperature agrees with marginal Fermi liquid. Increase temperature arc length increases.

- Underdoping - still has a d-wave like gap, evidence that d-wave gap persists into the insulating phase.

Pockets in Nd-doped LSCO? Chang et al. paper,  evidence for \pi-\pi reconstruction. But,  incommensurate.

- Meng et al. Single layer BSCCO - claimed to see the back-side of the pockets. Suspicion that it is structural effects. Indeed, this was subsequently shown experimentally.

- Bilayer BSCCO, see a pocket similar to YRZ ansatz. (Yang et al. - Nature (2008).)

Q (PC) - Can you show how and where flat part appears in the data? Mike explains that in ARPES they need to deconvolve the resolution.

Q (AC) - Any other example? Yang et al. claim arc length is temperature independent. They extract the arc tip. but, since Fermi function is strong function of temperature, conclusion is doubtful.

- Similar data from STM - quasiparticle interference. They do see states terminating at the magnetic zone boundary - it is also a structural zone boundary.

What about quantum oscillations (QO) - also very messy.  QO observed using UBC samples. Size of pockets agree with ARPES.
Hall number is negative - either large Hall background, or what they see is electron, not Hall pocket. Unresolved.

LeBoeuf observed hat negative Hall doping appears around 1/8, very narrow, Indicate formation of stripes.  Stripes proposed early, origin from segregation of holes.

- For magnetic stripes, electron pockets are stable for range of potentials. Charge-only model - no pockets.

- Kivelson proposed strong nematic order plus charge order - pockets.

- A larger hole Fermi surface from spin-spiral state was proposed. spin spiral instead of spin linear.

Experimental data of Sebastian et al. - three different periods, - but now all think that only one pocket plus bilayer splitting.

Riggs et al. - oscillations appear in specific heat. - there is also a zero-field offset. sqrt(H) persists above irreversibility. Hc2-inferred - 100 T.

Latest from cambridge - checkerboard order of charge, form a pocket centered around point closer to center.

NMR by Marc Julien, NMR agree with charge density wave - charge ordering. Field induced? - no RIX experiments - charge ordering peak - SC sets in charge order persist when superconductivity suppressed. Charge peaks around quantum oscillations. Keimer - edge of detectability. missed before because the wave-vector is not ordinary at \pi/2. they see larger wave-vector. but, ARPES does not see the same.

Q(AK) - but, you compare ARPES on BSCCO and YBCO. Mike replies that indeed this is the case, but indicates that BSCCO is very dirty and hopeless for QO.

Q(AK) - how about use data on LBCO? Mike just compares BSCCO and YBCO.

Q(AC) - charge or spin nematic ?  Mike answers that spin nematic. Nematic does not open a gap. Similar problem with Varma model, does not open a big energy gap.

 

Andrey:   Mike continues with the pocket scenario – there are data on Nd-doped LSCO which  were first interpreted as evidence for a pocket, but later re-interpreted as a structural effect.   There are data from P. Johnston group which show consistency with YRZ scenario.   Mike suspects that this may again be structural effect, but  stresses that there is  no proof of this.   In his view, one issue with the results from Brookhaven group is that they differ from other groups in the T dependence of the arc – Dessau and Campuzano groups argue that arcs are T dependent, while Brookhaven group argues that  the length of the arc is T-independent.

Mike then discusses the revival of quantum oscillation measurements.  The size of the pocket inferred from quantum oscillations is consistent with “closed arc”, but  the Hall number is negative, what implies that the pocket is likely an electron pocket.   He then  discusses the  stripe scenario by Millis and Norman and by Kivelson et al, and the results by Cambridge group which found that the effective mass extracted from quantum oscillations  diverges at the lowest doping at which oscillations are still seen.   Another scenario for quantum oscillations is checkerboard  charge order.   Mike discusses NMR evidence for charge order around 1/8 doping.  There is also evidence for charge order from x-ray data from Keimer’s group.  His  conclusion is that FS extracted from pocket scenario is inconsistent with ARPES.

 

Kristjan Haule (Center for Materials Theory, Rutgers University, USA)

Physics of Hunds metals and its relevance for Ruthenates and Iron pnictides and Chalcogenides.

Blogged by Natasha Perkins

Kristjan Haule started with acknowledging collaborators.

In the standard theory of solids electrons are well described wave ( quasiparticles) – Bloch theory. This is the good starting point for numerical calculations. For example, one can make  very good estimations of the gaps in semiconductors.

The problem of standard theory in correlated metals  comes from the fact that we do not  know which part of  electrons is localized and  which part  of electrons is itinerant.  Electrons have dual nature.

It is very challenging to deal with systems which are partly localized and partly itinerant. Our main focus is in understanding the electronic structure of complex correlated materials. We try to understand experiments – optics, ARPES, STM. We also developing DMFT as a computational tool.

Our workhorse is the DMFT. I do not know how many of you are familiar with that, so I briefly overview the technique.  The basic is – one spin is interacting with Weiss mean field. Details can be learned from RMP 2006. The DMFT is exact in the limit of large dimensionality. IN DMFT the special fluctuations are ignored. They can be partially taken into account in the cluster DMFT, but even one site DMFT often gives good description of systems with correlated electrons.

The simple test of the DMFT is to study the molecular hydrogen. When we pool apart the molecule, we should recover to H2 ions. This is in fact a nontrivial problem, and many numerical approaches have big difficulty in doing this. For example, HF fails, LDA fails, but DMFT captures exact atomic limit accurate at large R.

 Some people argue that DMFT does not work well. I will convince you that this is wrong. It is important to take local things correctly which we can do in DMFT.  

Piers asks about the symmetry. Cristjan answers that good choice of local symmetry help producing good results. You solve the HF first, look for the local symmetry, and then add correlations. 

 Next, Cristjan presents basic equations of the DMFT: Baym-Kadanoff functional, HF+DMFT approximation, LDA+DMFT approximation. He also discusses the double counting problem.

Next question is from Andy about the sum rules. Can you satisfy them by DMFT.

 Nest, let us discuss Hund’s coupling in impurities.

Old experiments on Kondo problem- magnetic impurities. High spin due to Hunds couplings. It is difficult to screen it, 1973 paper by Okada and Yosida  (Progress of theoretical physics) .  Having Hund’s coupling or  not having it make a huge difference. This paper was forgotten for many years  but its importance became obvious after discovering of pnictides.  Because otherwise how can we understand strong correlations in d5 systems.

Hund is important in understanding of correlation in itinerant metals. Fe has  one electron more than half-filled case, and Ru has one electrons less. Hubbard U is not the only relevant parameter. The Hund bring correlation in these systems.

Andrey: can you say a couple of words how you calculate local susceptibility in the presence of the Hund’s coupling? Cr.: I have to be careful with my answer. The local approximation in DMFT is done in real space. But of course, it will not be local in the band picture.

In order to get some insights in the role of Hund’s coupling, let us start with half-filed case. N=5. When you add one electron, you got a double occupancy. You have much less number of paths for screening. This leads to orbital and spin blocking of electron transport.

Next, let us discuss the phase diagram of 3 band Hubbard model. It turns out that the role of Hund’s coupling varies significantly with the number of electrons ( paper by L. de Medici).

At half-filling  orbital degrees of freedom are frozen. As orbital fluctuations are blocked, and you have only spin fluctuations.Now you switch spin-orbit coupling. This will allow orbital fluctuations.

We can compute orbital and spin susceptibilities. Orbital fluctuations are substantial away from half-filling, while spin fluctuations are maximum at half-filling.

 Let us go to specific materials.

Sr2RuO4. If there is no JH, you have small mass enhancement and it is the same for all orbitals. Once you switch JH, you have orbital differentiation. You would think that may be you can explain it just by U, but if you do it you will get a wrong trend. If you look to the coherence T, you will see that xy orbital has much lower coherence T compared with yz, zx orbitals.

There is a discussion between H.Kee and Cristijan  about the role of eg orbitals, pnictides vs ruthenates.

 If you look to 2 particle quantities, coherence temperature is even smaller.

 Few words about transport – huge anisotropy in optics  due to combination of orbital differentiation and matrix elements.

Very quickly about optics of Hunds’ metal.

 In Hubbard system you have Drude peak and Hubbard bands. In pnictides, there is a redistribution of weight with energy scale of JH.   The incoherent regime is very pronounced. There are sub-unitary powerlaws over an intermediate T and intermediate frequencies.

Very slow spin fluctuations but fast orbital fluctuations coupled to each other with leads to apparent powerlaws. DMFT can get powerlaws at very in self energy.

Question: what makes mass anisotropic? The answer is the crystal field. The orbital with occupation close to unity is the heaviest.

Andy: the band renormalization in pnictides and ruthenates are very different. Can you distinguish this by DMFT? Local in the band picture and local in the direct space is not the same thing. Self-energy in the band representation is very different from the self-energy in local representation.

YBK: What is the good way to estimate JH?

Answer: RPA is the standard way. It turns out that JH is not screened much compared with U. The ionic value is very close to the band value. Known for many years, starting with Sawadsky paper.

Sung-Sik Lee (McMaster U and Perimeter Institute, Canada)

From renormalization group to emergent gravity: holographic description of quantum many-body systems

Blogged by Piers Coleman.

Sung-Sik begins talking about examples of scs, CM systems, high Tc, heavy fermion systems near a QCP, but alos QCD, the quark gluon plasma.

The long distance, low energy physics is described by a strongly interacting QFT.  We need a new way of approaching these problems. 

One new approach he suggests, is "Duality", the idea that one theory can be mapped onto another. For example, the 3D xy model can be mapped to a U(1) gauge theory w charged boson. EM duality in 4D gauge theories.

The hope: find a new way of mapping strongly coupled theories onto weakly coupled theories, using duality.  This kind of thing can happen if 

Original particles remain strongly coupled and have a short life time, yet organized into long-lived, weakly coupled collective excitations

Non-trivial dynamical info contained in the change of variable

Dual variable may carry new, sometimes fractional quantum numbers

It may live in a different space. 

Q: when doesn't it work?
A: it doesn't work in MOST cases, but I will tell you about a case where it may! Holography.

Holography: AdS/CFT correspondence.   Here the bold new idea, due to Maldacena, is that a D-dimensional AFT is dual ot a D+1 dimensional gravity theory.

• N=4 SU(N) gauge theory in 4D = 11B superstring theory in AdS5xS5
• Weak coupling description for strongly coupled QFT for a large N 
• Believed to be a general framework for a large class of qFs
• The correspondence has been used to "reporoduce" many phenomena in CMT - from hydrodynamics to SC and NFL. 
• There is no first principle derivation. 
• Purely phenomenological, with a few exceptions.

 Now SS introduces the "Dictionary" in Duality. Given below.  There are a number of key ideas here, Quantities in D dimensions have their D+1 dimensional correspondence, eg T - energy momentum maps onto the metric tensor in D+1. There is also a mapping between the new dimension, z, and the RG flow, so that large z corresponds to low energy, small z to high energy.   There is also a boundary condition, so that the field j in the D+1 theory at the boundary z=0 is equal to the source term in the lower dimensional CFT. 

SS poses questions

Q- Can one explicitly construct hte gravitational theory form a a general QFT/quantum many body system? 

A- Yes we can!  One has to Quantize the beta function.   (Blogger: This is amazing - "third quantization"?! )

Here we go.  

Step 0 Write Z[J[x]] with sources Jn coupled to the fundamental ops On, such that any local operator allowed by symmetry can be written as a polynomail of the fundamental ops and their derivatives.  He gives the prescription for Ising, Vector and Matrix fields. 

Step 1  We need to do RG, keeping track of beta function for infinite many coupling constants. Let us simplify by removing the non-fundamental operators by introducing auxilliary fields. This is done with a delta function something linke

 jn (pn-On) - Jn pn + Jnm pn pm +....

jn is the Lagrange multiplier that enforces the constrain while pn is the dynamical operator.  

Step2  We integrate out the high energy modes of j. 

Q: why not j and p?
A: you can this, but lets see what we get by just integrating out the he j modes. 

If we do this, three things happen:

- By integrating out the quantum field, you generate energy that depends on the configuration of low energy j's and p's
- One obtains a quantum correction for the fundamental operators O.
- One also generates quadratic terms of the O's, which become p's.

Q: arent the fundamental fields the primary fields of CFT?
A: the fundamental fields are not the primary fields of CFT.  For example, they do not include spin...

Step 3 replace O by p. (Really the same as step 1).

Step 4 repeat 2-3 again and again until one has got rid of the original field completely.  One has now a theory in terms of a set of dynamical sources and dynamical operators. The interation parameter, has  become (magically) an additional dimension, with a j(n) and p(n) at each stage. 

Q: always local?
A: no - one needs arbitrary derivatives - locality is not guaranteed.

Q: you have two indices, m and n.... Whats the guarantee that the rank of the operators will not increase?
A:  you had this infinite no of fields at the beginning. It only becomes useful if you can truncate in tersm of a finite no of variables.

Q: how are you guaranteed that the truncation works at all stages?
A: so far I have not truncated... yet....

So now  the iteration variable has become a continuous extra dimension (idea of Verlindes...) and somehow, if it works, what is left is local with a truncated set of variables.  He says that this is sofar, an exact change of variables. A d-dimensinoal Z cn be written as a d+1 functional integration for dynamical sources and operator fields. Its a general scheme, but for a general theory, the holographic description is not useful.  When all sysmmetry allowed ops are large - some large N limit of the original theory - the holographic theory becomes classical.  The holographic theory always includes gravity - the energy momentum tensor becomes a spin-2 source. 

Q: whats the simplest CMT for which this can be carried out as an engineer?
A: I think its the O(N) model - vector model. I will show you.

Astonishing observation: Useful to consider z as time, one has p d_z j, as if p and j are conjugate to each other. So I can view the problem as a quantum problem in one higher dimension.   The partition fn is a transition amplitude of a D-dimensional Quantum wavefunction. The Hamiltonian generates scale transformation for the dynamical couplings.  The Heisenebrg equation, is a quantum beta function. 

Conventional RG is in J_n space, 

dJ_nm/Dl = beta(Jn,Jnm....). 

This is a "classical RG trajectory".  There are no fluctuations in the RG flow. 

Quantum RG is holography.  In this, flow, only fundamental operators appear. The price you pay is that these operators are now dynamical, and one has to consider a sum over  RG trajectories.  The RG flow is governed by a quantum hamiltonian

dJn/dl = [H,Jn]

If the large N theory is classical, this becomes classical.

Local RG prescription, spacetime dependent coarse graining - Gamma(x)=Gamma Exp [-alpha[x]dz]

By construction, Z is independent of alpha(x,z). Choosing different RG schemes corresponds to a gauge choice. 

Q: how will a fixed point arise in this quantum approach?
A: if you find a saddle point solution, then the sp soln will have scale invariance. 

Q: how can you justify one of the phenomenological models in the 1/N expansion?
A: I hope, but it has not been worked out so far.

Q: Can you reproduce or disprove the recent result of Verlinde, that gravity can be understood as an entropy. 
A: Yes - if you integrate high energy mode, you generate an action by a kind of order from disorder - gravity  appears - non trivial action a kind of entropic, quantum source.

Blogger- what a beautiful talk.  The idea of quantum RG as a route to holography may be a revolution. Lets hope so, because we need one.