Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems

Abstract

We develop a new theoretical framework for describing and analyzing exotic phases of strongly correlated electrons which support excitations with fractional quantum numbers. Starting with a class of microscopic models believed to capture much of the essential physics of the cuprate superconductors, we derive a new gauge theory - based upon a {\it discrete} Ising or Z_2 symmetry - which interpolates naturally between an antiferromagnetic Mott insulator and a conventional d-wave superconductor. We explore the intervening regime, and demonstrate the possible existence of an exotic fractionalized insulator - the nodal liquid - as well as various more conventional insulating phases exhibiting broken lattice symmetries. A crucial role is played by vortex configurations in the Z_2 gauge field. Fractionalization is obtained if they are uncondensed. Within the insulating phases, the dynamics of these Z_2 vortices in two dimensions (2d) is described, after a duality transformation, by an Ising model in a transverse field - the Ising spins representing the Z_2 vortices. The presence of an unusual Berry's phase term in the gauge theory, leads to a doping-dependent "frustration" in the dual Ising model, being fully frustrated at half-filling. The Z_2 gauge theory is readily generalized to a variety of different situations - in particular, it can also describe 3d insulators with fractional quantum numbers. We point out that the mechanism of fractionalization for d>1 is distinct from the well-known 1d spin-charge separation. Other interesting results include a description of an exotic fractionalized superconductor in two or higher dimensions.

36 pages, 9 figures; one reference added

References in corpus (1)

• Large N expansion for frustrated and doped quantum antiferromagnets

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• New state of matter: heavy-fermion systems, quantum spin liquids, quasicrystals, cold gases, and high temperature superconductors
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• Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematics
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• $Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas
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• Deconfined Metal-Insulator Transitions in Quantum Hall Bilayers
• Fractional solitons in non-Euclidian elastic plates
• Lower Pseudogap Phase: A Spin/Vortex Liquid State
• Lieb-Schultz-Mattis theorem for quasi-topological systems
• Theory of doped Mott insulators: duality between pairing and magnetism
• Berry Phases of Vison Transport in ${\mathbb{Z}}_2$ Topologically Ordered States from Exact Fermion-Flux Lattice Dualities
• Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder
• Dirac Nodes and Quantized Thermal Hall Effect in the Mixed State of d-wave Superconductors
• Optical symmetries and anisotropic transport in high-Tc superconductors
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• The Roton Fermi Liquid
• The Electron Spectral Function in Two-Dimensional Fractionalized Phases
• Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling
• Evidence for the topological order in a kagome antiferromagnet
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Disordered, Spin Liquid and Valence-Bond Ordered Phases of the Kagome Lattice Quantum Ising Models With Transverse Field and XXZ Dynamics
• Phases and Quantum Phase Transitions in an Anisotropic Ferromagnetic Kitaev-Heisenberg-$\Gamma$ Magnet
• ${\mathbb{Z}}_2$ metallic spin liquid on a frustrated Kondo lattice
• Some remarks about pseudo gap behavior of nearly antiferromagnetic metals
• Bond excitations in the pseudogap phase of the Hubbard Model
• Fractionalizing a local pair density wave: a good "recipe" for opening a pseudo-gap
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• Phases and phase transitions in a $U(1)\times U(1)$ system with $\theta =2\pi /3$ mutual statistics
• ${\mathbb{Z}}_3$ Topological Order in Face Centered Cubic Quantum Plaquette Model
• Thermodynamics of a gauge-frustrated Kitaev spin liquid
• Magnetization plateau and supersolid phases in the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice
• Vortex duality: watching the dual side with order propagators
• Translation symmetry-enriched toric code insulator
• Chiral spin liquids with crystalline ${\mathbb{Z}}_2$ gauge order in a three-dimensional Kitaev model
• Testing for topological order in variational wavefunctions for Z(2) spin liquids
• Topological order in Josephson junction ladders with Mobius boundary conditions
• Fractionalization in Spin Liquid Mott Insulators: Vison Wavefunctions and Gaps
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• Charge pairing, superconducting transition and supersymmetry in high-temperature cuprate superconductors
• Signatures for spinons in the quantum spin liquid candidate Ca${}_{10}$Cr${}_7$O${}_{28}$
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Quantum Destruction of Spiral Order in Two Dimensional Frustrated Magnets
• Braid Group, Gauge Invariance and Topological Order
• Symmetry breaking in low-dimensional SU(N) antiferromagnets
• Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model
• Possible Z2 phase and spin-charge separation in electron doped cuprate superconductors
• Topological order in interacting semimetals
• Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance
• Symmetry Transmutation and Anomaly Matching
• Flux period, spin gap, and pairing in the one-dimensional t-J-J'-model
• An Abelian two-Higgs model of strongly correlated electrons: phase structure, strengthening of phase transition and QCD at finite density
• Emergence of gravity from interacting simplices
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Superconductivity in Mutual Chern-Simons Gauge Theory
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Inelastic neutron scattering signal from deconfined spinons in a fractionalized antiferromagnet
• A quantum phase transition from $Z_2\times Z_2$ to $Z_2$ topological order
• Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions
• Anisotropic deconfined criticality in Dirac spin liquids
• Theory of quantum kagome ice and vison zero modes
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Properties and application of the SO(3) Majorana representation of spin: equivalence with the Jordan-Wigner transformation and exact $Z_2$ gauge theories for spin models
• Classification of symmetry-enriched topological quantum spin liquids
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Single hole and vortex excitations in the doped Rokhsar-Kivelson quantum dimer model on the triangular lattice
• Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids
• Theory of spin nematic to spin-Peierls quantum phase transition in ultracold spin-1 atoms in optical lattices
• Emergent Gauge Fields in Band Insulators
• A magnetic model with a possible Chern-Simons phase
• Tensor-product representations for string-net condensed states
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Dressed Rabi oscillation in a crystalline organic radical
• Is spontaneous vortex generation in superconducting 4Hb-TaS${}_2$ from vison-vortex nucleation with ${\mathbb{Z}}_2$ topological order?
• $U(1)$ symmetry-enriched toric code
• Charge and spin fractionalization in strongly correlated topological insulators
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Scattering theory of mesons in doped antiferromagnetic Mott insulators: Multichannel perspective and Feshbach resonance
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Topological phases of dipolar particles in elongated Wannier orbitals
• Fractionalization as an alternate to charge ordering in electronic insulators
• Quantum spin liquid from electron-phonon coupling
• Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics
• Spin-gapped incoherent metal with preformed pairing in the doped antiferromagnetic Mott insulator
• Hidden phases born of a quantum spin liquid: Application to pyrochlore spin ice
• Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
• Bound states of three fermions forming symmetry-protected topological phases
• Weyl-Luttinger phase transition in pyrochlore iridates revealed by Raman scattering
• Finite size effects in the Z_2 spin liquid on the kagome lattice
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Magnetic field-induced Landau Fermi Liquid in high-T_c metals
• Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits
• Deconfined quantum criticality in the two dimensional Kondo lattice model
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Quantum critical point in high-temperature superconductors
• Flux tubes, visons, and vortices in spin-charge separated superconductors
• Higher-form symmetries and $d-wave$ superconductors from doped Mott insulators
• Application of the scattering rate sum-rule to the interplane optical conductivity of high temperature superconductors: pseudogap and bi-layer effects
• Charge response of the Majorana toric code
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• Dihedral twist liquid models from emergent Majorana fermions
• Monopoles, confinement and charge localization in the t-J model with dilute holes
• Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states
• Jordan-Wigner fermionization of quantum spin systems on arbitrary 2D lattices: A mutual Chern-Simons approach
• Detecting non-magnetic excitations in quantum magnets
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• $Z_3$ topological order in the quantum dimer-pentamer model
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Loops, sign structures and emergent Fermi statistics in three-dimensional quantum dimer models
• From nodal liquid to nodal Mottness in a frustrated Hubbard model
• Quantum phase transitions and collective modes in d-wave superconductors
• Quasiparticles in the Superconducting State of High-T_c Metals
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Breakdown of the thermodynamic limit in quantum spin and dimer models
• Symmetry-deformed toric codes and the quantum dimer model
• Ordering the topological order in the fractional quantum Hall effect
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Re-entrant topological order in strongly correlated nanowire due to Rashba spin-orbit coupling
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• Field tuning Kitaev systems for spin fractionalization and topological order
• Vison excitations in near-critical quantum dimer models
• Ground-State Degeneracy of Correlated Insulators with Edges
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Majorana Fermi surface state in a network of quantum spin chains
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Simulation of the Ring-exchange Models with Projected Entangled Pair States
• Solvable lattice models for metals with Z2 topological order
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Spin-Charge Soldering from Tensor Higgs mechanism
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux
• Feynman path-integral approach to the QED3 theory of the pseudogap
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• Scalar gauge-Higgs models with discrete Abelian symmetry groups
• Continuous interpolation between the fully frustrated Ising and quantum dimer models
• Transport in vortex state of d-wave superconductors at zero temperature: Wiedemann-Franz violation
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model
• Phase diagram of the Kitaev-Hubbard model: ${\mathbb{Z}}_2$ slave-spin and QMC approaches
• Quantum theory of spin waves for Helical ground states in Hollandite lattice
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• Quantum criticality and confinement in weak Mott insulators
• Phase transition and fractionalization in superconducting Kondo lattice model
• Multiplicative Chern insulator
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Quantum spin liquids in a square lattice subject to an Abelian flux
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet
• Unveiling topological order through multipartite entanglement
• Orthogonal Dirac semimetal on honeycomb lattice and the electron spectral function in orthogonal metallic states