Auto-correlation Functions and Quantum Fluctuations of the Transverse Ising Chain by the Quantum Transfer Matrix Method

TL;DR

This paper extends the Quantum Transfer Matrix method to dynamical problems, deriving auto-correlation functions for the Transverse Ising chain and proposing a new measure of quantum fluctuation based on Trotter-directional correlations.

Contribution

The paper introduces an extension of the Quantum Transfer Matrix method to dynamical problems and interprets Trotter-directional correlation as a new measure of quantum fluctuation.

Findings

Derived auto-correlation functions for the Transverse Ising chain.

Interpreted Trotter-directional correlation as a Matsubara Green function.

Proposed Trotter-directional correlation as a measure of quantum fluctuation.

Abstract

The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is extended to dynamical problems. The auto-correlation functions of the Transverse Ising chain are derived by this method. It is shown that the Trotter-directional correlation function is interpreted as a Matsubara's temperature Green function and that the auto-correlation function is given by analytic continuation of the Green function. We propose the Trotter-directional correlation function is a new measure of the quantum fluctuation and show how it works well as a demonstration.