Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density

Abstract

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of ${\mathbb{Z}}_2$ lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions, and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the ${\mathbb{Z}}_2$ slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors; Luttinger liquids; and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem.

arXiv comment24 pages, 13 figures; v2: minor changes, published version

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• Symmetry-Breaking Topological Insulators in the ${\mathbb{Z}}_2$ Bose-Hubbard Model
• Interacting Majorana Fermions
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Disorder-free localization in a simple $U(1)$ lattice gauge theory
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Interpretable and unsupervised phase classification
• Z2 parton phases in the mixed-dimensional $t-J_z$ model
• Logarithmic spreading of out-of-time-ordered correlators without many-body localization
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Fractionalized Metal in a Falicov-Kimball Model
• Adaptive Quantum State Tomography with Active Learning
• Native three-body interaction in superconducting circuits
• Emergence of Gauss' Law in a $Z_2$ Lattice Gauge Theory
• Thermally induced metallic phase in a gapped quantum spin liquid - a Monte Carlo study of the Kitaev model with parity projection
• Geometric Criterion for Solvability of Lattice Spin Systems
• Soluble limit and criticality of fermions in Z2 gauge theories
• Exactly Solvable Kondo Lattice Model in Anisotropic Limit
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model
• Topological Green's function zeros in an exactly solved model and beyond
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model
• Exact Solution to Haldane-BCS-Hubbard Model Along the Symmetric Lines: Interaction Induced Topological Phase Transition
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• Dynamical localization transition in the non-Hermitian lattice gauge theory
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Confinement Induced Frustration in a One-Dimensional ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Generalized Falicov-Kimball Models
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Orthogonal metal in the Hubbard model with liberated slave spins
• 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
• Dynamics of a Lattice Gauge Theory with Fermionic Matter -- Minimal Quantum Simulator with Time-Dependent Impurities in Ultracold Gases
• Notes on Quantum oscillation for Hatsugai-Kohmoto model
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• Exactly solvable Majorana-Anderson impurity models
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions