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

AIP conference proceedings

Dynamic Hubbard model: a Monte Carlo study

F. Hébert

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added to already occupied orbitals, a phenomenon that is not present in the conventional Hubbard model and that may play a role in superconductivity. We use the determinant algorithm to study the properties of a particular dynamic Hubbard model on a two‐dimensional square lattice. We report preliminary results for a set of correlation functions, and our data are compared to results from the standard Hubbard model. We find that a dynamic interaction enhances the pair‐field susceptibility, signaling the possible on‐set of a superconducting phase.

DOI
10.1063/1.2178039

Related papers

Pairing in the two-dimensional Hubbard model: A Monte Carlo study

J. E. Hirsch, H. Q. Lin

We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-${T}_{c}$ superconductivity in oxides are discussed.

Physical review. B, Condensed matter•Apr 1, 1988•95 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

Superconducting Correlationof Two-Dimensional Hubbard Model near Half-Filling

Masatoshi Imada

Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12×12 lattice away from the half-filling and up to 16×16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s - nor d -wave superconducting state is possible in the two-dimensional Hubbard model.

Journal of the Physical Society of Japan•Aug 15, 1991•36 citations

Enhanced pair correlation functions in the two-dimensional Hubbard model

Takashi Yanagisawa

In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in the quantum Monte Carlo method which is free from the negative sign problem. We show that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling. When the system size becomes large, the pair correlation function P d increases for U > 0 compared to the non-interacting case, while P d is suppressed for U > 0 when the system size is small. The enhancement ratio P d [ U ]/ P d [ U = 0] will give a criterion on the existence of superconductivity. The ratio P d [ U ]/ P d [ U = 0] increases almost linearly ∝ L when the system size L × L is increased. This increase is a good indication of the existence of a superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions in the half-filled case, which indicates the absence of superconductivity without hole doping.

arXiv:1304.1273•New Journal of Physics•Mar 11, 2013•26 citations

Second-Neighbor Hopping Effects in the Two-Dimensional Attractive Hubbard Model

Rodrigo A. Fontenele, Nathan Vasconcelos, Natanael C. Costa +2 more

The emergence of superconductivity (SC) in lattice models, such as the attractive Hubbard one, has renewed interest since the realization of cold-atom experiments. However, reducing the temperature in these experiments is a bottleneck; therefore, investigating how to increase the energy scale for SC is crucial to cold atoms. In view of this, we examine the effects of next-nearest-neighbor hoppings (t′) on the pairing properties of the attractive Hubbard model in a square lattice. To this end, we analyze the model through unbiased Quantum Monte Carlo simulations for fixed density n=0.87, and perform finite-size scaling analysis to the thermodynamic limit. As our main result, we notice that the existence of further hopping channels leads to an enhancement of the pairing correlations, which, in turn, increases the ground-state order parameter Δ. Finally, at finite temperatures, for t′/t≠0, this enhancement of pairing correlations leads to an increase in the critical temperature Tc. That is, the fine-tuning of second-neighbor hoppings increases the energy scales for SC, and may be a route by which cold-atom experiments can achieve such a phase and to help us further understand the nature of this phenomenon.

Condensed Matter•Jan 17, 2023•2 citations

Variational Monte Carlo Study of Two Dimensional Multi-Orbital Hubbard Model

Akihisa Koga, N. Kawakami, H. Yokoyama +1 more

We investigate electron correlations in the two‐dimensional degenerate Hubbard model on the square lattice. By means of variational Monte Carlo simulations including nearest‐neighbor doublon‐holon correlations as well as on‐site correlations, we discuss the Mott transitions in the two‐orbital system at zero temperature.

AIP conference proceedings•Jan 1, 2006•6 citations
Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added to already occupied orbitals, a phenomenon that is not present in the conventional Hubbard model and that may play a role in superconductivity. We use the determinant algorithm to study the properties of a particular dynamic Hubbard model on a two‐dimensional square lattice. We report preliminary results for a set of correlation functions, and our data are compared to results from the standard Hubbard model. We find that a dynamic interaction enhances the pair‐field susceptibility, signaling the possible on‐set of a superconducting phase.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-Tc{T}_{c}Tc​ superconductivity in oxides are discussed.
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.
Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12×12 lattice away from the half-filling and up to 16×16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s - nor d -wave superconducting state is possible in the two-dimensional Hubbard model.
In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in the quantum Monte Carlo method which is free from the negative sign problem. We show that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling. When the system size becomes large, the pair correlation function P d increases for U > 0 compared to the non-interacting case, while P d is suppressed for U > 0 when the system size is small. The enhancement ratio P d [ U ]/ P d [ U = 0] will give a criterion on the existence of superconductivity. The ratio P d [ U ]/ P d [ U = 0] increases almost linearly ∝ L when the system size L × L is increased. This increase is a good indication of the existence of a superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions in the half-filled case, which indicates the absence of superconductivity without hole doping.
The emergence of superconductivity (SC) in lattice models, such as the attractive Hubbard one, has renewed interest since the realization of cold-atom experiments. However, reducing the temperature in these experiments is a bottleneck; therefore, investigating how to increase the energy scale for SC is crucial to cold atoms. In view of this, we examine the effects of next-nearest-neighbor hoppings (t′) on the pairing properties of the attractive Hubbard model in a square lattice. To this end, we analyze the model through unbiased Quantum Monte Carlo simulations for fixed density n=0.87, and perform finite-size scaling analysis to the thermodynamic limit. As our main result, we notice that the existence of further hopping channels leads to an enhancement of the pairing correlations, which, in turn, increases the ground-state order parameter Δ. Finally, at finite temperatures, for t′/t≠0, this enhancement of pairing correlations leads to an increase in the critical temperature Tc. That is, the fine-tuning of second-neighbor hoppings increases the energy scales for SC, and may be a route by which cold-atom experiments can achieve such a phase and to help us further understand the nature of this phenomenon.