Meron-Cluster Solution of Fermion Sign Problems

Abstract

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

4 pages, ReVTeX

References in corpus (2)

• Imaginary chemical potential and finite fermion density on the lattice
• Quantum Monte Carlo Loop Algorithm for the t-J Model

Cited by in corpus (155)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Quantum Monte Carlo with Directed Loops
• A new method to study lattice QCD at finite temperature and chemical potential
• Machine learning quantum phases of matter beyond the fermion sign problem
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
• Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
• QCD at small non-zero quark chemical potentials
• Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Towards Quantum Simulating QCD
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Recent Developments of World-Line Monte Carlo Methods
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• 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
• The fermion bag approach to lattice field theories
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Easing the Monte Carlo sign problem
• Solution to sign problems in half-filled spin-polarized electronic systems
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• Color Superconductivity in Compact Stars
• Solution of the Complex Action Problem in the Potts Model for Dense QCD
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Infinite Variance in Fermion Quantum Monte Carlo Calculations
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• 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
• Hamiltonian lattice QCD at finite chemical potential
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Does the complex Langevin method give unbiased results?
• Polynomial complexity despite the fermionic sign
• Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
• Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
• Fermion bag solutions to some sign problems in four-fermion field theories
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Subset method for one-dimensional QCD
• Intrinsic dimension of path integrals: data mining quantum criticality and emergent simplicity
• A perspective on machine learning and data science for strongly correlated electron problems
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
• Solutions to sign problems in lattice Yukawa models
• Stochastic series expansion simulation of the $t$-$V$ model
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• Meron-Cluster Simulation of a Chiral Phase Transition with Staggered Fermions
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems
• Quantum Monte Carlo study of mass-imbalanced Hubbard models
• Topological Origin of the Fermion Sign Problem
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models
• Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets
• Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
• Spinless fermions and charged stripes at the strong-coupling limit
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice
• Quantum Monte Carlo simulations of the t-Jz model with stripes on the square lattice
• Sign Problem in Quantum Monte Carlo Simulation
• Meron-Cluster Approach to Systems of Strongly Correlated Electrons
• Towards learning optimized kernels for complex Langevin
• Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions
• Melting the Diquark Condensate in Two-Color QCD: A Renormalization Group Analysis
• Kosterlitz-Thouless Universality in a Fermionic System
• Path-integral Monte Carlo method for the local Z_2 Berry phase
• Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations
• Mesoscopic QCD and the Theta Vacua
• Solution to sign problems in models of interacting fermions and quantum spins
• Composite Reweighting the Glasgow Method for Finite Density QCD
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Fermion loop simulation of the lattice Gross-Neveu model
• On the closedness and geometry of tensor network state sets
• From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
• Critical Behavior of a Chiral Condensate with a Meron Cluster Algorithm
• Permutation Matrix Representation Quantum Monte Carlo
• Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model
• Deconvolving the components of the sign problem
• Exact BCS stochastic schemes for a time dependent many-body fermionic system
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• Hadron Physics from Lattice QCD
• Semigroup approach to the sign problem in quantum Monte Carlo simulations
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Gibbs sampling of complex valued distributions
• Composite reweighting SU(2) QCD at Finite Temperature
• Biexciton Condensation in Electron-hole Doped Hubbard Bilayers -- A Sign-Problem-Free Quantum Monte Carlo Study
• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Solution to the sign problem in a frustrated quantum impurity model
• Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Hamiltonian Monte Carlo simulation of the two-dimensional Wess-Zumino model
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• QCD at a Finite Density of Static Quarks
• Recent progress on cluster and meron algorithms for strongly correlated systems
• Lattice QCD at Finite Temperature and Density
• Sign structure and ground state properties for a spin-$S$ $t$-$J$ chain
• Solution of the sign problem in the Potts model at fixed fermion number
• Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations
• Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions
• Real-time simulation of non-equilibrium transport of magnetization in large open quantum spin systems driven by dissipation
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Microscopic spectral density in random matrix models for chiral and diquark condensation
• Quantum Link Models with Many Rishon Flavors and with Many Colors
• Static correlation lengths in QCD at high temperature and finite density
• Unexpected Results in the Chiral Limit with Staggered Fermions
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• A Monte Carlo algorithm for spin foam intertwiners
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• On the Fermion Sign Problem in Imaginary-Time Projection Continuum Quantum Monte Carlo with Local Interaction
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Ground state of many-body lattice systems: an analytical probabilistic approach
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• Charge and spin ordering, and charge transport properties in a two-dimensional inhomogeneous t-J model
• Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation
• Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories
• Reduction of the sign problem using the meron-cluster approach
• The Color-Flavor Transformation and Lattice QCD
• Superconductivity and antiferromagnetism in a hard-core boson spin-1 model in two dimensions
• Quantum mean-field approximation for lattice quantum models: truncating quantum correlations, and retaining classical ones
• Superconductivity with the Meron-Cluster Algorithm
• Effects of interladder couplings in the trellis lattice
• Cluster Percolation and Chiral Phase Transition
• A Multi-level Algorithm for Quantum-impurity Models
• Worldline Monte Carlo method for few body nuclear physics
• Dual Non-Abelian Yang-Mills Simulations in Four Dimensions
• Quantum Monte Carlo Study of Disordered Fermions
• Fermion bag solutions to some sign problems in four-fermion field theories
• Positive representations of complex distributions on groups
• Finite size effect on the thermodynamics of a hot and magnetized hadron resonance gas
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• A new way to deal with fermions in Monte Carlo simulations
• Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration
• Geometric and computational aspects of chiral topological quantum matter
• Positivity of QCD at asymptotic density
• Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling
• Isocliny in spinor space and Wilson fermions
• Computing quantum phase transitions
• Sampling and the complexity of nature
• Complex path simulations of geometrically frustrated ladders
• Using a Fermionic Ensemble of Systems to Determine Excited States
• Notes on resummation-based quantum Monte Carlo vis-à-vis sign-problematic Heisenberg models on canonical geometrically frustrated lattices
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d
• Quantum Critical Phenomena in an $O(4)$ Fermion Chain