Thermodynamics of two-dimensional bosons in the lowest Landau level

TL;DR

This paper investigates the thermodynamics of two-dimensional bosons in the lowest Landau level, employing Monte Carlo methods to analyze their partition function and derive thermodynamic relations.

Contribution

It introduces a Monte Carlo approach that fully accounts for Landau level quantization and derives exact thermodynamic relations for the system.

Findings

Partition function expressed as a function of a single thermodynamic combination

Derived asymptotic behavior of the thermodynamic function

Numerical computation of thermodynamic observables

Abstract

We study the thermodynamics of short-range interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.