Efficient circular Dyson Brownian motion algorithm

Abstract

Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it describes the level dynamics of unitary ("circular") matrices. A common scenario is that one wants to know about an initial configuration evolved over a certain interval of time, without being interested in the intermediate dynamics. Numerical evaluation of this is computationally expensive as the time-evolution algorithm is accurate only on short time intervals because of an underlying perturbative approximation. This work proposes an efficient and easy-to-implement improved circular Dyson Brownian motion algorithm for the unitary class (Dyson index $\beta =2$, physically corresponding to broken time-reversal symmetry). The algorithm allows one to study time evolution over arbitrarily large intervals of time at a fixed computational cost, with no approximations being involved.

6 pages, 3 figures

References in corpus (12)

• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Dysonian dynamics of the Ginibre ensemble
• Note on entropy dynamics in the Brownian SYK model
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Random-matrix models of monitored quantum circuits
• Local random potentials of high differentiability to model the Landscape
• Random Functions via Dyson Brownian Motion: Progress and Problems
• Long-range spectral statistics of the Rosenzweig-Porter model
• Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
• Phase transitions in sampling and error correction in local Brownian circuits