Anomalies and entanglement renormalization

Bridgeman, Jacob C.; Williamson, Dominic J.

doi:10.1103/physrevb.96.125104

Cited by 33 publications

(33 citation statements)

References 127 publications

(205 reference statements)

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“…The possibility (7.26) can be eliminated by modular invariance of the torus one-point function of u with a spatial Y loop. 30 In the case of (7.25), the same consideration determines α by…”

Section: On Tqfts Admitting R C (S 3 ) Fusion Ringmentioning

confidence: 99%

Topological defect lines and renormalization group flows in two dimensions

Chang

Lin

Shao

et al. 2019

J. High Energ. Phys.

243

425

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We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

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Section: On Tqfts Admitting R C (S 3 ) Fusion Ringmentioning

confidence: 99%

Topological defect lines and renormalization group flows in two dimensions

Chang

Lin

Shao

et al. 2019

J. High Energ. Phys.

243

425

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show abstract

“…In Fig. 2b, we show that an arbitrary string defect of disorder operator [29][30][31] M (p,q) ≡ i,j ∈S(p,q) µ z i,j ending at plaquette p and q is free to fluctuate under the gauge symmetry. It can be identified as the magnetic flux tube, on whose end points live a pair of the magnetic flux excitations m p and m q on the plaquettes.…”

mentioning

confidence: 99%

Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State

Zhu

Zhang

2019

Phys. Rev. Lett.

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In the tensor network representation, a deformed Z2 topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the AT model, and possible topological phase transitions are precisely determined. With the electric-magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or confining phase.Introduction.-The toric code model proposed by Kitaev[1] is a prototypical model realizing the Z 2 intrinsic topological phase of matter with anyonic excitations. It is interesting and fundamentally important to consider the possible topological phase transitions out of the toric code phase, because such phase transitions are beyond the conventional Ginzburg-Landau paradigm for the symmetry breaking phases. From the perspective of lattice gauge theory, it has been known that there exists the Higgs/confinement transition, where the electric charge is condensed/confined accompanied by the confinement/condensation of magnetic flux due to electricmagnetic duality [2][3][4][5][6][7]. However, there is a long-standing puzzle: what is the nature of the phase transition along the self-dual line and how the Higgs and confinement transition lines merge into the self-dual phase transition point [6,8]. Should there be a tricritical point, it would go beyond the anyon condensation scenario[9], because the electric charge and magnetic flux are not allowed to simultaneously condense.In this Letter, we shall resolve this puzzle and provide new insight into the nature of this topological phase transition. Instead of solving a Hamiltonian with tuning parameters, we propose a deformed topological wave-function interpolating from the nontrivial to trivial phases in the tensor network representation [10][11][12], which provides a clearer scope into the essential physics of abelian anyonic excitations [13][14][15][16][17]. In this scheme, the usual pure Higgs/confinement transition of the toric code [14,18,19] has a special path, where the deformed wave-function can be exactly mapped to a twodimensional (2D) classical Ising model. The topological phase transition is associated with the 2D Ising phase transition, drawing the striking topological-symmetrybreaking correspondence [20].Further deformation of the toric code wave functions can span a generalized phase diagram [21][22][23], where the perturbed Higgs and confinement transitions were gener-ically obtained by the symmetry breaking pattern and long-range-...

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“…One-dimensional Hamiltonians with an anomalous Z 2 MPO symmetry have previously been studied in the literature [23,[64][65][66], but to the best of our knowledge these models do not contain a parameter that enables a spontaneous breaking of the anomalous symmetry, and are therefore not based on a physical picture of the unconventional domain wall fusion properties. Ref.…”

Section: Discussionmentioning

confidence: 99%

Anomalous domain wall condensation in a modified Ising chain

et al. 2019

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We construct a one-dimensional local spin Hamiltonian with an intrinsically non-local, and therefore anomalous, global Z2 symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and contains a parameter that can be tuned to spontaneously break the non-local Z2 symmetry. The Hamiltonian is constructed to capture the unconventional properties of the domain walls in the symmetry broken phase. Using uniform matrix product states, we obtain the phase diagram that results from condensing the domain walls. We find that the complete phase diagram includes a gapless phase that is separated from the ordered ferromagnetic phase by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered antiferromagnetic phase by a first order phase transition. arXiv:1812.04656v2 [cond-mat.str-el]

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Anomalies and entanglement renormalization

Cited by 33 publications

References 127 publications

Topological defect lines and renormalization group flows in two dimensions

Topological defect lines and renormalization group flows in two dimensions

Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State

Anomalous domain wall condensation in a modified Ising chain

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