Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

Abstract

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically-exact and intrinsically-unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion-sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously-broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progresses made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

Invited by Annual Review of Condensed Matter Physics, 21 pages

References in corpus (30)

• Continuous-time Monte Carlo methods for quantum impurity models
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Charge ordering in the electron-doped superconductor Nd2-xCexCuO4
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Theory of the striped superconductor
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Doping dependent charge order correlations in electron-doped cuprates
• Phase diagram of the Kane-Mele-Coulomb model
• Quantum critical properties of a metallic spin density wave transition
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Gauge-field-assisted Kekulé quantum criticality
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• Ultracold atoms in a square lattice with spin-orbit coupling: Charge order, superfluidity, and topological signatures
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Is charge order induced near an antiferromagnetic quantum critical point?
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Edge stability and edge quantum criticality in 2D interacting topological insulators

Cited by in corpus (81)

• Quantum algorithms for quantum chemistry and quantum materials science
• Tools for quantum simulation with ultracold atoms in optical lattices
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Fragile topology and flat-band superconductivity in the strong-coupling regime
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Quantum Critical Points and the Sign Problem
• Neural network wave functions and the sign problem
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Strong Coupling Limit of the Holstein-Hubbard Model
• Antiferromagnetism induced by electron-phonon-coupling
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Perturbative quantum simulation
• Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble
• Competing nodal d-wave superconductivity and antiferromagnetism
• A perspective on machine learning and data science for strongly correlated electron problems
• Mitigating the Sign Problem Through Basis Rotations
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Fermi-surface reconstruction without symmetry breaking
• Two-local qubit Hamiltonians: when are they stoquastic?
• Automatic Differentiable Monte Carlo: Theory and Application
• Superconductivity in the presence of strong electron-phonon interactions and frustrated charge order
• Rigorous results on the ground state of the attractive SU($N$) Hubbard model
• Sign Problem in Quantum Monte Carlo Simulation
• Gradient optimization of fermionic projected entangled pair states on directed lattices
• Electronic and phononic properties of a two dimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Numerical linked cluster expansions for inhomogeneous systems
• Quantum algorithms for scientific computing
• An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
• Mitigating the fermion sign problem by automatic differentiation
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Interaction-induced topological phase transition at finite temperature
• Robust Fermi liquid instabilities in sign problem-free models
• Thermodynamics of correlated electrons in a magnetic field
• Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice
• Fast and stable determinant quantum Monte Carlo
• Delay Update in determinant quantum Monte Carlo
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions
• The Radius of PSR J0437-4715 from NICER Data
• Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids
• Modeling unconventional superconductivity at the crossover between strong and weak electronic interactions
• Order-by-disorder and emergent Kosterlitz-Thouless phase in triangular Rydberg array
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• Emergent Gauge Fields in Band Insulators
• Imaginary-time Mpemba effect in quantum many-body systems
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Quantum computing quantum Monte Carlo algorithm
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• 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
• The Future of the Correlated Electron Problem
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• Sampling Problems on a Quantum Computer
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d=$\infty$
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• L-based numerical linked cluster expansion for square lattice models
• Constraints from anti-unitary symmetries on phase diagrams of sign problem-free models
• Addressing general measurements in quantum Monte Carlo
• Addressing the Infinite Variance Problem in Fermionic Monte Carlo Simulations: Retrospective Error Remediation and the Exact Bridge Link Method
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints
• Complex path simulations of geometrically frustrated ladders
• Quantum Monte Carlo and Stabilizer States
• Efficient Auxiliary-Field Quantum Monte Carlo using Isometric Tensor Hypercontraction
• Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness