Pyrochlore photons: TheU(1)spin liquid in aS=12three-dimensional frustrated magnet
2003/05/31 by Michael Hermele, Matthew P. A. Fisher, Leon Balents · 74 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.69.064404
published as Phys. Rev. B 69, 064404 (2004) · 22 pages, 14 figures. Further minor changes. To appear in Phys. Rev. B
arxiv created 2003/11/25 · openalex publication_date 2004/02/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
Abstract
We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground-state wave function with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped Sz=1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing Sz=0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as U(1) topological order. This state is stable to all zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wave function. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.
Citations
Cited by
- Flux confinement-deconfinement transition of dimer-loop models on three-dimensional bipartite lattices
- Closely competing valence bond crystal orders in the ground state of the spin-(1)/(2) antiferromagnetic Heisenberg model on the pyrochlore lattice: a large scale unrestricted variational study
- Signatures of field-induced multi-color kagome spin liquids in the dipole-octupole pyrochlore Ce2Hf2O7
- Disorder-induced proximate quantum spin ice phase in Pr2Sn2O7
- Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-1/2 model
- Disorder from disorder and confinement in the quantum Ising model in the pyrochlore lattice
- Gapless fracton quantum spin liquid and emergent photons in a 2D spin-1 model
- Geometric fragmentation and anomalous thermalization in cubic dimer model
- Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach
- Human-machine collaboration: Ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
- Breakdown of the thermodynamic limit in quantum spin and dimer models
- On bipartite Rokhsar-Kivelson points and Cantor deconfinement
- Symmetry-deformed toric codes and the quantum dimer model
- Cyclic exchange, isolated states, and spinon deconfinement in anXXZHeisenberg model on the checkerboard lattice
- Quantum Spin Liquids
- Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
- Coupling quantum spin ice to matter on the centered pyrochlore lattice
- A note on electromagnetic edge modes
- Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
- Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
- Charge degrees in the quarter-filled checkerboard lattice
- Resonating singlet valence plaquettes
- Anisotropic Spin Ice on a Breathing Pyrochlore Lattice
- Observation of the emergent photon in a metastable fractionalized phase of Bose-condensed excitons: Monte Carlo simulation
- Proposal for a [111] magnetization plateau in the spin liquid state of Tb2Ti2O7
- Quantum order by disorder in a spin-one frustrated magnet on the kagome lattice
- Mott insulating phases and quantum phase transitions of interacting spin-32fermionic cold atoms in optical lattices at half filling
- Dynamically Induced Frustration as a Route to a Quantum Spin Ice State inTb2Ti2O7via Virtual Crystal Field Excitations and Quantum Many-Body Effects
- Planar pyrochlore antiferromagnet: A large-Nanalysis
- Geometric criticality for transitions between plaquette phases in integer-spin kagome XXZ antiferromagnets
- Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
- Theory of a continuous Mott transition in two dimensions
- Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
- Nematic, vector-multipole, and plateau-liquid states in the classicalO(3)pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
- Gapless Symmetry-Protected Topological Order
- Compactz=2Electrodynamics in2+1Dimensions: Confinement with Gapless Modes
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
- Colloquium: Photons and electrons as emergent phenomena
- Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice
- Magnetic monopole dynamics in spin ice
- Muon Spin Relaxation Evidence for the U(1) Quantum Spin-Liquid Ground State in the Triangular AntiferromagnetYbMgGaO4
- Unconventional superconducting symmetry in a checkerboard antiferromagnet studied via renormalized mean-field theory
- Quantum and classical spins on the spatially distorted kagomé lattice: Applications to volborthiteCu3V2O7(OH)2∙2H2O
- From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition
- Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition ofp+ipSuperconducting Arrays
- Superfluid insulator transitions of hard-core bosons on the checkerboard lattice
- Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets
- Order by Disorder and Gaugelike Degeneracy in a Quantum Pyrochlore Antiferromagnet
- Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects
- Crystal electric field excitations in the quantum spin liquid candidate NaErS2
- Maxwell electromagnetism as an emergent phenomenon in condensed matter
- Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare-earth pyrochlore magnets: A fermionic parton approach
- A spin-liquid with pinch-line singularities on the pyrochlore lattice
- Measurement of the charge and current of magnetic monopoles in spin ice
- Geometric frustration inherent to the trillium lattice, a sublattice of the B20 structure
- Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices
- Models of degeneracy breaking in pyrochlore antiferromagnets
- Discrete sliding symmetries, dualities, and self-dualities of quantum orbital compass models andp+ipsuperconducting arrays
- Frustrated Quantum Rare-Earth Pyrochlores
- First-Principles Design of the Spinel Iridate Ir2O4 for High-Temperature Quantum Spin Ice
- Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases
- Persistent superfluid phase in a three-dimensional quantumXYmodel with ring exchange
- Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xO7+y
- Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
- The (2 + 1)-d U(1) quantum link model masquerading as deconfined criticality
- Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets
- Double vibronic process in the quantum spin ice candidate Tb2Ti2O7 revealed by terahertz spectroscopy
- Ultrasonic investigations of the spin icesDy2Ti2O7andHo2Ti2O7in and out of equilibrium
- Note on generalized symmetries, gapless excitations, generalized symmetry protected topological states, and anomaly
- Quantum percolation of monopole paths and the response of quantum spin ice
- Confinement of monopoles and scaling theory near unconventional critical points
- Flux quantization due to monopole and dipole currents
- Subdimensional particle structure of higher rank U(1) spin liquids
Related