Exact thermal properties of free-fermionic spin chains

TL;DR

This paper provides an exact algebraic solution for the thermal properties of free-fermionic spin chains, including the Ising and XY models, highlighting errors in common approximations near critical points.

Contribution

It introduces an exact method to compute thermal properties of free-fermionic spin chains, improving understanding of their behavior at finite temperature.

Findings

Exact partition function derived for free-fermionic chains

Errors in positive parity approximation identified near critical points

Full counting statistics of observables at thermal equilibrium provided

Abstract

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.