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

Physics Procedia

Stripes and d-wave Superconductivity in the Two-dimensional Hubbard Model

Mitake Miyazaki, Yamaji K., Takashi Yanagisawa

Published Jan 1, 2014• 2 citations
Publisher

Abstract

In order to study the material dependence of the correlation between stripes and dx2-y2-wave superconductivity (SC) among cuprate superconductors, we have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first-, second- and third-nearest-neighbor hopping terms (t, t’ and t”, respectively) by using the Gutzwiller-Jastrow-type wave function taking account of three-body correlations on a triangle, which is efficient for frustrated systems. The condensation energies of the vertical stripes and the homogeneous SC were computed as a function of t’/t with a fixed relation t”= –t’/2. We have found that, at the nearly optimal doping with moderately strong on-site Coulomb interaction, the state of maximum condensation energy switches from the vertical stripes to the homogeneous dSC as |t’/t| increases.

DOI
10.1016/j.phpro.2014.09.008

Related papers

Renormalization of hopping integrals in coexistence phase of stripe and d-wave superconductivity in two-dimensional Hubbard model

Mitake Miyazaki, Yamaji K., Takashi Yanagisawa +1 more

We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.

Physics Procedia•Jan 1, 2012•3 citations

Variational Monte Carlo study of stripes as a function of doping in the t−t′ Hubbard model

Antonio Lechiara, Vito Marino, Luca F. Tocchio

') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.

arXiv:2403.02073•Journal of Physics Condensed Matter•Jun 24, 2024•0 citations

Crossover between BCS Superconductor and Doped Mott Insulator of d -Wave Pairing State in Two-Dimensional Hubbard Model

Hisatoshi Yokoyama, Masao Ogata, Yukio Tanaka +2 more

With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of $U$ for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.

arXiv:1208.1102•Journal of the Physical Society of Japan•Jan 15, 2013•100 citations

Superconductivity in the two-dimensional Hubbard model: Gutzwiller wave function solution

Jan Kaczmarczyk, Józef Spałek, Tobias Schickling +1 more

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes $t$ (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters ($U$, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.

arXiv:1210.6249•Physical Review B•Sep 16, 2013•64 citations

Correlated-Electron Systems and High-Temperature Superconductivity

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.

arXiv:1307.2456•Journal of Modern Physics•Jan 1, 2013•23 citations

Stripe correlations in the two-dimensional Hubbard-Holstein model

Seher Karakuzu, Andy Tanjaroon Ly, Peizhi Mai +3 more

Abstract Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping $${t}^{{\prime} }$$ t′ or phonon energy Ω. Our results help elucidate how thee-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-Tccuprates.

arXiv:2205.15464•Communications Physics•Dec 2, 2022•23 citations
In order to study the material dependence of the correlation between stripes and dx2-y2-wave superconductivity (SC) among cuprate superconductors, we have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first-, second- and third-nearest-neighbor hopping terms (t, t’ and t”, respectively) by using the Gutzwiller-Jastrow-type wave function taking account of three-body correlations on a triangle, which is efficient for frustrated systems. The condensation energies of the vertical stripes and the homogeneous SC were computed as a function of t’/t with a fixed relation t”= –t’/2. We have found that, at the nearly optimal doping with moderately strong on-site Coulomb interaction, the state of maximum condensation energy switches from the vertical stripes to the homogeneous dSC as |t’/t| increases.
We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.
') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.
With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of UUU for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.
A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes ttt (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (UUU, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
Abstract Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t′{t}^{{\prime} }t′ t′ or phonon energy Ω. Our results help elucidate how thee-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-Tccuprates.