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:cond-mat/0110460 · Physical Review Letters

Superconductivity in the Two-Dimensional t−J Model

Sandro Sorella, George Balster Martins, Federico Becca, C. J. Gazza, Luca Capriotti, Alberto Parola, Elbio R. Dagotto

Published Feb 28, 2002• 213 citations
arXivHTMLPDF

Abstract

Using computational techniques, it is shown that pairing is a robust property of hole-doped antiferromagnetic insulators. In one dimension and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting long-range order in this case. However, in two dimensions it is argued-and numerically confirmed using several techniques, especially quantum Monte Carlo-that quantum fluctuations are not strong enough to suppress superconductivity.

DOI
10.1103/physrevlett.88.117002

Related papers

Two-hole ground state wavefunction: Non-BCS pairing in a t−J two-leg ladder

Shuai A. Chen, Zheng Zhu, Zheng-Yu Weng

Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is $if$ any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo approach. By comparing with density-matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t\text{\ensuremath{-}}J$ model, which is kinetic-energy driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.

arXiv:1808.06173•Physical review. B./Physical review. B•Dec 26, 2018•19 citations

Finite compressibility in the low-doping region of the two-dimensional t−J model

Massimo Lugas, Leonardo Spanu, Federico Becca +1 more

We reexamine the important issue of charge fluctuations in the two-dimensional $t\text{\ensuremath{-}}J$ model by using an improved variational method based on a wave function that contains both antiferromagnetic and $d$-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by Bouchaud, Georges, and Lhuillier [J. Phys. (Paris) 49, 553 (1988)] by considering also a long-range spin-spin Jastrow factor, in order to correctly reproduce the small-$q$ behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J∕t\ensuremath{\sim}0.4$ and find that, contrary to a previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain clear evidence that the $t\text{\ensuremath{-}}J$ model does not phase separate for $J∕t\ensuremath{\lesssim}0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.

arXiv:cond-mat/0606659•Physical Review B•Oct 31, 2006•37 citations

Two-Hole Ground State: Dichotomy in Pairing Symmetry

Jingyu Zhao, Shuai A. Chen, Hao-Kai Zhang +1 more

A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method.Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics.In this work, we further investigate the ground state of two holes by VMC.It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations.A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d wave in terms of the electron c operators and an s wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function.A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result.We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase strings created by the hopping of holes.The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation.Physical implications to superconductivity at finite doping are also discussed.

arXiv:2106.14898•Physical Review X•Mar 31, 2022•23 citations

Absence of the coexistence of superconductivity and antiferromagnetism in the hole-doped two-dimensional extended t−J model

C. T. Shih, Y. C. Chen, Chung-Pin Chou +1 more

The possibility of coexistence of superconductivity (SC) and antiferromagnetic long-range order (AFLRO) of the two-dimensional extended $t\text{\ensuremath{-}}J$ model in the very underdoped region is studied by the variational Monte Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and $d$-wave SC for the physical parameters, $J∕t=0.3$, ${t}^{\ensuremath{'}}∕t=\ensuremath{-}0.3$ and ${t}^{\ensuremath{''}}∕t=0.2$, is located near hole density ${\ensuremath{\delta}}_{c}\ensuremath{\cong}0.06$, and there is no coexistence. The phase transition is first order between these two homogeneous phases at ${\ensuremath{\delta}}_{c}$.

arXiv:cond-mat/0408422•Physical Review B•Dec 3, 2004•30 citations

Fidelity and superconductivity in two-dimensional t−J models

Marcos Rigol, B. Sriram Shastry, Stephan Haas

We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional $t\text{\ensuremath{-}}J$-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain $t\text{\ensuremath{-}}J$ and $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ models, (ii) for the $t\text{\ensuremath{-}}J$ model perturbed by infinite-range $d$-wave or extended-$s$-wave superconductivity inducing terms, and (iii) the $t\text{\ensuremath{-}}J$ model, plain and with a $d$-wave perturbation, in the presence of nonmagnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case, our results are consistent with previous work that concluded that the plain $t\text{\ensuremath{-}}J$ model supports $d$-wave superconductivity. As a consequence of the strong correlations present in the low hole doping regime, we find that the magnitude of the $d$-wave condensate occupation is small even in the presence of large $d$-wave superconductivity inducing terms. In the dirty case, we show the robustness of the ground state in the strongly correlated regime against disorder.

arXiv:0906.5347•Physical Review B•Sep 29, 2009•26 citations

Superconductivity, Antiferromagnetism, and Kinetic Correlation in Strongly Correlated Electron Systems

Takashi Yanagisawa

We investigate the ground state of two-dimensional Hubbard model on the basis of the variational Monte Carlo method. We use wave functions that include kinetic correlation and doublon-holon correlation beyond the Gutzwiller ansatz. It is still not clear whether the Hubbard model accounts for high-temperature superconductivity. The antiferromagnetic correlation plays a key role in the study of pairing mechanism because the superconductive phase exists usually close to the antiferromagnetic phase. We investigate the stability of the antiferromagnetic state when holes are doped as a function of the Coulomb repulsion U . We show that the antiferromagnetic correlation is suppressed as U is increased exceeding the bandwidth. High-temperature superconductivity is possible in this region with enhanced antiferromagnetic spin fluctuation and pairing interaction.

Advances in Condensed Matter Physics•Jan 1, 2015•0 citations
Using computational techniques, it is shown that pairing is a robust property of hole-doped antiferromagnetic insulators. In one dimension and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting long-range order in this case. However, in two dimensions it is argued-and numerically confirmed using several techniques, especially quantum Monte Carlo-that quantum fluctuations are not strong enough to suppress superconductivity.
Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is ififif any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo approach. By comparing with density-matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t\text{\ensuremath{-}}J$ model, which is kinetic-energy driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.
We reexamine the important issue of charge fluctuations in the two-dimensional $t\text{\ensuremath{-}}J$ model by using an improved variational method based on a wave function that contains both antiferromagnetic and ddd-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by Bouchaud, Georges, and Lhuillier [J. Phys. (Paris) 49, 553 (1988)] by considering also a long-range spin-spin Jastrow factor, in order to correctly reproduce the small-qqq behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J∕t\ensuremath{\sim}0.4$ and find that, contrary to a previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain clear evidence that the $t\text{\ensuremath{-}}J$ model does not phase separate for $J∕t\ensuremath{\lesssim}0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.
A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method.Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics.In this work, we further investigate the ground state of two holes by VMC.It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations.A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d wave in terms of the electron c operators and an s wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function.A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result.We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase strings created by the hopping of holes.The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation.Physical implications to superconductivity at finite doping are also discussed.
The possibility of coexistence of superconductivity (SC) and antiferromagnetic long-range order (AFLRO) of the two-dimensional extended $t\text{\ensuremath{-}}J$ model in the very underdoped region is studied by the variational Monte Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and ddd-wave SC for the physical parameters, J∕t=0.3J∕t=0.3J∕t=0.3, ${t}^{\ensuremath{'}}∕t=\ensuremath{-}0.3$ and ${t}^{\ensuremath{''}}∕t=0.2$, is located near hole density ${\ensuremath{\delta}}_{c}\ensuremath{\cong}0.06$, and there is no coexistence. The phase transition is first order between these two homogeneous phases at ${\ensuremath{\delta}}_{c}$.
We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional $t\text{\ensuremath{-}}J$-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain $t\text{\ensuremath{-}}J$ and $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ models, (ii) for the $t\text{\ensuremath{-}}J$ model perturbed by infinite-range ddd-wave or extended-sss-wave superconductivity inducing terms, and (iii) the $t\text{\ensuremath{-}}J$ model, plain and with a ddd-wave perturbation, in the presence of nonmagnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case, our results are consistent with previous work that concluded that the plain $t\text{\ensuremath{-}}J$ model supports ddd-wave superconductivity. As a consequence of the strong correlations present in the low hole doping regime, we find that the magnitude of the ddd-wave condensate occupation is small even in the presence of large ddd-wave superconductivity inducing terms. In the dirty case, we show the robustness of the ground state in the strongly correlated regime against disorder.
We investigate the ground state of two-dimensional Hubbard model on the basis of the variational Monte Carlo method. We use wave functions that include kinetic correlation and doublon-holon correlation beyond the Gutzwiller ansatz. It is still not clear whether the Hubbard model accounts for high-temperature superconductivity. The antiferromagnetic correlation plays a key role in the study of pairing mechanism because the superconductive phase exists usually close to the antiferromagnetic phase. We investigate the stability of the antiferromagnetic state when holes are doped as a function of the Coulomb repulsion U . We show that the antiferromagnetic correlation is suppressed as U is increased exceeding the bandwidth. High-temperature superconductivity is possible in this region with enhanced antiferromagnetic spin fluctuation and pairing interaction.