Diagnosing Fractionalization from the Spin Dynamics of $Z_2$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations

TL;DR

This study uses quantum Monte Carlo simulations to analyze the spin dynamics of a kagome lattice quantum spin model, revealing signatures of fractionalized excitations characteristic of a $Z_2$ quantum spin liquid phase.

Contribution

It introduces a novel combination of correlation-matrix sampling and stochastic analytic continuation to resolve spectral functions in an anisotropic quantum spin model with a three-site unit cell.

Findings

Identification of a gapped two-spinon continuum in the $Z_2$ spin liquid phase.

Detection of gapped vison excitations and their translational symmetry fractionalization.

Monitoring of spin dynamics across different phases of the model.

Abstract

Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice quantum spin-$1/2$ model, which is known to harbor an extended $Z_2$ quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit-cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the $Z_2$ quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.