Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal de Physique II

Numerical simulation of the double layer Hubbard model

I. Morgenstern, Th. Hußlein, Johannes Maria Singer, Hans‐Georg Matuttis

Published Aug 1, 1992• 4 citations
Publisher

Abstract

We have carried out Quantum Monte Carlo studies to investigate the double layer Hubbard model using the groundstate projector formalism. Evidence for off diagonal long range order in the nodeless d-wave pairing channel is provided. It is emphasized that the Projector Quantum Monte Carlo method has the potential to detect superconducting mechanisms in strongly correlated electron systems, which are not treatable by standard analytic methods. The Monte Carlo technique provides useful information about systems much larger than those accessible for exact diagonalization methods.

DOI
10.1051/jp2:1992215

Related papers

Double layer Hubbard model : off-diagonal long range order in the nodeless d-wave channel

I. Morgenstern, Th. Hußlein, Johannes Maria Singer +1 more

We report on a numerical study of the double layer Hubbard model describing the CuO2 sheets in the high-Tc oxides. For the simulation we employed the projector quantum Monte Carlo method (PQMC) to study the ground state properties of this correlated electron system. Our results provide evidence for off-diagonal long range order in the nodeless d-wave channel. The implications with respect to possible mechanisms for high-Tc superconductivity in oxides in combination which phononic booster mechanisms are discussed.

Journal de Physique I•Apr 1, 1993•4 citations

Pairing correlations in a two-layer Hubbard model

R. E. Hetzel, Wolfgang von der Linden, Werner R. Hanke

Superconducting properties of coupled Hubbard planes are studied by quantum Monte Carlo simulations. It is found that the interlayer coupling supports the pairing mechanism but it does not lead to off-diagonal long-range order in the purely electronic system. In addition, we have performed Monte Carlo studies based on a recently proposed variational wave function. Yielding identical results, the variational wave function overcomes the sign problem and allows us to analyze ground-state properties of strongly correlated many-body problems for system sizes and complexities not accessible otherwise.

Physical review. B, Condensed matter•Aug 1, 1994•23 citations

Detection of pairing correlation in the two-dimensional Hubbard model

Kazuhiko Kuroki, Hideo Aoki, Takashi Hotta +1 more

The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.

arXiv:cond-mat/9606143•Physical review. B, Condensed matter•Feb 1, 1997•10 citations

Superconductivity and Inhomogeneous Charge-Ordered State in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV—

Takashi Yanagisawa

We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp($-S$)-type where $S$ is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The $d$-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the $d$-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.

arXiv:2506.12736•Journal of the Physical Society of Japan•Jun 20, 2025•0 citations

OFF-DIAGONAL LONG RANGE ORDER IN AN ELECTRON-PHONON MODEL FOR HIGH- T c SUPERCONDUCTORS

M. Frick, I. Morgenstern, Wolfgang von der Linden

We study a model for high- T c superconductors describing both the strong electronic correlations and a coupling of the carriers to anharmonic phonons. The Projector Quantum Monte Carlo Scheme has been employed to investigate ground state properties. We analyze the superconducting properties of the model by directly addressing to the existence of Off-Diagonal Long Range Order (ODLRO). We review the numerical algorithm and discuss the possibility to observe ODLRO. In the presented model, we find ODLRO pointing towards superconductivity instead of the presence of strong electronic correlations. We discuss several features of the superconducting condensate.

International Journal of Modern Physics C•Feb 1, 1992•4 citations

Quantum Monte Carlo and exact diagonalization study of a dynamic Hubbard model

J. E. Hirsch

A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of dynamic Hubbard models that describe the relaxation of an atomic orbital upon double-electron occupancy due to electron-electron interactions. We study the parameter regime where pairing occurs in this model by exact diagonalization of small clusters. World-line quantum Monte Carlo simulations support the results of exact diagonalization for larger systems and show that the kinetic energy is lowered when pairing occurs. The qualitative physics of this model and others in its class, obtained through approximate analytic calculations, is that superconductivity occurs through hole undressing even in parameter regimes where the effective on-site interaction is strongly repulsive. Our numerical results confirm the expected qualitative behavior and show that pairing will occur in a substantially larger parameter regime than predicted by the approximate low-energy effective Hamiltonian.

arXiv:cond-mat/0201005•Physical review. B, Condensed matter•May 22, 2002•27 citations
We have carried out Quantum Monte Carlo studies to investigate the double layer Hubbard model using the groundstate projector formalism. Evidence for off diagonal long range order in the nodeless d-wave pairing channel is provided. It is emphasized that the Projector Quantum Monte Carlo method has the potential to detect superconducting mechanisms in strongly correlated electron systems, which are not treatable by standard analytic methods. The Monte Carlo technique provides useful information about systems much larger than those accessible for exact diagonalization methods.
We report on a numerical study of the double layer Hubbard model describing the CuO2 sheets in the high-Tc oxides. For the simulation we employed the projector quantum Monte Carlo method (PQMC) to study the ground state properties of this correlated electron system. Our results provide evidence for off-diagonal long range order in the nodeless d-wave channel. The implications with respect to possible mechanisms for high-Tc superconductivity in oxides in combination which phononic booster mechanisms are discussed.
Superconducting properties of coupled Hubbard planes are studied by quantum Monte Carlo simulations. It is found that the interlayer coupling supports the pairing mechanism but it does not lead to off-diagonal long-range order in the purely electronic system. In addition, we have performed Monte Carlo studies based on a recently proposed variational wave function. Yielding identical results, the variational wave function overcomes the sign problem and allows us to analyze ground-state properties of strongly correlated many-body problems for system sizes and complexities not accessible otherwise.
The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.
We study a model for high- T c superconductors describing both the strong electronic correlations and a coupling of the carriers to anharmonic phonons. The Projector Quantum Monte Carlo Scheme has been employed to investigate ground state properties. We analyze the superconducting properties of the model by directly addressing to the existence of Off-Diagonal Long Range Order (ODLRO). We review the numerical algorithm and discuss the possibility to observe ODLRO. In the presented model, we find ODLRO pointing towards superconductivity instead of the presence of strong electronic correlations. We discuss several features of the superconducting condensate.
A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of dynamic Hubbard models that describe the relaxation of an atomic orbital upon double-electron occupancy due to electron-electron interactions. We study the parameter regime where pairing occurs in this model by exact diagonalization of small clusters. World-line quantum Monte Carlo simulations support the results of exact diagonalization for larger systems and show that the kinetic energy is lowered when pairing occurs. The qualitative physics of this model and others in its class, obtained through approximate analytic calculations, is that superconductivity occurs through hole undressing even in parameter regimes where the effective on-site interaction is strongly repulsive. Our numerical results confirm the expected qualitative behavior and show that pairing will occur in a substantially larger parameter regime than predicted by the approximate low-energy effective Hamiltonian.