Free energy of disordered urn models in the canonical ensemble

Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our results confirm predictions of Aharony and Harris based on Renormalization group considerations. For an Ashkin-Teller model with strong but irrelevant bond randomness we find that the relative squared width, $R_X$, of $P(X)$ is weakly self averaging. $R_X\sim l^{α/ν}$, where $α$ is the specific heat exponent and $ν$ is the correlation length exponent of the pure model fixed point governing the transi…

Machine learning electron correlation in a disordered medium

Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-body techniques with a deep learning approach, we demonstrate that a fully-connected neural network is able to learn the complex collective behavior of electrons in strongly correlated systems. Specifically, we consider the Anderson-Hubbard (AH) model, which is a canonical system fo…

Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons

The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner- Liouville's type equation has been derived. The numerical procedure for solving this equation combining bot…

无序海森堡自旋孤立量子系统中磁滞现象的观测

Observation of hysteresis in an isolated quantum system of disordered Heisenberg spins

本文在无序 Heisenberg 孤立量子自旋系统中观测到能量依赖磁滞现象，通过设计退火协议控制能量，并结合十二粒子精确对角化模拟与数千 Rydberg 原子实验，揭示了低能区可能存在的新相变。