We present a many body approach for nonequilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean-field theory of equilibrium systems with the replica theory for classical glasses without quenched disorder. We apply this approach to study a quantized version of the Brazovskii model and find a self-generated quantum glass that remains in a quantum mechanically mixed state as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This quantum glass is formed by a large number of competing states spread over an energy region which is determined within our theory.We present a many body approach for nonequilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean-field theory of equilibrium systems with the replica theory for classical glasses without quenched disorder. We apply this approach to study a quantized version of the Brazovskii model and find a self-generated quantum glass that remains in a quantum mechanically mixed state as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This quantum glass is formed by a large number of competing states spread over an energy region which is determined within our theory.

arXiv:cond-mat/0202099Physical review. B, Condensed matterOct 7, 200333 citations

Classical mutual information in mean-field spin glass models

Vincenzo Alba, Stephen Inglis, Lode Pollet

We investigate the classical R\'enyi entropy ${S}_{n}$ and the associated mutual information ${\mathcal{I}}_{n}$ in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the $n$ -sheet booklet. This is achieved by gluing together $n$ independent copies of the model, and it is the main ingredient for constructing the R\'enyi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for ${S}_{n}$ and ${\mathcal{I}}_{n}$ and for standard thermodynamic quantities. Both ${S}_{n}$ and ${\mathcal{I}}_{n}$ exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, ${S}_{n}/N$ and ${\mathcal{I}}_{n}/N$ , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.We investigate the classical R\'enyi entropy ${S}_{n}$ and the associated mutual information ${\mathcal{I}}_{n}$ in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the $n$-sheet booklet. This is achieved by gluing together $n$ independent copies of the model, and it is the main ingredient for constructing the R\'enyi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for ${S}_{n}$ and ${\mathcal{I}}_{n}$ and for standard thermodynamic quantities. Both ${S}_{n}$ and ${\mathcal{I}}_{n}$ exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, ${S}_{n}/N$ and ${\mathcal{I}}_{n}/N$, in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.

arXiv:1507.01274Physical review. B./Physical review. BMar 4, 201611 citations

Quantum Dynamics with Mean Field Interactions: a New Approach

László Erdős, Benjamin Schlein

arXiv:0804.3774Journal of Statistical PhysicsMar 1, 200935 citations

A mean field model for many-electron systems

Ajit J. Thakkar

Institute of Physics eBooksOct 1, 20210 citations

The Renormalization Group for Disordered Systems

Michele Castellana

In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on hierarchical lattices, which are the simplest non-mean-field systems where the RG framework emerges in a natural way. The resulting critical properties shed light on the critical behavior of spin and structural glasses beyond mean field, and suggest future directions for understanding the criticality of more realistic glassy systems.In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on hierarchical lattices, which are the simplest non-mean-field systems where the RG framework emerges in a natural way. The resulting critical properties shed light on the critical behavior of spin and structural glasses beyond mean field, and suggest future directions for understanding the criticality of more realistic glassy systems.

arXiv:1307.6891Jul 25, 20136 citations

We investigate the classical R\'enyi entropy

{S}_{n}

and the associated mutual information

{\mathcal{I}}_{n}

in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the

n

-sheet booklet. This is achieved by gluing together

n

independent copies of the model, and it is the main ingredient for constructing the R\'enyi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for

{S}_{n}

and

{\mathcal{I}}_{n}

and for standard thermodynamic quantities. Both

{S}_{n}

and

{\mathcal{I}}_{n}

exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities,

{S}_{n}/N

and

{\mathcal{I}}_{n}/N

, in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.