Power-Law Decay Exponents of Nambu-Goldstone Transverse Correlations

TL;DR

This paper investigates the decay exponents of transverse correlations in quantum antiferromagnetic models, proving they follow specific power laws depending on temperature and dimension, with implications for understanding Nambu-Goldstone modes.

Contribution

It establishes the exact power-law decay exponents for transverse correlations in higher-dimensional quantum antiferromagnetic models at different temperatures.

Findings

Decay exponent at non-zero low temperatures is 2 - d.

Decay exponent at zero temperature is 1 - d.

Method applies to quantum XY and classical Heisenberg models.

Abstract

We study a quantum antiferromagnetic Heisenberg model on a hypercubic lattice in three or higher dimensions $d\ge 3$. When a phase transition occurs with the continuous symmetry breaking, the nonvanishing spontaneous magnetization which is obtained by applying the infinitesimally weak symmetry breaking field is equal to the maximum spontaneous magnetization at zero or non-zero low temperatures. In addition, the transverse correlation in the infinite-volume limit exhibits a Nambu-Goldstone-type slow decay. In this paper, we assume that the transverse correlation decays by power law with distance. Under this assumption, we prove that the power is equal to $2-d$ at non-zero low temperatures, while it is equal to $1-d$ at zero temperature. The method is applied also to a quantum XY model and a classical Heisenberg model at non-zero low temperatures in three or higher dimensions. The resulting power is given by the same $2-d$ at non-zero low temperatures.