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.
Highlights
Competing interactions in a quantum antiferromagnet with spin-rotationally invariant interactions can lead to the destruction of the conventional Néel antiferromagnetic (AFM) O(3) symmetry-broken ground state in two or higher dimensions
We introduce a two-dimensional (2D) quantum spin model in which the AFM ground state successively transitions into two different types of VBS states; a fourfold degenerate plaquette VBS (PVBS) followed by an eightfold degenerate state we name the alternating VBS (AVBS)
The existence of the AVBS phase suggests that the plaquette valencebond solid (PVBS) phase could be realized as an intermediate (“vestigial”) phase that only partially breaks the symmetry broken in the AVBS phase
Summary
Competing interactions in a quantum antiferromagnet with spin-rotationally invariant interactions can lead to the destruction of the conventional Néel antiferromagnetic (AFM) O(3) symmetry-broken ground state in two or higher dimensions. Signs of a VBS with singlets forming on four-spin plaquettes were detected in the quasitwo-dimensional system SrCu2(BO3) under high pressure [14] This material hosts an adjacent AFM phase at still higher pressures [15], for the first time opening prospects for detailed experimental studies of a direct transition between AFM and VBS states in two dimensions. We introduce a two-dimensional (2D) quantum spin model in which the AFM ground state successively transitions into two different types of VBS states; a fourfold degenerate plaquette VBS (PVBS) followed by an eightfold degenerate state we name the alternating VBS (AVBS) These states are schematically depicted, along with the more commonly studied columnar VBS (CVBS) state. In the remainder of this introductory section, we discuss further the origins and basics of these notions and summarize our aims and findings
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