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

Zhao, Bowen; Weinberg, Phillip; Sandvik, Anders W.

doi:10.1038/s41567-019-0484-x

Cited by 75 publications

(150 citation statements)

References 56 publications

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“…Our work also helps shed light upon other emergent symmetries of a FOQPT. 43 In this section, we show that Eq. (1) of the main text is the most general rotationally invariant action to φγ T σ y γ and φ 4 order if assuming φ has uniform classical vacuum.…”

Section: Conclusion and Discussionmentioning

confidence: 78%

Finite-scale emergence of 2+1D supersymmetry at first-order quantum phase transition

Roiban

Jian

et al. 2019

Phys. Rev. B

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Supersymmetry, a symmetry between fermions and bosons, provides a promising extension of the standard model but is still lack of experimental evidence. Recently, the interest in supersymmetry arises in the condensed matter community owing to its potential emergence at the continuous quantum phase transition. In this work, we demonstrate that 2+1D supersymmetry, relating massive Majorana and Ising fields, might emerge at the first-order quantum phase transition of the Ising magnetization by tuning a single parameter. Although the emergence of the SUSY is only allowed in a finite range of scales due to the existence of relevant masses, the scale range can be large when the masses before scaling are small. We show that the emergence of supersymmetry is accompanied by a topological phase transition for the Majorana field, where its non-zero mass changes the sign but keeps the magnitude. An experimental realization of this scenario is proposed using the surface state of a 3+1D time-reversal invariant topological superconductor with surface magnetic doping.

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Section: Conclusion and Discussionmentioning

confidence: 78%

Finite-scale emergence of 2+1D supersymmetry at first-order quantum phase transition

Roiban

Jian

et al. 2019

Phys. Rev. B

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“…In these models, the Heisenberg interaction J is supplemented by multispin correlated singlet projectors Q, which open up possibilities of designing sign-problem free Hamiltonians with the desired phase diagrams containing AFM and VBS phases. A large number of QMC studies with different variants of 2D J-Q models have been reported [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Concurrently, various discrete versions of the proposed DQC action have also been studied numerically [66][67][68], and three-dimensional classical loop [69,70] and dimer [71,72] models with arguably the same low-energy fixed points have also been studied extensively.…”

Section: A Valence-bond Solid States and Deconfined Quantum Criticalitymentioning

confidence: 99%

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

Takahashi

Sandvik

2020

Phys. Rev. Research

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We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the two-dimensional square lattice, designed so that the system can host a fourfold degenerate plaquette valencebond solid (PVBS) ground state that spontaneously breaks Z 4 symmetry. The system is sign-problem free and amenable to large-scale quantum Monte Carlo simulations, thus allowing us to carry out a detailed study of the quantum phase transition between the standard Néel antiferromagnetic (AFM) and PVBS states. We find a first-order transition, in contrast to previously studied continuous transitions from the AFM phase into a columnar valence-bond solid (CVBS) phase. The theory of deconfined quantum criticality predicts generic continuous AFM-CVBS and AFM-PVBS transitions, and, in one version of the theory, the two critical order parameters transform under SO(5) symmetry. Emergent SO(5) symmetry has indeed been observed in studies of the AFM-CVBS transition, and here we show that the first-order AFM-PVBS transition also exhibits SO(5) symmetry at the transition point. Such unexpected symmetry of the coexistence state, which implies a lack of energy barriers between the coexisting phases, has recently been observed at other first-order transitions, but the case presented here is the first example with SO(5) symmetry. The extended symmetry 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. Furthermore, we discover a novel type of eightfold degenerate VBS phase, arising when the PVBS state breaks a remaining Z 2 symmetry. This second phase transition, which is continuous, implies that the PVBS phase can be regarded as an intermediate "vestigial" phase, a concept recently introduced to describe multistage phase transitions involving a continuous symmetry. Here we construct a six-dimensional order parameter and also introduce a general graph-theoretic approach to describe the two-stage discrete symmetry breaking. We discuss different ways of breaking the symmetries in one or two stages at zero and finite temperatures. In the latter case, we observe fluctuation-induced first-order transitions, which are hallmarks of vestigial phase transitions. We also mention possible connections of the AFM-PVBS transition to the SO(5) theory of high-T c superconductivity.

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“…Recently, unconventional first-order transitions with emergent spherical symmetry of the order parameters were identified where no cumulant minimums are observed, which can be traced to the lack of tunneling barriers when the two order parameters can be continuously rotated into each other [36][37][38]. The results for h ≥ 0.2 in Figs.…”

Section: B Nature Of the Afm-cvbs Transitionmentioning

confidence: 99%

“…There is still some remnants of Z 4 symmetry here (a slightly diamond-like deviation from circular symmetry of the distribution), which would further diminish if we move even closer to the transition. Proper analysis of the size dependence of the distribution [36,38] would be required to draw firm conclusions, but at least it appears plausible here that the system has the emergent U(1) symmetry expected at a DQC transition.…”

Section: Fluctuations In the Vbs Phasesmentioning

confidence: 99%

Tunable deconfined quantum criticality and interplay of different valence-bond solid phases*

2020

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We use quantum Monte Carlo simulations to study a quantum S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS-AFM and AFM-cVBS boundaries merge into a direct sVBS-cVBS transition. Unlike previous models with putative deconfined AFM-cVBS transitions, e.g., the standard J-Q model, in our extended J-Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order the clock-like Z4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries. arXiv:2003.07844v1 [cond-mat.str-el]

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

Cited by 75 publications

References 56 publications

Finite-scale emergence of 2+1D supersymmetry at first-order quantum phase transition

Finite-scale emergence of 2+1D supersymmetry at first-order quantum phase transition

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

Tunable deconfined quantum criticality and interplay of different valence-bond solid phases*

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