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.

arXiv comment6 pages, 3 figures

References in corpus (39)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• A random matrix model with localization and ergodic transitions
• Spectral statistics across the many-body localization transition
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• How Dynamical Quantum Memories Forget
• Operator Dynamics in Brownian Quantum Circuit
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Measurement-induced purification in large-N hybrid Brownian circuits
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Dysonian dynamics of the Ginibre ensemble
• Emergent fractal phase in energy stratified random models
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Dyson's Brownian Motion and Universal Dynamics of Quantum Systems
• Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles
• Simple emergent power spectra from complex inflationary physics
• Note on entropy dynamics in the Brownian SYK model
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Random-matrix models of monitored quantum circuits
• The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion
• Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
• Fermionic eigenvector moment flow
• Inflation with a graceful exit in a random landscape
• Dynamical Correlations for Circular Ensembles of Random Matrices
• Correlations for the Dyson Brownian motion model with Poisson initial conditions
• Local random potentials of high differentiability to model the Landscape
• Quantum Error Correction from Complexity in Brownian SYK
• Random Functions via Dyson Brownian Motion: Progress and Problems
• Noisy monitored quantum dynamics of ergodic multi-qubit systems
• Long-range spectral statistics of the Rosenzweig-Porter model
• Some exact correlations in the Dyson Brownian motion model for transitions to the CUE
• Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• Dip-ramp-plateau for Dyson Brownian motion from the identity on $U(N)$
• Phase transitions in sampling and error correction in local Brownian circuits
• Universal Level dynamics of Complex Systems