Topological phase transition and single/multi anyon dynamics of Z2 spin liquid

Zheng Yan,Zi Yang Meng,Yan-Cheng Wang,Nvsen Ma,Yang Qi

doi:10.1038/s41535-021-00338-1

Abstract

Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a suitable playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Our results reveal the single vison excitations inside the Z2 quantum spin liquid (QSL) and its condensation towards the sqrt{12}times sqrt{12} valence bond solid (VBS), and demonstrate the translational symmetry fractionalization and emergent O(4) symmetry at the QSL-VBS transition. We find the single vison excitations, whose convolution qualitatively reproduces the dimer spectra, are not free but subject to interaction effects throughout the transition. The nature of the VBS with its O(4) order parameters are unearthed in full scope. Our approach opens the avenue for generic solution of the static and dynamic properties of QDMs and has relevance towards the realization and detection of fractional excitations in programmable quantum simulators.

Highlights

Fractionalized anyon excitations are among the most important features of topologically ordered phases, a class of phases beyond the Landau paradiam of classifying phases with symmetry breaking[1]
A continuum in inelastic neutron scattering spectrum is often used as a signature to detect quantum spin liquids with fractionalized spin excitations, which is considered as a two-spinon continuum[2,3,4,5,6]
5 Received: 17 December 2020; Accepted: 24 March 2021; Via the sweeping cluster QMC algorithm, supplemented with stochastic analytic continuation (SAC) scheme to obtain the real-frequency data and symmetry analysis of the valence bond solid (VBS) order parameter, we reveal the excitation spectra in different phases of the triangular lattice quantum dimer models (QDM), in particular, the single vison epxcffiiffitffiaffiffitiopnsffiffiffiffiffiinside the Z2 quantum spin liquid (QSL) and its condensation towards the 12 ́ 12 VBS with the translational symmetry fractionalization

Summary

Introduction

Fractionalized anyon excitations are among the most important features of topologically ordered phases, a class of phases beyond the Landau paradiam of classifying phases with symmetry breaking[1]. The fractionalized nature of these anyon excitations renders that they cannot be created or annihilated individually by physical probes. This phenomenon is both a blessing and a curse: it reflects the topological nature of the excitations and the phase, and obscures any direct detection of single anyon excitations. Instead, they can only be observed indirectly from a multi-particle continuum of spectral functions. Understanding the relation between physical spectra and underlying single-anyon excitation is an essential question in the study of topologically ordered phases

Methods

Results

Conclusion