2020
DOI: 10.1103/physrevb.101.134111
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Gauging defects in quantum spin systems: A case study

Abstract: The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. We illustrate the construction with the example of a… Show more

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Cited by 6 publications
(5 citation statements)
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“…are both back-scattered within a wire or in-between wires. Similar to (38), a trivial topological phase of decoupled wires is obtained when all degrees of freedom are gapped by complete intra-wire interactions,…”
Section: Dihedral Twist Liquidsmentioning
confidence: 87%
See 1 more Smart Citation
“…are both back-scattered within a wire or in-between wires. Similar to (38), a trivial topological phase of decoupled wires is obtained when all degrees of freedom are gapped by complete intra-wire interactions,…”
Section: Dihedral Twist Liquidsmentioning
confidence: 87%
“…In some cases, by tuning the relative strengths of intra-and inter-wire backscattering interactions, a gap-closing phase transition can be driven from one topological phase to another. For example, (32), (35), (38) and (39) describe exactly-solvable models for the U (1) l , SU (n) 1 , trivial and SO(2n) 1 topological order respectively. These models are special points in a moduli space of Hamiltonians and can go from one to another by tuning the density-density interaction strengths u intra ⊥ , u inter ⊥ , ũintra , ũinter and the sine-Gordon backscattering bare strength ∆ intra ⊥ , ∆ inter ⊥ , ∆ intra , ∆ inter .…”
Section: +1d Quantum Critical Phase Transitionsmentioning
confidence: 99%
“…We derive a standalone effective theory for the edge of a quantum double model with group G. The only requirement we impose on the edge Hamiltonian is commutation with the bulk, encompassing special cases such as gapped edges [61][62][63][64][65], gapless points [69,70], and combinations thereof [72][73][74]. The theory is obtained by course-graining the 2D quantum-double bulk [24,[75][76][77][78] and projecting its edge into a 1D subspace defined by the bulk being in a ground state.…”
Section: Lattice Edge Theorymentioning
confidence: 99%
“…When symmetry is present, these phases are further distinguished by their symmetryprotected or symmetry-enriched topological (SPT/SET) orders. [5,6,7,8,9,10,11,12,13,14,15] Symmetries in topological phases can be analyzed theoretically by studying the statistical properties of fluxes, referred to as twist defects [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. These topological point defects "rotate" the local winding low-energy degrees of freedom according to the symmetry actions.…”
Section: Introductionmentioning
confidence: 99%