Probing infinite many-body quantum systems with finite-size quantum simulators

TL;DR

This paper introduces a protocol for using finite-size quantum simulators to accurately approximate the properties of infinite many-body quantum systems, especially near quantum phase transitions, by preparing a mixed state in the bulk region.

Contribution

It proposes a novel method to optimize finite quantum simulators for studying infinite systems, utilizing local Hamiltonian deformations and coherent evolution to better capture bulk properties.

Findings

Effective for free fermions in 1D and 2D

Improves study of quantum phase transitions in non-integrable models

Applicable to interacting spinful Fermi-Hubbard models

Abstract

Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in the vicinity of a quantum phase transition (QPT). Here, we propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state representing the reduced density operator of the translation-invariant infinite-sized system of interest. This protocol is based on coherent evolution with a local deformation of the system Hamiltonian. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasi-particle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a non-integrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs. In addition, we demonstrate the protocol for an interacting spinful Fermi-Hubbard model with doping for 1D chains and a small two-leg ladder, where the initial state is a random superposition of energetically low-lying states.