Abstract
The fixed-node Monte Carlo method is extended to lattice fermion models. This method replaces the problem of finding the ground state of a many-fermion system by an effective eigenvalue problem of finding the lowest-energy wave function in a given region of the configuration space. It has previously only been applied to fermions moving in continuous space. The discreteness of the configuration space causes the algorithm to differ from that of the continuum. The method is tested against a known limiting case where exact results are available for comparison. Good agreement is found. Using the fixed-node Monte Carlo method, we study the domain-wall phase in the ground state of the two-dimensional Hubbard model. The existence of a domain-wall phase which has domains of antiferromagnetic phases separated by walls of holes is recently suggested by inhomogeneous Hartree-Fock (HF) and variational Monte Carlo (VMC) calculations. Large improvements of the energies are found. The domain walls are broader than those obtained by the HF and VMC calculations.
Keywords
Monte Carlo methodVariational Monte CarloPhysicsDiffusion Monte CarloFermionHybrid Monte CarloQuantum Monte CarloHubbard modelMonte Carlo method in statistical physicsMonte Carlo molecular modelingDynamic Monte Carlo methodLattice (music)Ground stateEigenvalues and eigenvectorsStatistical physicsQuantum mechanicsMathematicsMarkov chain Monte Carlo
Affiliated Institutions
Related Publications
Attractive Interaction and Pairing in Fermion Systems with Strong On-Site Repulsion
It is shown that an effective attractive interaction between nearest-neighbor antiparallel spins a-rises in the Hubbard and Anderson lattice models in the limit of large on-site...
Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity
We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a ...
Surface tension, roughening, and lower critical dimension in the random-field Ising model
A continuum interface model is constructed to study the low-temperature properties of domain walls in the random-field Ising model (RFIM). The width of the domain wall and its s...
Pairing and superfluid properties of dilute fermion gases at unitarity
We study the system of a dilute gas of fermions in 3-dimensions, with\nattractive interactions tuned to the unitarity point, using the\nnon-perturbative Restricted Path Integral...
Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold\ndegeneracy is realized by two inequivalent crystalline states with a four- and\ntwo-fold degeneracy...
Publication Info
- Year
- 1991
- Type
- article
- Volume
- 44
- Issue
- 17
- Pages
- 9410-9417
- Citations
- 29
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
29
OpenAlex
Cite This
Guozhong An,
J. M. J. van Leeuwen
(1991).
Fixed-node Monte Carlo study of the two-dimensional Hubbard model.
Physical review. B, Condensed matter
, 44
(17)
, 9410-9417.
https://doi.org/10.1103/physrevb.44.9410
Identifiers
- DOI
- 10.1103/physrevb.44.9410