Nonrelativistic Fermions in Magnetic Fields: a Quantum Field Theory Approach

TL;DR

This paper develops a quantum field theory approach to analyze the statistical mechanics of nonrelativistic fermions in magnetic fields, providing explicit formulas and exploring duality properties in different magnetic regimes.

Contribution

It introduces a general regularization procedure for fermionic determinants and expresses thermodynamic quantities using special functions like polylogarithms and the Dedekind eta function.

Findings

Explicit formulas for grand-potential and partition function in magnetic fields.

Demonstrates duality properties in strong and weak magnetic field limits.

Provides a unified quantum field theory framework for nonrelativistic fermions in magnetic fields.

Abstract

The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible regularizations. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.