Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Abstract

Motivated by the fermion bag approach we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete-time with a finite temporal lattice spacing $\epsilon$, when $\epsilon \to 0$, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion bag algorithms run relatively faster when $\epsilon =1$ as compared to $\epsilon \to 0$, but still allow us to compute universal quantities near the quantum critical point even at such a large value of $\epsilon$. As an example of this new approach, here we study the $N_f=1$ Gross-Neveu chiral Ising universality class in $2+1$ dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to $100^2$ sites when $\epsilon =1$, while with comparable resources we can only reach lattice sizes of up to $64^2$ when $\epsilon \to 0$. The critical exponents obtained in both these studies match within errors.

arXiv comment19 pages, 7 figures, 4 tables

References in corpus (76)

• Critical Phenomena and Renormalization-Group Theory
• A Method for Simulating Chiral Fermions on the Lattice
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Chiral Determinant as an Overlap of Two Vacua
• Theory of interacting electrons on the honeycomb lattice
• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• Meron-Cluster Solution of Fermion Sign Problems
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Four - Fermi Theories in Fewer Than Four Dimensions
• Bootstrapping 3D Fermions
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Fermion-induced quantum critical points
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• The fermion bag approach to lattice field theories
• Bootstrapping 3D Fermions with Global Symmetries
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Solution to sign problems in half-filled spin-polarized electronic systems
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Critical behavior of Dirac fermions from perturbative renormalization
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Massive fermions without fermion bilinear condensates
• Chiral anomalies and rooted staggered fermions
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code
• Ising and Gross-Neveu model in next-to-leading order
• Origin of fermion masses without spontaneous symmetry breaking
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Critical Flavor Number in the Three Dimensional Thirring Model
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Actions for dynamical fermion simulations: are we ready to go?
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Dynamical Generation of Topological Masses in Dirac Fermions
• Large $N_f$ quantum field theory
• Fermion bag solutions to some sign problems in four-fermion field theories
• Novel phases in strongly coupled four-fermion theories
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Critical flavour number of the Thirring model in three dimensions
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• Stochastic series expansion simulation of the $t$-$V$ model
• Interplay of universality classes in a three-dimensional Yukawa model
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions
• Three dimensional four-fermion models - A Monte Carlo study
• Asymptotically safe and free chiral theories with and without scalars
• Solution to sign problems in models of interacting fermions and quantum spins
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• From Domain Wall to Overlap in 2+1d
• On the O(1/N^2) Beta-Function of the Nambu-Jona-Lasinio Model with Non-Abelian Chiral Symmetry
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation

Cited by in corpus (24)

• The Gross-Neveu-Yukawa Archipelago
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• New Developments in the Numerical Conformal Bootstrap
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Quantum phase transitions in Dirac fermion systems
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Strong Coupling Lattice QCD in the Continuous Time Limit
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• SO(4) multicriticality of two-dimensional Dirac fermions
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Worldline Monte Carlo method for few body nuclear physics
• Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions
• Strictly incoherent operations for one-qubit systems