Effective gauge theories of superfluidity with topological order

Abstract

We discuss the low-energy dynamics of superfluidity with topological order in $(3+1)$ spacetime dimensions. We generalize a topological $BF$ theory by introducing a non-square $K$ matrix, and this generalized $BF$ theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed 't Hooft anomaly between discrete higher-form symmetries. We apply this framework to the color-flavor locked phase of dense QCD, which shows anyonic particle-vortex statistics while no topological order appears. An explicit example of superfluidity with topological order is discussed.

arXiv comment34 pages, no figure; v2: added discussions and Appendix D

References in corpus (49)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Generalized Global Symmetries
• Color superconductivity in dense quark matter
• Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD
• The phase diagram of dense QCD
• Symmetries and Strings in Field Theory and Gravity
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Coupling a QFT to a TQFT and Duality
• Theta, Time Reversal, and Temperature
• Continuity of Quark and Hadron Matter
• Superconductors are topologically ordered
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• The "Parity" Anomaly On An Unorientable Manifold
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Comments on Abelian Higgs Models and Persistent Order
• Topological BF field theory description of topological insulators
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Semi-superfluid strings in High Density QCD
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Vortices and Other Topological Solitons in Dense Quark Matter
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Anomaly constraints on deconfinement and chiral phase transition
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Topological order in the pseudogap metal
• Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Gauge theory for the cuprates near optimal doping
• Circle compactification and 't Hooft anomaly
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Two-flavor adjoint QCD
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• On time-reversal anomaly of 2+1d topological phases
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Canonical BF-type Topological Field Theory and Fractional Statistics of Strings
• C-P-T anomaly matching in bosonic quantum field theory and spin chains
• Quark-hadron continuity beyond Ginzburg-Landau paradigm
• Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves
• Wilson operator algebras and ground states for coupled BF theories
• Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter
• Anomaly matching in QCD thermal phase transition
• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD
• Insulators and metals with topological order and discrete symmetry breaking
• Non-Abelian vortex in lattice gauge theory

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