Transition from quantum to classical Heisenberg trimers: Thermodynamics and time correlation functions

TL;DR

This paper investigates how quantum spin trimers transition to classical behavior in thermodynamics and time correlation functions, revealing detailed differences and convergence patterns as spin quantum number increases.

Contribution

It provides exact quantum calculations of time correlation functions for spin s ≤ 7 and demonstrates convergence to classical results using acceleration methods.

Findings

Partition function and susceptibility become classical with increasing s.

Quantum autocorrelation functions are periodic, unlike classical ones.

Levin u-sequence acceleration reproduces classical limits with high precision.

Abstract

We focus on the transition from quantum to classical behavior in thermodynamic functions and time correlation functions of a system consisting of three identical quantum spins s that interact via isotropic Heisenberg exchange. The partition function and the zero-field magnetic susceptibility are readily shown to adopt their classical forms with increasing s. The behavior of the spin autocorrelation function (ACF) is more subtle. Unlike the classical Heisenberg trimer where the ACF approaches a unique non-zero limit for long times, for the quantum trimer the ACF is periodic in time. We present exact values of the time average over one period of the quantum trimer for s less or equal 7 and for infinite temperature. These averages differ from the long-time limit, (9/40)\ln3+(7/30), of the corresponding classical trimer by terms of order 1/(s*s). However, upon applying the Levin u-sequence acceleration method to our quantum results we can reproduce the classical value to six significant figures.