Quantum Phase Transition between Z2 spin liquid and columnar Valence Bond Crystals on a Triangular lattice

TL;DR

This paper investigates the quantum phase transition between Z2 spin liquids and valence bond solid orders on a triangular lattice, revealing complex transition scenarios including intermediate nematic phases and different universality classes.

Contribution

It introduces a detailed phase diagram for the transition, including the possibility of an intermediate nematic Z2 spin liquid and different transition orders on isotropic and distorted lattices.

Findings

First order q=3 Potts transition to nematic Z2 spin liquid.

Second order 3d XY* transition to VBS state.

Distorted lattice reduces transition to a single 3d XY* transition.

Abstract

We study the quantum phase transition between the $Z_2$ spin liquid and valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic triangular lattice, the transition from a columnar or resonating-plaquette VBS order can be either first order or there could be two transitions with an intermediate phase. If the transition splits into two, then the $Z_2$ spin liquid will first experience a first order $q=3$ Potts transition to a new nematic $Z_2$ spin liquid that breaks the $2\pi/3$ lattice rotation symmetry (but retain translation symmetry unlike the VBS states). The second transition will then take this new nematic $Z_2$ spin liquid to a columnar or resonating-plaquette VBS state through a second order $3d$ XY$^*$ transition. On a distorted triangular lattice, the degeneracy between some of the different columnar VBS orders is lifted, and the phase transition can reduce to a single $3d$ XY$^*$ transition.