Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries

Abstract

$U(1)$ gauge theories, including conventional Maxwell electromagnetism, allow $\theta$-terms when parity and time-reversal symmetry are broken. In condensed matter systems, the physics of $\theta$ as a magnetoelectric response has been explored extensively within the context of topological insulators and multiferroics. We show how $\theta$-terms can arise in the internal dynamics of the emergent electromagnetism in a $U(1)$ quantum spin liquid. In its Coulomb phase, the minimal model of pyrochlore quantum spin ice is governed by a six-spin ring exchange Hamiltonian. We identify the next-order contribution to the microscopic Hamiltonian when parity, time-reversal, and all improper spatial symmetries are broken -- a seven-spin term which leads to a two-parameter lattice gauge theory with a $\theta$-electromagnetic phase. We derive how the seven-spin term is generated perturbatively within each of the three symmetry classes of short-range pyrochlore spin ice. Within a complete microscopic symmetry analysis, we find that the most general nearest-neighbor Hamiltonians fail to generate the seven-spin term, and one must include next-nearest-neighbor interactions to obtain an emergent $\theta$. Using gauge mean-field theory we compute additional contributions to the $\theta$-term from the spinon sector. Finally, we determine the conditions required for an internal $\theta$-term to generate a significant external magnetoelectic response.

26 pages, 5 figures

References in corpus (56)

• Topological Insulators
• Quantum Spin Liquids
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• A Field Guide to Spin Liquids
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Electromagnetic Response of Weyl Semimetals
• Quantum Excitations in Quantum Spin Ice
• Axions as Dark Matter Particles
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Chiral anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals
• Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
• Coulomb and Liquid Dimer Models in Three Dimensions
• Axion Electrodynamics in Topological Materials
• Generic quantum spin ice
• Frustrated quantum rare-earth pyrochlores
• Orbital magnetoelectric coupling in band insulators
• Quantum Ice : a quantum Monte Carlo study
• Three dimensional resonating valence bond liquids and their excitations
• Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Axion topological field theory of topological superconductors
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• Time-reversal symmetric U(1) quantum spin liquids
• Bosonic Many-body Theory of Quantum Spin Ice
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• Quantum spin configurations in Tb2Ti2O7
• Monopole Flux State on the Pyrochlore Lattice
• Flat bands and Dirac cones in breathing lattices
• Quantum spin ice on the breathing pyrochlore lattice
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Ground-state selection and spin-liquid behaviour in the classical Heisenberg model on the breathing pyrochlore lattice
• Fragmentation in Frustrated Magnets -- A review
• Fragmented monopole crystal, dimer entropy and Coulomb interactions in Dy${}_2$Ir${}_2$O${}_7$
• Monopole density and antiferromagnetic domain control in spin-ice iridates
• Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
• Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Monopole holes in a partially ordered spin liquid
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Behavior of the breathing pyrochlore lattice Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$ in applied magnetic field
• Semi-classical Approach to Quantum Spin Ice
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Synthesis, physical and magnetic properties of CuAlCr${}_4$S${}_8$: a new Cr-based breathing pyrochlore
• Hybrid Dyons, inverted Lorentz force and magnetic Nernst effect in quantum spin ice
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Beyond Single Tetrahedron Physics of Breathing Pyrochlore Compound Ba3Yb2Zn5O11
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• Breathing pyrochlore magnet CuGaCr${}_4$S${}_8$: Magnetic, thermodynamic, and dielectric properties
• Mössbauer spectroscopy study of the magnetostructural and spin-state transitions in the breathing pyrochlore LiFeCr${}_4$O${}_8$
• Synthetic magnetoelectric response of lattice bosonic insulators

Cited by in corpus (1)

• Hearing the light: stray-field noise from the emergent photon in quantum spin ice