From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids

Abstract

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL) which can be defined on the honeycomb, square, triangular and kagomé lattices. At low energies, the DSL on all these lattices is described by an emergent Quantum Electrodynamics (QED${}_3$) with $N_f=4$ flavors of Dirac fermions coupled to a $U(1)$ gauge field. However the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom, behave very differently on different lattices. In particular, we show that the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulator. We also show that for DSLs on bipartite lattices, there always exists a monopole that transforms trivially under all microscopic symmetries owing to the existence of a parent SU(2) gauge theory. We connect our results to generalized Lieb-Schultz-Mattis theorems and also derive the time-reversal and reflection properties of monopoles. Our results indicate that recent insights into free fermion band topology can also guide the description of strongly correlated quantum matter.

arXiv comment26 pages, 7 figures

References in corpus (50)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Liquids
• Quantum Spin Liquid States
• "Deconfined" quantum critical points
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Lieb-Schultz-Mattis in Higher Dimensions
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Theta, Time Reversal, and Temperature
• Fermion Path Integrals And Topological Phases
• Fragile Topology and Wannier Obstructions
• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• Deconfined quantum critical points: symmetries and dualities
• Is 1T-TaS${}_2$ a 40 year old quantum spin liquid?
• On the stability of U(1) spin liquids in two dimensions
• Properties of an algebraic spin liquid on the kagome lattice
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Field-tunable quantum disordered ground state in the triangular lattice antiferromagnet NaYbO${}_2$
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Algebraic spin liquid as the mother of many competing orders
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Boson topological insulators: A window into highly entangled quantum phases
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Dirac, Anderson, and Goldstone on the Kagome
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Topological phases protected by point group symmetry
• Gauging spatial symmetries and the classification of topological crystalline phases
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Intrinsic and emergent anomalies at deconfined critical points
• Topology of Disconnected Elementary Band Representations
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Scale-invariance of parity-invariant three-dimensional QED
• Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• Criticality in quantum triangular antiferromagnets via fermionized vortices
• Entanglement signatures of emergent Dirac fermions: kagome spin liquid & quantum criticality
• Fragile topological phases in interacting systems
• Deconfined Quantum Critical Point on the Triangular Lattice
• Monopole Quantum Numbers in the Staggered Flux Spin Liquid
• Mermin-Wagner physics, (H,T) phase diagram, and candidate quantum spin-liquid phase in the spin-1/2 triangular-lattice antiferromagnet Ba8CoNb6O24
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD

Cited by in corpus (54)

• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• New Developments in the Numerical Conformal Bootstrap
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Dynamical Signatures of Symmetry Broken and Liquid Phases in an $S=1/2$ Heisenberg Antiferromagnet on the Triangular Lattice
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Unquantized anomalies in topological semimetals
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Gauge Theories for the Thermal Hall Effect
• Magnetic and spin-liquid phases in the frustrated $t-t^{\prime }$ Hubbard model on the triangular lattice
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Correlated Fragile Topology: a Parton Approach
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Monopole Josephson Effects in a Dirac Spin Liquid
• Candidate quantum spin liquids on the maple-leaf lattice
• Monopole excitations in the $U(1)$ Dirac spin liquid on the triangular lattice
• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
• Twisted bilayer U(1) Dirac spin liquids
• Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Symmetry-breaking effects of instantons in parton gauge theories
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Modified large-$N$ approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Classical and quantum spin liquids
• Destabilization of U(1) Dirac spin-liquids on two dimensional non-bipartite lattices by quenched disorder
• Fractionalized Fermi liquids and the cuprate phase diagram
• Spin-Peierls instability of deconfined quantum critical points
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Monopoles in Dirac spin liquids and their symmetries from instanton calculus
• Spin excitations arising from anisotropic Dirac spinons in YCu${}_3$(OD)${}_6$Br${}_2$[Br${}_{0.33}$(OD)${}_{0.67}$]
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Stability of algebraic spin liquids coupled to quantum phonons
• Emergent Symmetry-Protected Topological Phases via Polyakov Confinement in Quantum Spin Systems
• Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study
• When Wannier centers jump: Critical points between atomic insulating phases
• Thermal Properties and Instability of a $U(1)$ Spin Liquid on the Triangular Lattice