Finite-size-scaling ansatz for the helicity modulus of the triangular-lattice three-spin interaction model

TL;DR

This paper proposes a finite-size-scaling ansatz for the helicity modulus in a triangular-lattice three-spin interaction model, confirming it through Monte Carlo simulations and discussing its relevance to quantum spin chain phase transitions.

Contribution

It introduces a new finite-size-scaling ansatz for the helicity modulus in the model, supported by Monte Carlo simulations and theoretical analysis.

Findings

The ansatz exhibits an exponent ar=3/5 for the correlation length.

Monte Carlo simulations confirm the validity of the ansatz.

The relevance of the ansatz to quantum spin chain ground-state transitions is discussed.

Abstract

The Berezinskii-Kosterlitz-Thouless-type continuous phase transition observed in the three-spin interaction model is discussed. The relevant field theory describes the topological defects involved and enables us to perform the renormalization-group analysis. Based on it, we shall propose the finite-size-scaling ansatz for the helicity modulus which exhibits the exponent $\bar\nu=3/5$ for the correlation length in the disordered phase. We perform the Monte Carlo simulations to confirm the ansatz. Also, we argue its relevance to the ground-state phase transition in the quantum spin chain.