Solving fermion sign problem in quantum Monte Carlo by Majorana representation

Abstract

In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC is fermion sign free in simulating a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions. To the best of our knowledge, MQMC is the first auxiliary field QMC method to solve fermion sign problem in spinless (more generally, odd number of species) fermion models. MQMC simulations can be performed efficiently both at finite and zero temperatures. We believe that MQMC could pave a new avenue to solve fermion sign problem in more generic fermionic models.

Selected as an Editors' Suggestion in PRB Rapid Communication, published version with updated reference

References in corpus (13)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Continuous-time Monte Carlo methods for quantum impurity models
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Topological Mott Insulators
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Solution to sign problems in half-filled spin-polarized electronic systems
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions

Cited by in corpus (154)

• Machine learning quantum phases of matter beyond the fermion sign problem
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Fermion-induced quantum critical points
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Quantum Critical Points and the Sign Problem
• Variational Quantum Boltzmann Machines
• Monte Carlo Studies of Quantum Critical Metals
• Easing the Monte Carlo sign problem
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• A simple fermionic model of deconfined phases and phase transitions
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures
• The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Infinite Variance in Fermion Quantum Monte Carlo Calculations
• Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Correlated spinless fermions on the honeycomb lattice revisited
• Antiferromagnetism induced by electron-phonon-coupling
• Interacting Majorana Fermions
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Edge quantum criticality and emergent supersymmetry in topological phases
• On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
• Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model
• Charge-4e superconductors: a Majorana quantum Monte Carlo study
• Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
• Fermion-induced quantum critical points in three-dimensional Weyl semimetals
• Majorana-Hubbard model on the square lattice
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Quantum phase transitions in Dirac fermion systems
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• A perspective on machine learning and data science for strongly correlated electron problems
• Wavefunction positivization via automatic differentiation
• Stochastic series expansion simulation of the $t$-$V$ model
• Mitigating the Sign Problem Through Basis Rotations
• Solution of the "sign problem" for the half filled Hubbard-Holstein model
• Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice
• Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Quantum Monte Carlo study of mass-imbalanced Hubbard models
• Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models
• Universality and Critical Exponents of the Fermion Sign Problem
• On the thermodynamics of fermions at any temperature based on parametrized partition function
• Automatic Differentiable Monte Carlo: Theory and Application
• Rigorous results on the ground state of the attractive SU($N$) Hubbard model
• Field-Induced Quantum Phases in Frustrated Spin-Dimer Model: A Sign-Problem-Free Quantum Monte Carlo Study
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• Superconductivity in the presence of strong electron-phonon interactions and frustrated charge order
• Sign Problem in Quantum Monte Carlo Simulation
• Electronic and phononic properties of a two dimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering
• Chiral tricritical point: a new universality class in Dirac systems
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Solution to sign problems in models of interacting fermions and quantum spins
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations
• An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
• Mitigating the fermion sign problem by automatic differentiation
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Ground State Degeneracy of Interacting Spinless Fermions
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Irreducible Projective Representations and Their Physical Applications
• Antiferromagnetic fluctuations and a dominant $d_{xy}$-wave pairing symmetry in nickelate-based superconductors
• Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Trion states and quantum criticality of attractive SU(3) Dirac fermions
• Robust Fermi liquid instabilities in sign problem-free models
• Phase space methods for Majorana fermions
• Semigroup approach to the sign problem in quantum Monte Carlo simulations
• Delay Update in determinant quantum Monte Carlo
• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid
• Biexciton Condensation in Electron-hole Doped Hubbard Bilayers -- A Sign-Problem-Free Quantum Monte Carlo Study
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• Unusual Hole-doping-dependent Electronic Instability and Electron-Phonon Coupling in Infinite-layer Nickelates
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• Universal properties of many-body quantum chaos at Gross-Neveu criticality
• Solution to the sign problem in a frustrated quantum impurity model
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
• Fermion-induced quantum critical point in the Landau-Devonshire model
• Order-by-disorder and emergent Kosterlitz-Thouless phase in triangular Rydberg array
• Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Theory Perspective: SCES 2016
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Quantum spin liquid from electron-phonon coupling
• Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
• Imaginary-time Mpemba effect in quantum many-body systems
• Lefschetz Thimble Quantum Monte Carlo for Spin Systems
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Classification of sign-problem-free relativistic fermions on the basis of the Majorana positivity
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• On the Fermion Sign Problem in Imaginary-Time Projection Continuum Quantum Monte Carlo with Local Interaction
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• Effective p-wave Fermi-Fermi Interaction Induced by Bosonic Superfluids
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Quantifying the fragility of unprotected quadratic band crossing points
• Quantum phase transition and criticality in quasi one-dimensional spinless Dirac fermions
• Hamming Distance and the onset of quantum criticality
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Ising Antiferromagnet in the 2D Hubbard Model with Mismatched Fermi Surfaces
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Worldline Monte Carlo method for few body nuclear physics
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Addressing general measurements in quantum Monte Carlo
• Constraints from anti-unitary symmetries on phase diagrams of sign problem-free models
• Simultaneous Stoquasticity
• Lowest energy states of an $O(N)$ fermionic chain
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• A lattice pairing-field approach to ultracold Fermi gases
• Spontaneous mass generation and chiral symmetry breaking in a lattice Nambu-Jona-Lasinio model
• Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator
• Boundary criticality in two-dimensional interacting topological insulators
• Lattice simulation with the Majorana positivity
• The statistical mechanics and machine learning of the $\alpha$-Rényi ensemble
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
• Probing the Critical Behavior of a Sign-Problematic Model with Monte Carlo Simulations