Density of states of the lattice Schwinger model

Irene Papaefstathiou,Mari Carmen Bañuls,J Ignacio Cirac,Daniel Robaina

doi:10.1103/physrevd.104.014514

Abstract

Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum simulations. We identify regimes of parameters where the spectrum appears to be symmetric and displays the expected continuum properties even for finite lattice spacing and number of sites. However, we find that for moderate system sizes and lattice spacing of $ga\ensuremath{\sim}O(1)$, the spectral density can exhibit very different properties with a highly asymmetric form. We also explore how the method can be exploited to extract thermodynamic quantities.

Highlights

Interacting quantum many-body systems represent a challenge for analytical and numerical methods, yet they are key to the understanding of many fundamental physical phenomena
Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, and the object of recent experimental quantum simulations
We explore the potential of the density of states (DOS) approximation to calculate different observables in the canonical ensemble, in the spirit of the linear logarithmic relaxation method (LLR) method, and what are the limitations of this method in comparison to directly approximating thermal states with tensor network (TN)

Summary

Introduction

Interacting quantum many-body systems represent a challenge for analytical and numerical methods, yet they are key to the understanding of many fundamental physical phenomena. For this reason, and because most of the interesting systems are not exactly solvable, considerable effort is devoted to the development of very different numerical techniques to address these problems. One of the most significant properties of a quantum manybody problem is the density of states (DOS). In the context of lattice gauge theories (LGT), approximating the DOS has been proposed [5] as a method to overcome the sign problem [6] that appears, for instance, in the presence of a finite chemical potential. Computing the DOS of a many body problem in general, or a LGT in particular, is a difficult task

Methods

Results

Conclusion