Time-reversal symmetric U(1) quantum spin liquids

Abstract

We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the 7 spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground state wave functions. One of these phases is the `topological Mott insulator' conventionally described as a topological insulator of an emergent fermionic `spinon'. We show that this phase admits a remarkable dual description as a topological insulator of emergent fermionic magnetic monopoles. This results in a new (possibly natural) surface phase for the topological Mott insulator and a new slave particle construction. We describe some of the continuous quantum phase transitions between the different $U(1)$ spin liquids. Each of these seven families of states admits a finer distinction in terms of their surface properties which we determine by combining these spin liquids with symmetry protected topological phases. We discuss lessons for materials such as pyrochlore quantum spin ices which may harbor a $U(1)$ spin liquid. We suggest the topological Mott insulator as a possible ground state in some range of parameters for the quantum spin ice Hamiltonian.

25 pages, 11 figures, 1 table

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• Gapless Symmetry Protected Topological Order
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• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Emergent Phases of Fractonic Matter
• Non-invertible Time-reversal Symmetry
• Topological Luttinger Liquids from Decorated Domain Walls
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• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Composite fermi liquids in the lowest Landau level
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Composite fermion duality for half-filled multicomponent Landau Levels
• Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Entanglement Entropy of U(1) Quantum Spin Liquids
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Realizing topological surface states in a lower-dimensional flat band
• Symmetry enriched U(1) quantum spin liquids
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Symmetry Enrichment in Three-Dimensional Topological Phases
• Luttinger's theorem in presence of Luttinger surfaces
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Landau ordering phase transitions beyond the Landau paradigm
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Trial wave functions for a Composite Fermi liquid on a torus
• Fractionalization on the Surface: Is Type-II Terminated $1T$-TaS${}_2$ Surface an Anomalously Realized Spin Liquid?
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Topological $s$-wave superconductors driven by electron correlation
• Fingerprints of quantum spin ice in Raman scattering
• Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
• Duality of a compact topological superconductor model and the Witten effect
• Classification of symmetry-enriched topological quantum spin liquids
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach
• Inelastic neutron scattering on Ce pyrochlores: Signatures of electric monopoles
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Viewpoint: duality for fermionic vortices