Non-Ergodicity of the 1D Heisenberg Model

TL;DR

This paper investigates the non-ergodic behavior of zero-energy functions in the 1D Heisenberg spin-1/2 chain, highlighting their importance in response properties and analyzing finite-size effects and extrapolation methods.

Contribution

It provides a detailed analysis of zero-energy functions in the Heisenberg chain, challenging the assumption of ergodicity and exploring their dependence on system size, temperature, and magnetic field.

Findings

Zero-energy functions are not always fixed by ergodicity assumptions.

Finite-size effects significantly influence zero-energy function calculations.

Extrapolation methods to the thermodynamic limit are evaluated.

Abstract

The relevance of zero-energy functions, coming from zero-energy modes and present in the structure of bosonic Green's functions, is often underestimated. Usually, their values are fixed by assuming the ergodicity of the dynamics, but it can be shown that this is not always correct. As the zero-energy functions are connected to fundamental response properties of the system under analysis (specific heat, compressibility, susceptibility, etc.), their correct determination is not an irrelevant issue. In this paper we present some results regarding the zero-energy functions for the Heisenberg chain of spin-1/2 with periodic boundary conditions as functions of the number of sites, temperature and magnetic field. Calculations are pursued for finite chains, using equations of motion, exact diagonalization and Lanczos technique, and the extrapolation to thermodynamic limit is studied.