Quantum Monte Carlo simulations on interaction effects in the 2D Kane-Mele-Hubbard model

Here we discuss quantum Monte Carlo and the Hubbard model. We note that while there is a fermion sign problem for the doped Hubbard model, Monte Carlo calculations have shown that the leading pairfield susceptibility has d-wave symmetry and that the pairing interaction is mediated by S = 1 particle-hole fluctuations.

10.1088/1742-6596/529/1/012002

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Quantum Monte-Carlo study of a two-band boson Hubbard model

Bulletin of the American Physical Society (2008)

Siegfried Guertler Matthias Troyer Fu‐Chun Zhang

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Constrained Path Quantum Monte Carlo Simulations of the Disordered Two-Dimensional Hubbard Model

arXiv (Cornell University) (2001)

Matthew Enjalran F. Hébert G. G. Batrouni R. T. Scalettar Shiwei Zhang

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Improved Full Configuration Interaction Monte Carlo for the Hubbard Model

Bulletin of the American Physical Society (2012)

Hitesh J. Changlani Adam Holmes F. R. Petruzielo Garnet Kin‐Lic Chan Chris Henley

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Quantum Monte Carlo Simulations of the Disordered, -U Hubbard Model

APS March Meeting Abstracts (1996)

Nandini Trivedi Mohit Randeria Carey Huscroft Richard Scalettar

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NONEXISTENCE OF d-WAVE-SUPERCONDUCTIVITY IN THE QUANTUM MONTE CARLO SIMULATION OF THE HUBBARD MODEL

International Journal of Modern Physics C (2005)

Hans‐Georg Matuttis Nobuyasu Ito

For the existence of d-wave-superconductivity in the Hubbard model, previous quantum Monte Carlo results by other authors, which showed a power law increase of the d-wave susceptibility, seem to contradict a recently published theorem. We show those quantum Monte Carlo calculations were numerically contaminated, analyze the numerical problem and propose a numerically more stable computing scheme.

10.1142/s0129183105007571

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The sign problem in quantum Monte Carlo simulations of the Hubbard model in a weak interaction region

EPL (Europhysics Letters) (2019)

Tao Ying

Determinant quantum Monte Carlo (QMC) simulations of fermion models normally face the sign problem, which has a strong dependence of the interaction strength, electron filling, temperature, lattice geometry and lattice size. It is useful to set up the data set of such dependence, to make it clear which parameter region is accessible or not. To supplement the previous study, here we report the behavior of the average sign in the weak interaction region, as functions of lattice geometry, lattice size, electron filling and temperature. Furthermore, we find that in the weak interaction region, for several interesting lattice geometries (except for the kagome lattice) the average sign gets improved when the lattice sizes increase, which is in contrast to the general understanding of the lattice size dependence of the average sign. This finding points out that when the sign problem is present in the weak interaction region, the simulation of a larger lattice size can be better under control.

10.1209/0295-5075/125/27001

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Correlations in the Two-Dimensional Hubbard Model: a Quantum Monte Carlo Study

APS March Meeting Abstracts (1996)

J. E. Gubernatis J. Carlson Shiwei Zhang

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Quantum Monte Carlo Study of BCS Correlations in the 2D Hubbard Model

APS March Meeting Abstracts (1998)

J. E. Gubernatis M. Guerrero Gerardo Ortíz