Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator

Liu, Yuhai; Wang, Zhenjiu; Sato, Toshihiro; Hohenadler, Martin; Wang, Chong; Guo, Wenan; Assaad, Fakher F.

doi:10.1038/s41467-019-10372-0

Cited by 82 publications

(69 citation statements)

References 55 publications

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“…It may then be possible to observe DQC physics with less anomalies and scaling corrections than with the spin models studied so far [59]. Recently, a fermionic model argued to have a DQC-type transition without any discrete perturbation was studied [127], but in this case the system sizes are very small because of the unfavorable scaling of the fermion determinant QMC algorithm.…”

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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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: 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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“…The scaling ansatz with two relevant arguments was introduced in that context to account for anomalous scaling behavior in 2D quantum antiferromagnets [7], and the extended approach presented here should allow for further tests. In this case the DIP cannot easily be tuned away (except by studying completely different models [23]), because it is intimately connected to the lattice itself. Thus, the method of studying scaling and RG flows in the presence of a finite DIP is ideal.…”

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confidence: 99%

Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models

2020

Self Cite

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We present a way to visualize and quantify renormalization group flows in a space of observables computed using Monte Carlo simulations. We apply the method to classical three-dimensional clock models, i.e., the planar (XY) spin model perturbed by a Zq symmetric anisotropy field. The method performs significantly better than standard techniques for determining the scaling dimension yq of the Zq field at the critical point if it is irrelevant (q ≥ 4). Furthermore, we analyze all stages of the complex renormalization flow, including the cross-over from the U(1) Nambu-Goldstone fixed point to the ultimate Zq symmetry-breaking fixed point due to the relevance of the Zq field inside the ordered phase. We expect our method to be particularly useful in the context of quantum-critical points with inherent dangerously irrelevant operators that cannot be tuned away microscopically but whose renormalization flows can be analyzed exactly as we do here for the clock models. SUPPLEMENTARY INFORMATION

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“…In this case the massive fermion phase breaks flavor symmetry but preserves chiral symmetry. Such a Hamiltonian is expected to describe the Semi-Metal (SM) to Quantum-Spin-Hall (QSH) insulator transition as was recently studied in [94]. Since for N f = 2, the SU (2) chiral symmetry and SU (2) flavor symmetries are equivalent Eq.…”

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confidence: 99%

“…The phase transition in this model is expected to describe the Semi-Metal (SM) and an Anti-Ferromagnet (AFM) [48,97]. It has been suggested that the SM-QSH phase transition and SM-AFM transition could in fact belong to the same universality class [88,94]. Estimates for the critical exponents have been obtained from a variety of methods.…”

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confidence: 99%

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Huffman

Chandrasekharan

2020

Phys. Rev. D

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Motivated by the fermion bag approach we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points. As a test of our method we construct the partition function of a simple lattice Hamiltonian in 2 + 1 dimensions in discrete time, with a temporal lattice spacing ε. When ε → 0 we obtain the partition function of the original lattice Hamiltonian. But when ε = 1 we obtain a new type of space-time lattice field theory which treats space and time differently. Here we show that both continuous-time and discrete-time lattice models have a fermionic quantum critical point with critical exponents that match within errors. The fermion bag algorithms run relatively faster on the discrete-time model and allow us to compute quantities even on 100 3 lattices near the quantum critical point.

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Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator

Cited by 82 publications

References 55 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

Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

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