Lattice Approximation of Quantum Statistical Traces at a Complex Temperature

TL;DR

This paper establishes conditions under which lattice approximations accurately compute quantum statistical traces at complex temperatures, providing explicit bounds for lattice kernels at real temperatures.

Contribution

It introduces a simple potential condition ensuring the validity of lattice approximations for quantum traces at complex temperatures, with explicit bounds for real-temperature kernels.

Findings

Lattice approximation works under the condition xp(-tV) <  for all t>0.

Explicit bounds for real-temperature lattice kernels are derived.

The condition applies to a large class of potentials and bounded functions.

Abstract

We prove that the simple condition on the potential V, \int exp(-t V) < \infty for all t>0, is sufficient for the lattice approximation of the trace Tr[A exp(-b H)] with (Re b)>0 to work for all bounded functions A and a large class of potentials. As a by-product we obtain an explicit bound for the real-temperature lattice kernels.