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

Zhao, Bowen; Takahashi, Jun; Sandvik, Anders W.

doi:10.1088/1674-1056/ab889b

Cited by 13 publications

(19 citation statements)

References 64 publications

(193 reference statements)

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“…In spin-isotropic systems such as the J-Q 2 and J-Q 3 models with a columnar arrangement of the singlet projectors, no clear-cut signs of firstorder transitions have been observed, though there are unusual scaling corrections [52,59] that have also been interpreted as a consequence of a weak first-order transition [23,50,57,73,74]. By introducing other types of Q interactions in a J-Q 3 model with columnar Q 3 interactions, it was recently found that the DQC point can evolve to a clearly first-order transition [126]. It is also interesting to study columnar J-Q n models with Q terms containing more than n = 3 singlet projectors.…”

Section: B First-order Transitions and Emergent Symmetrymentioning

confidence: 99%

“…Another interesting prospect is to mix different kinds of Q terms and investigate the interplay between interactions favoring PVBS and CVBS states (in a way similar to what was recently done with competing interactions favoring CVBS and staggered VBS states [126]). It may be possible in this way to design a Hamiltonian which can be fine-tuned to have an eightfold degenerate VBS state, with both CVBS and PVBS order.…”

Section: Future Prospectsmentioning

confidence: 99%

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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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Section: B First-order Transitions and Emergent Symmetrymentioning

confidence: 99%

Section: Future Prospectsmentioning

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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show abstract

“…In spin-isotropic systems such as the J-Q 2 and J-Q 3 models with a columnar arrangement of the singlet projectors, no clear-cut signs of firstorder transitions have been observed, though there are unusual scaling corrections [52,59] that have also been interpreted as a consequence of a weak first-order transition [23,50,57,73,74]. By introducing other types of Q interactions in a J-Q 3 model with columnar Q 3 interactions, it was recently found that the DQC point can evolve to a clearly first-order transition [122]. It is also interesting to study columnar J-Q n models with Q terms containing more than n = 3 singlet projectors.…”

Section: B First-order Transitions and Emergent Symmetrymentioning

confidence: 99%

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

Takahashi,

Sandvik

2020

Preprint

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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 four-fold degenerate plaquette valence-bond solid (PVBS) ground state that spontaneously breaks Z4 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 is associated with SO(5) symmetry. 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 eight-fold degenerate VBS phase, arising when the PVBS state breaks a remaining Z2 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 multi-stage 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-Tc superconductivity.

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“…Moreover, it has recently been argued that the DQCP is actually a multicritical point [63,64]; a second relevant scaling field with all the symmetries of the Hamiltonian was detected in the conventional critical J-Q model [63], for which motivation was found in a deformed self-dual field theory [64]. In the J-Q model it was found that the system flows toward a first-order transition when a certain interaction is turned on in such a way as to maintain a sign-free path integral [60]. It is possible that the interaction with the opposite sign could instead open up an SL phase.…”

mentioning

confidence: 96%

“…In some variants of the J-Q model, clearly first-order transitions were observed [5,60,61]. The "checker-board" J-Q (CBJQ) model [5] (and a closely related loop model [62]) has a Z 2 breaking PS phase like that in the SS model.…”

mentioning

confidence: 99%

Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model

Yang,

Sandvik,

Wang

2021

Preprint

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Using the density-matrix renormalization group method for the ground state and excitations of the Shastry-Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu2(BO3)2 show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.

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

Cited by 13 publications

References 64 publications

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

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

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

Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model

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