Featureless quantum insulator on the honeycomb lattice

Kim, Panjin; Lee, Hyun Yong; Jiang, Shenghan; Ware, Brayden; Jian, Chao-Ming; Zaletel, Michael P.; Han, Jung Hoon; Ran, Ying

doi:10.1103/physrevb.94.064432

Cited by 27 publications

(46 citation statements)

References 38 publications

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“…On the other hand, on the honeycomb lattice, we find no anomalies for the symmetries listed above. Again, this is consistent since a trivial symmetric gapped state on the honeycomb lattice has been recently constructed [13,14]. The treatment of lattice symmetries as internal symmetries for the purpose of anomaly computation is consistent with Ref.…”

Section: Introductionsupporting

confidence: 84%

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Intrinsic and emergent anomalies at deconfined critical points

2018

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It is well known that theorems of Lieb-Schultz-Mattis type prohibit the existence of a trivial symmetric gapped ground state in certain systems possessing a combination of internal and lattice symmetries. In the continuum description of such systems, the Lieb-Schultz-Mattis theorem is manifested in the form of a quantum anomaly afflicting the symmetry. We demonstrate this phenomenon in the context of the deconfined critical point between a Neel state and a valence bond solid in an S = 1/2 square lattice antiferromagnet and compare it to the case of S = 1/2 honeycomb lattice where no anomaly is present. We also point out that new anomalies, unrelated to the microscopic Lieb-Schultz-Mattis theorem, can emerge, prohibiting the existence of a trivial gapped state in the immediate vicinity of critical points or phases. For instance, no translationally invariant weak perturbation of the S = 1/2 gapless spin chain can open up a trivial gap even if the spin-rotation symmetry is explicitly broken. The same result holds for the S = 1/2 deconfined critical point on a square lattice.

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Section: Introductionsupporting

confidence: 84%

“…Hence, in this case there are neither emergent nor intrinsic anomalies. The absence of an intrinsic anomaly is in agreement with the existence of a trivial gapped state on the honeycomb lattice [13,14]. Let us now discuss possible consequences of the absence of emergent anomalies.…”

Section: B S = 1/2 Honeycomb Latticesupporting

confidence: 68%

Intrinsic and emergent anomalies at deconfined critical points

2018

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“…For instance, when SG involves translation symmetries in two and higher spatial dimensions d, our construction related to H d+1 (SG, U (1)) clearly demonstrates so-called "weak topological indices", whose physical origin is related to lower dimensional SPT phases. As a concrete example, previously we demonstrated that there are 4 distinct featureless Mott insulators on the honeycomb lattice at half-filling 25 . These distinct featureless Mott insulators now can be nicely interpreted as the consequence of two weak topological indices.…”

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confidence: 94%

Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases

Jiang

Ran

2017

Phys. Rev. B

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We present systematic constructions of tensor-network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries. From the classification point of view, our results show that in spatial dimensions d = 1, 2, 3, the cohomological bosonic SPT phases protected by a general symmetry group SG involving onsite and spatial symmetries are classified by the cohomology group H d+1 (SG, U (1)), in which both the time-reversal symmetry and mirror reflection symmetries should be treated as anti-unitary operations. In addition, for every SPT phase protected by a discrete symmetry group and some SPT phases protected by continuous symmetry groups, generic tensor-network wavefunctions can be constructed which would be useful for the purpose of variational numerical simulations. As a by-product, our results demonstrate a generic connection between rather conventional symmetry enriched topological phases and SPT phases via an anyon condensation mechanism. CONTENTS

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“…(See Ref. [34][35][36] for a tensor-network construction of a state with similar transformation properties.) In the thermodynamic limit N → ∞, a band insulator would transform trivially under all point group operations for both N/2 odd and N/2 even, i.e., independently of how the thermodynamic limit is approached.…”

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confidence: 99%

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

et al. 2016

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We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state -protected by time-reversal and reflection symmetries -cannot be connected adiabatically to a free-fermion topological phase. Introduction. The discovery of topological band insulators (TBI) of noninteracting electrons in certain strongly spin-orbit coupled semiconductors is one of the most important advances of the last decade in condensed matter physics [1]. TBI are an example of symmetry-protected topological phases (SPT) [2], which are devoid of intrinsic topological order such as that found in fractional quantum Hall systems, but possess protected edge/surface states with exotic characteristics. A major focus of current research is to discover interacting SPT phases that cannot be adiabatically deformed into noninteracting TBI. While progress has been made in the classification [3][4][5][6][7] and theoretical realization in model of SPT phases of bosons, much less is known about SPT phases of fermions, which are relevant for electrons in solids. Although recent theories suggest that fermionic SPT phases distinct from free-fermion TBI should exist in principle [14,15], apart from the special case of one spatial dimension (1D) there has been no explicit realization of a fermionic SPT as the ground state of a microscopic model Hamiltonian. In this paper, we provide evidence that a 2D fermionic SPT protected by time-reversal and reflection symmetries and distinct from a free-fermion TBI can be realized as the ground state of a simple Hubbard model for spin-1/2 electrons on a decorated honeycomb lattice.Fermionic Hubbard model. We consider the Hubbard model for spin-1/2 fermions hopping on the decorated triangular and honeycomb lattices (Fig. 1), where each site R of the original triangular and honeycomb lattices is decorated by a single hexagon. Fermions hop within each hexagon with a nearest-neighbor amplitude t and a next-nearest-neighbor amplitude t 2 , and interact via an

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Featureless quantum insulator on the honeycomb lattice

Cited by 27 publications

References 38 publications

Intrinsic and emergent anomalies at deconfined critical points

Intrinsic and emergent anomalies at deconfined critical points

Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

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