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Broken quantum symmetry and confinement phases in planar physics
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Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasi-triangular Hopf algebras). In this letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it provides an effective tool for analysing a wide variety of phases exhibiting many distinct confinement phenomena.
Forward citations
Cited by 3 Pith papers
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Self-dual $S_3$ gauge theory in 2+1d: lattice model and topological phase transitions
A new sign-problem-free lattice Hamiltonian realizes the S3 quantum double with electric-magnetic duality as translation, yielding a tetracritical Ising boundary and three predicted topological transitions.
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QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow
A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.
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Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary
When an entanglement cut ends on a gapped boundary of a 2+1D topological phase, the topological entanglement entropy is controlled by the half-linking matrix, which replaces the modular S matrix used without boundaries.
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