Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid

TL;DR

This paper uses advanced quantum Monte Carlo methods to study the excitation spectra of a $Z_2$ quantum spin liquid in a triangular lattice quantum dimer model, revealing insights into anyon dynamics, phase transitions, and emergent symmetries.

Contribution

It provides the first controlled numerical analysis of single and multi-anyon spectra in the QDM across different phases, uncovering interaction effects and symmetry fractionalization.

Findings

Vison excitations inside the $Z_2$ QSL are identified.

Transition to the VBS phase involves vison condensation and symmetry changes.

Single vison convolution reproduces dimer spectra qualitatively.

Abstract

Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a unique 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 the newly developed 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 $Z_2$ 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.