Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Levin and Z.-C
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase." We describe a simple physical construction that distinguishes this system from a conventional paramagnet: we couple the system to a Z_2 gauge field and then show that the \pi-flux excitations have different braiding statistics from that of a usual paramagnet. In addition, we show that these braiding statistics directly imply the existence of protected edge modes. Finally, we analyze a particular microscopic model for the edge and derive a field theoretic description of the low energy excitations. We believe that the braiding statistics approach outlined in this paper can be generalized to a large class of symmetry-protected topological phases.
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Twisted quantum double phases for finite groups can be realized in sign problem-free local Hamiltonians via stochastic series expansion, contrary to the prior belief that non-positive wavefunctions imply an intrinsic sign problem.
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
citing papers explorer
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Twisted quantum doubles are sign problem-free
Twisted quantum double phases for finite groups can be realized in sign problem-free local Hamiltonians via stochastic series expansion, contrary to the prior belief that non-positive wavefunctions imply an intrinsic sign problem.
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Constructing Bulk Topological Orders via Layered Gauging
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
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There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
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Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
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Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.