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

arXiv:1401.7226 · Physical Review B

Determinant quantum Monte Carlo study of d -wave pairing in the plaquette Hubbard hamiltonian

Tao Ying, Rubem Mondaini, Xiudong Sun, Thereza Paiva, Richard M. Fye, Richard T. Scalettar

Published Aug 13, 2014• 28 citations
arXivHTMLPDF

Abstract

Determinant quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters---a two-dimensional square lattice consisting of elemental $2\ifmmode\times\else\texttimes\fi{}2$ plaquettes with hopping $t$ and on-site repulsion $U$ coupled by an interplaquette hopping ${t}^{\ensuremath{'}}\ensuremath{\le}t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.4$ at which the pairing vertex is most attractive. The optimal ${t}^{\ensuremath{'}}/t$ increases with $U/t$. We then contrast our results for this plaquette model with a hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three-band ${\mathrm{CuO}}_{2}$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.

DOI
10.1103/physrevb.90.075121

Related papers

Quantum Monte Carlo study of the dominating pairing symmetry in doped honeycomb lattice*

Xingchuan Zhu, Tao Ying, Huaiming Guo +1 more

We perform a systematic determinant quantum Monte Carlo (DQMC) study of the dominating pairing symmetry in a doped honeycomb lattice. The Hubbard model is simulated over a full range of filling levels for both weak and strong interactions. For weak couplings, the d-wave state dominates. The effective susceptibility as a function of filling shows a peak, and its position moves toward half filling as the temperature is increased, from which the optimal filling of the superconducting ground state is estimated. Although the sign problem becomes severe for strong couplings, the simulations access the lowest temperature at which the DQMC method generates reliable results. As the coupling is strengthened, the d-wave state is enhanced in the high-filling region. Our systematic DQMC results provide new insights into the superconducting pairing symmetry in the doped honeycomb lattice.

Chinese Physics B•Jul 1, 2019•8 citations

Suppression of d -wave superconductivity in the checkerboard Hubbard model

D. G. S. P. Doluweera, Alexandru Macridin, Thomas Maier +2 more

Using a dynamical cluster quantum Monte Carlo approximation, we investigate the $d$-wave superconducting transition temperature ${T}_{c}$ in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses ${T}_{c}$. The characteristic spin excitation energy and the strength of $d$-wave pairing interaction decrease with decreasing ${T}_{c}$, suggesting a strong correlation between these quantities.

arXiv:0806.1504•Physical Review B•Jul 9, 2008•19 citations

Determinant quantum Monte Carlo study of the enhancement of d -wave pairing by charge inhomogeneity

Rubem Mondaini, Tao Ying, Thereza Paiva +1 more

Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO${}_{2}$ planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the $d$-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a $\ensuremath{\pi}$-phase shift in the magnetic order.

arXiv:1209.0049•Physical Review B•Nov 7, 2012•36 citations

Quantum Monte Carlo study of the Hubbard model with next-nearest-neighbor hopping t ′: pairing and magnetism

Shuhui Yang, Tao Ying, Weiqi Li +3 more

Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t' on square lattices. By varying the value of t', we find that the d-wave pairing is suppressed by the onset of t', while the p + ip-wave pairing tends to emerge for low electron density and t' around -0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.

Journal of Physics Condensed Matter•Dec 14, 2020•9 citations

Sign change of the extended s -wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study

Karim Bouadim, Matthew Enjalran, F. Hébert +2 more

The ``dynamic'' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant quantum Monte Carlo method. Our key result is that the extended $s$-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.

arXiv:0710.1356•Physical Review B•Jan 22, 2008•9 citations

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

Steven Johnston, Elizabeth Nowadnick, Y. F. Kung +3 more

We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here, we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic orders at half-filling.

arXiv:1306.2968•Physical Review B•Jun 24, 2013•82 citations
Determinant quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters---a two-dimensional square lattice consisting of elemental 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 plaquettes with hopping ttt and on-site repulsion UUU coupled by an interplaquette hopping t\ensuremath′\ensuremath≤t{t}^{\ensuremath{'}}\ensuremath{\le}tt\ensuremath′\ensuremath≤t. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half filling by the inhomogeneous hopping or not. For U/t=4U/t=4U/t=4, DQMC indicates an optimal t\ensuremath′/t\ensuremath≈0.4{t}^{\ensuremath{'}}/t\ensuremath{\approx}0.4t\ensuremath′/t\ensuremath≈0.4 at which the pairing vertex is most attractive. The optimal t\ensuremath′/t{t}^{\ensuremath{'}}/tt\ensuremath′/t increases with U/tU/tU/t. We then contrast our results for this plaquette model with a hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three-band CuO2{\mathrm{CuO}}_{2}CuO2​ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.
We perform a systematic determinant quantum Monte Carlo (DQMC) study of the dominating pairing symmetry in a doped honeycomb lattice. The Hubbard model is simulated over a full range of filling levels for both weak and strong interactions. For weak couplings, the d-wave state dominates. The effective susceptibility as a function of filling shows a peak, and its position moves toward half filling as the temperature is increased, from which the optimal filling of the superconducting ground state is estimated. Although the sign problem becomes severe for strong couplings, the simulations access the lowest temperature at which the DQMC method generates reliable results. As the coupling is strengthened, the d-wave state is enhanced in the high-filling region. Our systematic DQMC results provide new insights into the superconducting pairing symmetry in the doped honeycomb lattice.
Using a dynamical cluster quantum Monte Carlo approximation, we investigate the ddd-wave superconducting transition temperature Tc{T}_{c}Tc​ in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and ttt in the form of a checkerboard pattern where ttt is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses Tc{T}_{c}Tc​. The characteristic spin excitation energy and the strength of ddd-wave pairing interaction decrease with decreasing Tc{T}_{c}Tc​, suggesting a strong correlation between these quantities.
Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO2{}_{2}2​ planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the ddd-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a $\ensuremath{\pi}$-phase shift in the magnetic order.
Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t' on square lattices. By varying the value of t', we find that the d-wave pairing is suppressed by the onset of t', while the p + ip-wave pairing tends to emerge for low electron density and t' around -0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.
The ``dynamic'' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant quantum Monte Carlo method. Our key result is that the extended sss-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.
We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here, we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic orders at half-filling.