**Massimo Capone (SISSA, Italy)**

Blogged by Maxim Dzero(See below)

**Ryotaro ARITA (ISSP, Tokyo)**

Density functional theory for superconductors and its application to layered nitride superconductors

Blogged by Genady Chitov(See below)

**Michelle Fabrizio**Break-down of ergodicity in quantum phase transitions

Blogged by Piers Coleman (See below)

**Massimo Capone (SISSA, Italy)**

Blogged by Maxim Dzero

In his talk Dr. Massimo Capone has presented very intriguing
theoretical results on superconductivity in organic molecular superconductors

_{.}After spending the first 15 min. of his talk reviewing the current challenges in our understanding of superconductivity in various “aromatic” molecular conductors. The examples specific examples discussed were K_{3.3}picene (T_{c}=18K) , Rb_{3.3}picene (T_{c}=7K) and K_{2.9}picene (T_{c}=7K). Massimo noted that it seems there is a magic number=3 of electrons per molecule corresponding to the maximum value of superconducting transition. Massimo emphasized that one of the major challenges is to understand the role of correlation effects in stabilizing superconductivity. To address this challenges, Massimo suggested to use fullerides as a reference (North Star) point to get an insight into the microscopic nature of superconductivity. In the remainig part of his talk, Massimo has presented the results of the DMFT calculations for fulleride Cs_{3}C_{60.}He argued, that contrary to common expectations, correlation effects may actually lead to the enhancement of superconductivity as opposed to suppressing it. The subtle issue was the renormalization of an interplay between electron-phonon and magnetic interactions. Massimo’s talk induced quite a bit of discussion in the audience. Here are the few questions that has been asked:
Q: Is it known where ordered moment resides? What is it
size?

A: The exact location of the moments are not known, since
neutron scattering experiments have not been done. NMR measurements suggest
that the moments are on carbon. The size of the moment correspond to the full
S=1/2 state.

Q: What is the symmetry of the superconducting order
parameter in Cs

_{3}C_{60}?
A: It is likely an s-wave

Q: Are superconducting and AFM orders co-exist for certain
values of U/W or the phase separation takes place?

A: It is likely a phase separation, although co-existence
cannot be fully ruled out.

Q: What is known about the nature of the normal state?

A: Bad (i.e. poor) metal

Q: How phonons are
treated in the DMFT analysis?

A: Phonons are integrated out to provide an effective bath
for the conduction electrons. The treatment is essentially exact.

Q: The classical single-site version of the DMFT has been
used, which clearly excludes the d-wave order parameter?

A: Yes, motivated by the experimental findings only
superconducting instability in the s-wave channel was analyzed.

Q: Did you calculate the frequency dependence of the normal
and anomalous self-energies?

A: Yes.

**Ryotaro ARITA (ISSP, Tokyo)**

Density functional theory for superconductors and its application to layered nitride superconductors

Blogged by Genady Chitov

Nice well-thought introduction. Especially useful for someone unfamiliar with those materials. The speaker made a strong case to show that the strong electron-phonon interactions are not sufficient to explain the SC properties, most notably the large BCS ratio. It seems however that the shortcomings of the electron-phonon analysis do not necessarily indicate towards an unconventional SC, but could also be a sign of strong electron interactions. Various Peierls-type transitions provide examples of fermionic interactions driving the BCS ratio away from the free-fermion (mean-field) value.

Overall, a nice talk, gives a strong motivation to take a closer look at the nitride superconductors

**Michelle Fabrizio**Break-down of ergodicity in quantum phase transitions

Blogged by Piers Coleman

Michelle discusses how, in a classical phase transition, broken symmetry means a break-down of ergodicity. Question is - what happens for quantum systems. He talks about Anderson localization and Many Body localization as examples of a kind of "quantum ergodicity breakdown".

Now we are turning to photo-induced phase transitions. Here light is exciting the system. Commonly, optical pumping is regarded as a non-equilibrium, heated state. One would like to use photo-excitation to induce phase transitions from insulator to metal. This would, he said, have important technological applications.

Q: How is this something to do with ergodicity.

A: But because of an ultra-fast laser, one can heat very rapidly. Pumping is not heating - but perhaps ergodicity is broken - so we can't think of it as heating. There isn't enough time to explore all phase space - so is it really true that one explores typical areas of phase space.

Now he defines a kind of Lanzcos procedure for the operation of H on a starting state. This generates a set of states |psi_n> with parameters t_n and E_n, this produces a tight-binding Hamiltonian, and the quantum evolution of the initial wavefunction is equivalent to a particle that starts at time t=0 from the state 0 of the chain. The underlying dimensionality is hidden in the correlation of the various parameters.

The quantum evolution of |Psi_0> is not ergodic if a particle that starts at the intial site of the Lanczos chain does not propagate to the end. (Becomes localized, stops defusing.)

Natan Andrei points out that you don't need full ergodicity -but what you need is "typicality" - splitting up into sections that are somehow typical of the entire Hilbert space.

So - next - a case study - the Bose Hubbard model, hopping of bosons in a 2D lattice. Experiments on cold atoms trapped in optical lattices offer an opportunity to explore the ergodicity issue experimentally. In a recent expt, Trotkzky et al used Rb atoms in a 1D optical lattice, and let them propagate from their intiial density cofiguration - does the system equilibrate to uniform denity? Indeed, they found that the density did rapidly equilibrate, and the result were consistent with a density functional renormalization calcn.

But! The Bose Hubbard odel in 1D has a Mott transition for integer filling and large enough U/J. Worth considering the case of n=1, rather than 1/2. So to examine this case, Fabrizzio and collaborators did a numerical simulation with 2-0-2-0 inital configuration. He says that they found that for large U, the denisty remains inhomogeneous for extremely long times - the system does not relax.. the density kind of oscillated between 2 and 0 without any clear relaxation. So they decided to define a relaxation time - n_odd(t_R)=1. They found a sharp dynamical crossover at Uf~ 4.5 - a genuine transition though? Above this value of interaction, the system is trapped into an inhomogenious state.

So to examine this using the protocol MF and co. used the Lanczos chain approach, with up to 1k sites. For the U=2K - the ti are smooth, as are the energies, but for large U there is an oscillating component to the "potential" that lasts out to 300 or so sites. So does the particle propagate along the chain? This depends on U/J. For small U, the state is able to move to the end and is reflected back and so on, but for U = 10J, he says, the R(t)/Rmax never exceeds 0.2 - the state is localized.

Natan Andrei comments that this is related to his talk yesterday - that in a Leib Linniger model, you get localization for large interaction strength.

MF says that the simplest explanation of this situation can be made in terms of an effective spin chain description - from a kind of Schrieffer Wolff transformation. up spin is doubly occupied, down spin is empty. The singly occupied states are much lower energy and can be integrated out.

H* = 2 J^2/U sum [-8 S_z(i)S_z(j)+ (S+(i)S-(j) + h.c)]

For large enough U, you stay in an AFM. (Blogger didn't understand).

Further evidence of glassy-like dynamical transition, Study the correlation function

C(t) = (1/L)\sum i=1^L <delta n_i delta n_j>

One defines tau_R as the first time where C(t_R) =0, then one finds a sharp increase in tau_R. To explore this further, MF and co have applied variational Monde Carlo and found evidence of a dynamical transition around U~ 4.5.

MF ends with a speculation: he argues that there has to be a mobility edge separating low energy eigenstates of H, which are translationally invariant, from high energy eigenstates that are not translationally invariant. He argues that the dynamical transition will occur when E^*~ N.

A very nice talk. What is not clear is the relation between this and many body localization. It would appear to be quite similar (bloggers state).

Yu Lu states that it appears that you are making a description of the Upper Hubbard band. You are providing a snap shot of this.

AF agrees.