Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases

Abstract

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f=4$, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

arXiv comment16 pages, 16 figures

References in corpus (67)

• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• The Flux-Phase of the Half-Filled Band
• On the stability of U(1) spin liquids in two dimensions
• Algebraic spin liquid as the mother of many competing orders
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Theta-terms in nonlinear sigma-models
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Fate of CP(N-1) fixed points with q-monopoles
• Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions
• Constrained sampling method for analytic continuation
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Microscopic models for fractionalized phases in strongly correlated systems
• On the Phase Structure of Many-Flavor QED${}_3$
• Scale-invariance of parity-invariant three-dimensional QED
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Permanent confinement in the compact QED3 with fermionic matter
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• A simple fermionic model of deconfined phases and phase transitions
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Massive fermions without fermion bilinear condensates
• Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
• Diagnosing Deconfinement and Topological Order
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• Dynamics of Topological Excitations in a Model Quantum Spin Ice
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Criticality in quantum triangular antiferromagnets via fermionized vortices
• Infinite Variance in Fermion Quantum Monte Carlo Calculations
• Fermion mass without symmetry breaking
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Dynamical Generation of Topological Masses in Dirac Fermions
• Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge
• Fermion masses through four-fermion condensates
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Erratum: algebraic spin liquid as the mother of many competing orders
• A square lattice algebraic spin liquid with SO(5) symmetry
• Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis
• Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
• Metal-Insulator Transition in Two- and Three-Dimensional Logarithmic Plasmas
• Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model
• QED${}_3$ on a space-time lattice: compact versus noncompact formulation
• Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas
• Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion
• Self-consistent theory of compact QED3 with relativistic fermions
• Massless Fermions and the Instanton Dipole Liquid in Compact QED_3

Cited by in corpus (76)

• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Possible Dirac quantum spin liquid in a kagome quantum antiferromagnet YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots
• Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
• Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
• Yukawa-SYK model and Self-tuned Quantum Criticality
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Fermi-surface reconstruction without symmetry breaking
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Sign Problem in Quantum Monte Carlo Simulation
• Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Metal to Orthogonal Metal Transition
• Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Critical properties of the Néel/algebraic-spin-liquid transition
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Mitigating the fermion sign problem by automatic differentiation
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Delay Update in determinant quantum Monte Carlo
• Solving quantum rotor model with different Monte Carlo techniques
• Emergent Kondo behavior from gauge fluctuations in spin liquids
• Frustrated Kondo impurity triangle: A simple model of deconfinement
• Development of long-range phase coherence on the Kondo lattice
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Symmetry-breaking effects of instantons in parton gauge theories
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• Monopole hierarchy in transitions out of a Dirac spin liquid
• Spin excitations arising from anisotropic Dirac spinons in YCu${}_3$(OD)${}_6$Br${}_2$[Br${}_{0.33}$(OD)${}_{0.67}$]
• Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition
• Monopoles in Dirac spin liquids and their symmetries from instanton calculus
• Coupling quantum spin ice to matter on the centered pyrochlore lattice
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• (2+1)D quantum electrodynamics at finite density on a quantum computer
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions
• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge