Symmetry-enhanced discontinuous phase transition in a two-dimensional quantum magnet


In a quantum phase transition, the ground state and low-temperature properties of a system change drastically as some parameter controlling zero-point quantum fluctuations is tuned to a critical value. Like classical phase transitions driven by thermal fluctuations, a ground-state transition can be discontinuous (first order) or continuous. Theoretical studies have suggested exotic continuous transitions where a system develops higher symmetries than those of the underlying Hamiltonian. Here, we demonstrate an unconventional discontinuous transition between two ordered ground states of a quantum magnet, with an emergent symmetry of its coexistence state. We present a Monte Carlo study of a two-dimensional S = 1/2 spin system hosting an antiferromagnetic state and a plaquette-singlet solid state of the kind recently detected in SrCu2(BO3)2. We show that the O(3) symmetric antiferromagnetic order and the scalar plaquette-singlet solid order form an O(4) vector at the transition. Unlike conventional first-order transitions, there are no energy barriers between the two coexisting phases, as the O(4) order parameter can be rotated at constant energy. Away from the transition, the O(4) surface is uniaxially deformed by the control parameter (a coupling ratio). This phenomenon may be observable in SrCu2(BO3)2.

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Fig. 1: Quantum spin models discussed in this work.
Fig. 2: Demonstration of a two-fold degenerate PSS state.
Fig. 3: CBJQ results from SSE simulations.
Fig. 4: Direct evidence for emergent O(4) symmetry.
Fig. 5: Inverse PSS critical temperature versus the shifted coupling δ = gc − g.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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The authors thank F. Assaad, R. Kaul, N. Kawashima, S. Li, Z.Y. Meng, A. Nahum, Y. Ran, S. Sachdev, H. Shao, L. Sun, J. Takahashi and Z.-C. Yang for stimulating discussions. This work was supported by the NSF under grant no. DMR-1710170 and by a Simons Investigator Award. The calculations were carried out on Boston University’s Shared Computing Cluster.

Author information

A.W.S. conceived the CBJQ model and planned the study. The numerical simulations of the CBJQ model were implemented and carried out by B.Z. P.W. simulated the classical Heisenberg model. B.Z. analysed all data under the supervision of A.W.S. and with input from P.W. B.Z. wrote the initial draft of the manuscript, which was finalized by A.W.S. with input from B.Z. and P.W.

Correspondence to Anders W. Sandvik.

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