Phase transitions in topological lattice models via topological symmetry breaking

Abstract

We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar example to elucidate our results concretely, we describe in detail a transition between a fully gapped achiral 2D $p$-wave superconductor ($p+ip$ for pseudospin up/$p-ip$ for pseudospin down) to an $s$-wave superconductor which we show to be in the 2D transverse field Ising universality class.

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Cited by in corpus (37)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Anyon condensation and its applications
• Diagrammatics for Bose condensation in anyon theories
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Boson Condensation in Topologically Ordered Quantum Liquids
• Topological Phase Transitions in the Golden String-Net Model
• Generalized string-net models: A thorough exposition
• Cage-Net Fracton Models
• Shadows of Anyons
• Breakdown of a perturbed Z_N topological phase
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Topological phases in two-dimensional arrays of parafermionic zero modes
• String-Net Models with $Z_N$ Fusion Algebra
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Ising anyons with a string tension
• Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Composing topological domain walls and anyon mobility
• Focus on topological quantum computation
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Josephson Coupled Moore-Read States
• No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids
• Russian doll spectrum in a non-Abelian string-net ladder
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Renormalization of Ising cage-net model and generalized foliation
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Ising versus $SU(2{)}_2$ string-net ladder
• Edge Theories for Anyon Condensation Phase Transitions
• Gauging Defects in Quantum Spin Systems
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Dualities between 2+1d fusion surface models from braided fusion categories
• Ground state degeneracy of the Ising cage-net model
• Proliferation transitions from a topological phase in $2+1$ dimensions
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries