Zonal Estimators for Quasiperiodic Bosonic Many-Body Phases.

Matteo Ciardi,Fabio Cinti,Tommaso Macrì

doi:10.3390/e24020265

Abstract

In this work, we explore the relevant methodology for the investigation of interacting systems with contact interactions, and we introduce a class of zonal estimators for path-integral Monte Carlo methods, designed to provide physical information about limited regions of inhomogeneous systems. We demonstrate the usefulness of zonal estimators by their application to a system of trapped bosons in a quasiperiodic potential in two dimensions, focusing on finite temperature properties across a wide range of values of the potential. Finally, we comment on the generalization of such estimators to local fluctuations of the particle numbers and to magnetic ordering in multi-component systems, spin systems, and systems with nonlocal interactions.

Highlights

Path-integral Monte Carlo (PIMC) methods [1] are of great importance for the simulation of strongly correlated systems where other techniques fail, especially in two and three spatial dimensions
Zonal estimators can be relevant to the detection of correlated phases, such as the Bose glass phase, which is characterized by rare regions where superfluidity and finite compressibility coexist [34]
We introduce the physical estimators obtained via PIMC, and we discuss the results achieved for trapped bosons in a quasiperiodic potential in two dimensions

Summary

Introduction

Path-integral Monte Carlo (PIMC) methods [1] are of great importance for the simulation of strongly correlated systems where other techniques fail, especially in two and three spatial dimensions. Quasicrystalline properties have been observed in a variety of physical systems, for instance, in nonlinear optics [26,27,28], on twisted bilayer graphene [29] and in ultra-cold trapped atoms [30,31] In the latter case, quasicrystalline structures generated by means of optical lattices are employed to experimentally investigate remarkable effects such as many-body localization in one and two-dimensions [32], and have been suggested as a candidate to probe the existence of twodimensional Bose glasses [33]. Other works have delineated zero-temperature phase diagrams, in the mean-field approximation as well as for a strong interactions using ab-initio techniques [36,37,38,39]

Objectives

Methods

Conclusion