Numerical diagonalization analysis of the criticality of the (2+1)-dimensional XY model: Off-diagonal Novotny's method

TL;DR

This study applies an off-diagonal Novotny's numerical diagonalization method to analyze the critical behavior of the (2+1)-dimensional XY model, successfully estimating critical exponents despite system size limitations.

Contribution

It develops an off-diagonal version of Novotny's method and demonstrates its effectiveness in analyzing criticality in larger quantum spin systems.

Findings

Estimated critical exponent ν=0.675(20)

Estimated ratio γ/ν=1.97(10)

Extended system size analysis up to N=20 spins

Abstract

The criticality of the (2+1)-dimensional XY model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions (d \ge 3); in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny's method, which enables us to treat a variety of system sizes N=6,8,...,20 (N: the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny's method to adopt the off-diagonal (quantum-mechanical XY) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point. As a result, we estimate the critical indices as \nu=0.675(20) and \gamma/\nu=1.97(10).