Unraveling long-time quantum dynamics using flow equations

TL;DR

This paper introduces a novel method combining flow equations and scrambling transforms to simulate long-time quantum dynamics in two-dimensional strongly-correlated systems, overcoming previous computational limitations.

Contribution

The authors develop a new technique that reliably predicts long-time quantum dynamics in 2D systems, challenging the belief that Hamiltonian diagonalization cannot yield accurate long-term results.

Findings

Method works well in both localized and delocalized phases.

Reliable predictions for infinite-temperature autocorrelation functions.

Provides rigorous bounds on truncation errors.

Abstract

The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part reflecting complexity theoretic obstructions. In this work, we present a new technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the prejudice that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. To the contrary, we show that the method works well in both localized and delocalized phases, and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. This approach shows that in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.