Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

Abstract

We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.

14 pages in revtex v3.0, no figures

Cited by in corpus (60)

• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Beyond the locality approximation in the standard diffusion Monte Carlo method
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
• Applications of quantum Monte Carlo methods in condensed systems
• Semistochastic Projector Monte Carlo Method
• Size-consistent variational approaches to non-local pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited
• Diffusion Monte Carlo with lattice regularization
• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Ground state properties of the one dimensional Coulomb gas
• Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Backflow correlations in the Hubbard model: an efficient tool for the metal-insulator transition and the large-U limit
• Dissociation energy of the water dimer from Quantum Monte Carlo calculations
• Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of $\kappa$-(ET)${}_2$X
• TurboRVB: a many-body toolkit for {\it ab initio} electronic simulations by quantum Monte Carlo
• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• Magnetism and superconductivity in the $t-t^{\prime }-J$ model
• Hidden Mott transition and large-$U$ superconductivity in the two-dimensional Hubbard model
• A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: improving reproducibility and reducing the trial-wave-function bias
• Variational wave functions for the $S=1/2$ Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders
• Hybrid phase at the quantum melting of the Wigner crystal
• Absence of static stripes in the two-dimensional $t-J$ model by an accurate and systematic quantum Monte Carlo approach
• The itinerant ferromagnetic phase of the Hubbard model
• Finite compressibility in the low-doping region of the two-dimensional $t-J$ model
• Anatomy of the quantum melting of the two dimensional Wigner crystal
• Molecular hydrogen adsorbed on benzene: insights from a quantum Monte Carlo study
• Microscopically constrained mean field models from chiral nuclear thermodynamics
• Quantum Monte Carlo with Coupled-Cluster wave functions
• Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model
• Resonating valence bond wave function for the two dimensional fractional spin liquid
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• All-electron quantum Monte Carlo with Jastrow single determinant Ansatz: application to the sodium dimer
• Quantum Monte Carlo with Variable Spins
• Finite temperature properties of strongly correlated systems via variational Monte Carlo
• Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo
• Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme
• Quantum-assisted Monte Carlo algorithms for fermions
• Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas
• Diffusion Monte Carlo methods for Spin-Orbit-Coupled ultracold Bose gases
• Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo
• Metal-insulator transition and strong-coupling spin liquid in the $t-t^{\prime }$ Hubbard model
• Towards chemical accuracy using the Jastrow correlated antisymmetrized geminal power ansatz
• From the triangular to the kagome lattice: Following the footprints of the ordered state
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• Combination of Tensor Network States and Green's function Monte Carlo
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Fixed and partial-node approximations in Slater determinant space for molecules
• A rapidly mixing Markov chain from any gapped quantum many-body system
• Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
• Metal-Insulator transitions in generalized Hubbard models
• One-electron bands, quantum Monte Carlo, and real superconductors
• A constrained stochastic state selection method applied to quantum spin systems
• A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities
• Electron-hole asymmetry in magnetic properties of lightly doped high-$T_{\mathrm{C}}$ superconductors: a quantum Monte Carlo study
• Fixed-Node Monte Carlo Calculations for the 1d Kondo Lattice Model
• Density-Functional Theory on Graphs