Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet

• URL: http://arxiv.org/abs/2001.10045v1
• Date: Mon, 27 Jan 2020 20:01:30 GMT
• Title: Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Authors: Jun Takahashi and Anders W. Sandvik
• Abstract summary: We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the 2D square lattice. We carry out a detailed quantum Monte Carlo study of the quantum phase transition between the antiferromagnetic (AFM) and PVBS states. We show that the coexistence state at the AFM--PVBS transition is unexpectedly associated with SO(5) symmetry, which may indicate that the transition is connected to a deconfined critical point.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the 2D square lattice, designed to host a plaquette valence-bond solid (PVBS) ground state breaking $\mathbb{Z}_4$ symmetry. We carry out a detailed quantum Monte Carlo study of the quantum phase transition between the antiferromagnetic (AFM) and PVBS states. We find a first-order transition, in contrast to previously studied continuous 'deconfined' transitions between the AFM and columnar valence-bond solids. We show that the coexistence state at the AFM--PVBS transition is unexpectedly associated with SO(5) symmetry, which may indicate that the transition is connected to a deconfined critical point. We also discuss the first-order transition in the context of a recent proposal of spinons with fracton properties in the PVBS state, concluding that the fracton scenario is unlikely. Further, we discover a novel type of eight-fold degenerate VBS phase that breaks the remaining $\mathbb{Z}_2$ symmetry of the PVBS phase. The PVBS phase can then be regarded as an intermediate 'vestigial' phase, and we develop a general graph-theoretic approach to describe the two-stage discrete symmetry breaking. At finite temperature, we observe fluctuation-induced first-order transitions, which are hallmarks of vestigial phase transitions. We also mention possible connections to the SO(5) theory of high-T$_{\rm c}$ superconductivity.

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