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:1305.2727 · Physical Review B

d -wave superconductivity and its coexistence with antiferromagnetism in the t – J – U model: Statistically consistent Gutzwiller approach

Marcin Abram, Jan Kaczmarczyk, Jakub Jȩdrak, Józef Spałek

Published Sep 3, 2013• 39 citations
arXivHTMLPDF

Abstract

We discuss the coexistence of antiferromagnetism and $d$-wave superconductivity within the so-called statistically consistent Gutzwiller approximation (SGA) applied to the $t$--$J$--$U$ model. In this approach, the averages calculated in a self-consistent manner coincide with those determined variationally. Such consistency is not guaranteed within the standard renormalized mean-field theory. With the help of SGA, we show that for the typical value $J/|t|=\frac{1}{3}$, coexistence of antiferromagnetism (AF) and superconductivity (SC) appears only for $U/|t|>10.6$ and in a very narrow range of doping $(\ensuremath{\delta}\ensuremath{\lesssim}0.006)$ in the vicinity of the Mott insulating state, in contrast to some previous reports. In the coexistent AF+SC phase, a staggered spin-triplet component of the superconducting gap appears also naturally; its value is very small.

DOI
10.1103/physrevb.88.094502

Related papers

Antiferromagnetism, charge density wave, and d -wave superconductivity in the extended t - J - U model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory

Marcin Abram, M. Zegrodnik, Józef Spałek

In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.

arXiv:1607.05399•Journal of Physics Condensed Matter•Jun 19, 2017•22 citations

Antiferromagnetism, charge density wave, and d-wave superconductivity in the $t$-$J$-$U$-$V$ model of correlated electrons: Role of direct Coulomb interactions

Marcin Abram, M. Zegrodnik, Józef Spałek

We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the $t$-$J$-$U$-$V$ model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term $V$ in stabilizing the CDW phase and show it appears only above some critical values of $V$ and in a limited hole doping range $\delta$. The effect of the term $V$ on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.

•Jul 19, 2016•0 citations

Coexistence of dx2−y2 superconductivity and antiferromagnetism in the two-dimensional t−J model and numerical estimation of Gutzwiller factors

Akihiro Himeda, Masao Ogata

The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-$J$ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the $\mathrm{xy}$ components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.

Physical review. B, Condensed matter•Oct 1, 1999•128 citations

Gossamer superconductivity and antiferromagnetism in the t‐J‐U model

Feng Yuan, Qingshan Yuan, C. S. Ting

The $d$-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean-field theory for a two-dimensional $t\text{\penalty1000-\hskip0pt}J$ model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no-double-occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\ensuremath{\delta}$ and $U$ are studied. Using the standard value of $t∕J=3.0$ and in the large-$U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\ensuremath{\delta}\ensuremath{\sim}0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\ensuremath{\delta}\ensuremath{\sim}0.15$. In the small-$U$ limit, only the dSC order survives while the AF order disappears. As $U$ increases up to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half-filling, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean-field approach, we show that the ground-state energy of the coexistent state is always lower than that of the pure dSC state.

arXiv:cond-mat/0409596•Physical Review B•Mar 8, 2005•17 citations

Superconductivity and Antiferromagnetism in an Extended Gutzwiller Approximation fort–JModel: Effect of Double-Occupancy Exclusion

Masao Ogata, Akihiro Himeda

The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.

Journal of the Physical Society of Japan•Feb 15, 2003•74 citations

Statistically-consistent mean-field approach to t-J-U model: Antiferromagnetism versus superconductivity

Marcin Abram, Jan Kaczmarczyk, J. Jdrak +1 more

We study the t-J-U model within the Gutzwiller approximation (GA). A coexistence of antiferromagnetism and superconductivity is found. We incorporate statistical-consistency conditions into GA and find that only a pure antiferromagnetic phase is stable. We argue that in the latter situation we need to incorporate not only pure spin-singlet pairing, but also an admixture of the spin-triplet pairing, the latter caused by the inequivalence of antiferromagnetic sublattices in the paired state.

AIP conference proceedings•Jan 1, 2012•0 citations
We discuss the coexistence of antiferromagnetism and ddd-wave superconductivity within the so-called statistically consistent Gutzwiller approximation (SGA) applied to the ttt--JJJ--UUU model. In this approach, the averages calculated in a self-consistent manner coincide with those determined variationally. Such consistency is not guaranteed within the standard renormalized mean-field theory. With the help of SGA, we show that for the typical value J/∣t∣=13J/|t|=\frac{1}{3}J/∣t∣=31​, coexistence of antiferromagnetism (AF) and superconductivity (SC) appears only for U/∣t∣>10.6U/|t|>10.6U/∣t∣>10.6 and in a very narrow range of doping (\ensuremathδ\ensuremath≲0.006)(\ensuremath{\delta}\ensuremath{\lesssim}0.006)(\ensuremathδ\ensuremath≲0.006) in the vicinity of the Mott insulating state, in contrast to some previous reports. In the coexistent AF+SC phase, a staggered spin-triplet component of the superconducting gap appears also naturally; its value is very small.
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Antiferromagnetism, charge density wave, and d-wave superconductivity in the ttt-JJJ-UUU-VVV model of correlated electrons: Role of direct Coulomb interactions
We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the ttt-JJJ-UUU-VVV model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term VVV in stabilizing the CDW phase and show it appears only above some critical values of VVV and in a limited hole doping range δ\deltaδ. The effect of the term VVV on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.
The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-JJJ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the xy\mathrm{xy}xy components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.
The ddd-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean-field theory for a two-dimensional $t\text{\penalty1000-\hskip0pt}J$ model plus an on-site repulsive Hubbard interaction UUU. The purpose of introducing the UUU term is to partially impose the no-double-occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\ensuremath{\delta}$ and UUU are studied. Using the standard value of t∕J=3.0t∕J=3.0t∕J=3.0 and in the large-UUU limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\ensuremath{\delta}\ensuremath{\sim}0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\ensuremath{\delta}\ensuremath{\sim}0.15$. In the small-UUU limit, only the dSC order survives while the AF order disappears. As UUU increases up to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half-filling, the system is in the dSC state for small UUU and becomes an AF insulator for large UUU. Within the present mean-field approach, we show that the ground-state energy of the coexistent state is always lower than that of the pure dSC state.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.