Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches

TL;DR

This paper evaluates the Density-of-States Monte Carlo method for simulating real-time quantum spin chains with severe sign problems, finding it less effective than reweighting due to non-smooth density of states.

Contribution

The study critically assesses the DoS approach in challenging quantum real-time simulations and proposes analytical calculations to improve accuracy, revealing its limitations.

Findings

Both DoS and reweighting simulate chains up to length 40.

Discontinuities in the density of states hinder DoS effectiveness.

Analytical contributions improve precision but do not make DoS superior.

Abstract

We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real time evolution of a non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as $L=40$, far beyond exact diagonalisability, though only for short evolution times $t\lesssim 1$. We identify discontinuities of the density of states as one of the key problems in the MC simulations and propose to calculate some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements the density of states is found highly non-smooth and therefore the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real time simulations with discrete degrees of freedom.