Z4-U(1) crossover of the order parameter symmetry in a two-dimensional valence-bond-solid

TL;DR

This study uses ground-state projector simulations to explore a quantum phase transition in a 2D Heisenberg model, revealing an emergent U(1) symmetry near the transition and characterizing the Z4-U(1) crossover in the valence-bond-solid phase.

Contribution

It demonstrates a continuous or weakly first-order transition from antiferromagnetism to a VBS with emergent U(1) symmetry and characterizes the associated length scale.

Findings

No signs of discontinuity in the transition

Emergent U(1) symmetry near the critical point

Quantified the Z4-U(1) crossover length scale

Abstract

We discuss ground-state projector simulations of a modified two-dimensional S=1/2 Heisenberg model in the valence bonds basis. Tuning matrix elements corresponding to the diagonal and off-diagonal terms in the quantum dimer model, we show that there is a quantum phase transition from the antiferromagnet into a columnar valence-bond-solid (VBS). There are no signs of discontinuities, suggesting a continuous or very weakly first-order transition. The Z4-symmetric VBS order parameter exhibits an emergent U(1) symmetry as the phase transition is approached. We extract the associated length-scale governing the U(1)-Z4 cross-over inside the VBS phase.