Numerical Study on Spontaneous Symmetry Breaking in a XY Quantum Antiferromagnet on a Finite Triangular Lattice

TL;DR

This study numerically investigates spontaneous symmetry breaking and low-energy excitations in a finite XY quantum antiferromagnet on a triangular lattice, confirming the presence of Nambu-Goldstone bosons and analyzing their properties.

Contribution

It provides numerical confirmation of Nambu-Goldstone bosons in a finite triangular lattice XY antiferromagnet and explores their relation to symmetry-breaking operators and quantum numbers.

Findings

Confirmed existence of Nambu-Goldstone bosons

Analyzed dependence of physical quantities on quantum numbers

Provided insights into macroscopic wave functions in quantum spin systems

Abstract

Motivated by recent experiments that require more complicated macroscopic wave functions in the condensed matters, we make numerical study on a XY quantum antiferromagnet on a finite triangular lattice using the variational Monte Carlo method and the stochastic state selection method. One of our purpose is a numerical confirmation on dominance of a Nambu-Goldstone boson in low energy excitation. For another purpose, we calculate energy, an expectation value of a symmetry breaking operator and structure functions of spin by fixing a quantum number of the symmetry. These calculations are made for states that become degenerate in an infinitely large lattice. By numerical calculations we confirm existence of a Nambu-Goldstone boson, and find dependence of a square of the quantum number for the above quantities. Using these results we can discuss on complicated macroscopic wave functions in quantum spin systems.