"Helicity Modulus and Chiral Symmetry Breaking for Boundary Conditions " by Gaurav Khairnar and Thomas Vojta
 

Abstract

We study the response of a two-dimensional classical XY model to a finite (noninfinitesimal) twist of the boundary conditions. We use Monte Carlo simulations to evaluate the free energy difference between periodic and twisted-periodic boundary conditions and find deviations from the expected quadratic dependence on the twist angle. Consequently, the helicity modulus (spin stiffness) shows a nontrivial dependence on the twist angle. We show that the deviation from the expected behavior arises because of the mixing of states with opposite chirality which leads to an additional entropy contribution in the quasi-long-range ordered phase. We give an improved prescription for the numerical evaluation of the helicity modulus for a finite twist, and we discuss the spontaneous breaking of the chiral symmetry for the antiperiodic boundary conditions. We also discuss applications to discrete spin systems and some experimental scenarios where boundary conditions with finite twist are necessary.

Department(s)

Physics

Comments

National Science Foundation, Grant DMR-1506152

International Standard Serial Number (ISSN)

2470-0053; 2470-0045

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2025 American Physical Society, All rights reserved.

Publication Date

01 Feb 2025

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