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:1605.03969 · Bulletin of the American Physical Society

Crossover From Strong to Weak Pairing States in $t-J-U$ Model Studied by A Slave Spin Method

Wei-Cheng Lee

Published May 12, 2016• 1 citation
arXivHTMLPDF

Abstract

We investigate the superconductivity in the $t-J-U$ model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons $Δ_f$ and the Cooper pairing gap of the electrons $Δ_{SC} = ZΔ_f$, where $Z$ is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by $Z$ but the its pairing term is not. As a result, if $U$ exceeds the critical value for the Mott insulating state at half-filling, $Z$ develops a strong doping dependence, leading to a doping-driven crossover from strong to weak pairing states. In the strong pairing state, while $Δ_f$ is enhanced as $x\to 0$, $Δ_{SC}\sim x$ due to the renormalization of $Z$. In the weak pairing state, $Z$ does not change with $x$ significantly. Therefore, $Δ_{SC}$ is mainly controlled by $Δ_f$, and both of them go to zero at larger doping. The crossover from strong to weak pairing states is well captured by the slave spin formalism within reasonable range of parameters just at the mean-field level, indicating the slave spin formalism is a powerful tool to study correlated materials. For charge interactions, we find that the bandwidth of the spinon hopping term and its pairing term are renormalized by $Z$ and $Z^2$ respectively. Consequently, both $Δ_f$ and $Δ_{SC}$ are suppressed at small $x$ in large U, and no crossover will occur. The implication of our results for the superconducting states in correlated materials will be discussed.

DOI
10.48550/arxiv.1605.03969

Related papers

Superconductivity in the Hubbard model with correlated hopping: Slave-boson study

Bogdan R. Bułka

Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral $t$ equals the correlated hopping integral $X.$ The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of $X$ and any electron concentration $n.$ At the half-filled band $(n=1)$ a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for $n$ close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral $U$ close to the phase-transition point.

arXiv:cond-mat/9703040•Physical review. B, Condensed matter•May 1, 1998•29 citations

Antiferromagnetism in the Hubbard model using a cluster slave-spin method

Wei‐Cheng Lee, Ting-Kuo Lee

The cluster slave-spin method is introduced to systematically investigate the solutions of the Hubbard model including the symmetry-broken phases. In this method, the electron operator is factorized into a fermionic spinon describing the physical spin and a slave-spin describing the charge fluctuations. Following the $U(1)$ formalism derived by Yu and Si [Phys. Rev. B 86, 085104 (2012)], it is shown that the self-consistent equations to explore various symmetry-broken density wave states can be constructed in general with a cluster of multiple slave-spin sites. We employ this method to study the antiferromagnetic (AFM) state in the single band Hubbard model with the two- and four-site clusters of slave spins. While the Hubbard gap, the charge gap due to the doubly occupied states, scales with the Hubbard interaction $U$ as expected, the AFM gap $\mathrm{\ensuremath{\Delta}}$, the gap in the spinon dispersion in the AFM state, exhibits a crossover from the weak- to strong-coupling behaviors as $U$ increases. Our cluster slave-spin method reproduces not only the traditional mean-field behavior of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}U$ in the weak-coupling limit, but also the behavior of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}{t}^{2}/U$ predicted by the superexchange mechanism in the strong-coupling limit. In addition, the holon-doublon correlator as functions of $U$ and doping $x$ is also computed, which exhibits a strong tendency toward the holon-doublon binding in the strong coupling regime. We further show that the quasiparticle weight obtained by the cluster slave-spin method is in a good agreement with the generalized Gutzwiller approximation in both AFM and paramagnetic states, and the results can be improved beyond the generalized Gutzwiller approximation as the cluster is enlarged from a single site to four sites. Our results demonstrate that the cluster slave-spin method can be a powerful tool to systematically investigate the strongly correlated system.

arXiv:1707.03042•Physical review. B./Physical review. B•Sep 8, 2017•10 citations

Dynamical effects on superconductivity in a BCS-BEC crossover: Dynamical mean field theory and numerical renormalization group study of the Holstein model in infinite dimensions

Tae-Ho Park, Han-Yong Choi

We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique to study the frequency dependence of phonon mediated interaction between electrons in a superconductive state. The frequency dependence induces distinct features such as the absence of the dispersion back bending of Bogoliubov quasiparticles, nonmonotonous coupling dependence of the pairing gap, and the critical temperature ${T}_{c}$ being maximum at ${g}_{c1}$, the lower critical coupling of the normal state insulator to metal transition. Some of these features have intriguing similarities with the recent observations in the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ and ${\mathrm{Fe}}_{1+y}{\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ iron chalcogenides in the BCS-BEC crossover.

arXiv:1812.11698•Physical review. B./Physical review. B•May 6, 2019•4 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

Slave-boson formalism for superconducting pairing at strong coupling

Sarbajit Mazumdar, Jonas Issing, Jannis Seufert +4 more

We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.

arXiv:2605.26233•Physical review. B./Physical review. B•Sep 28, 2026•0 citations

New interpretation of slave boson mean-field theory of the $t-J$ model: short-range antiferromagnetic and d-wave pairing correlations

Bumsoo Kyung

The $t-J$ Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field approximation and the limitation of the $t-J$ model near half-filling, we give a new interpretation to the slave boson mean-field theory of the $t-J$ model. We argue that due to phase coherence-breaking antiferromagnetic fluctuations and quantum fluctuations, superconducting long-range order does not appear strictly in two dimensions. $T_{c}$ resulting from interlayer pairing hopping can lead to a universal relation, when $T_{c}$ is scaled by $T^{max}_{c}$. Systematic reduction of superfluid density and increase of $(Δ_{d})_{max}/K_{B}T_{c}$ ratio below and near optimal doping have their natural explanation in our picture. A crossover temperature $T^{0}$ found in some of magnetic experiments such as NMR is also easily understood in the present framework.

arXiv:cond-mat/0008384•Aug 25, 2000•0 citations
Crossover From Strong to Weak Pairing States in t−J−Ut-J-Ut−J−U Model Studied by A Slave Spin Method
We investigate the superconductivity in the t−J−Ut-J-Ut−J−U model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons ΔfΔ_fΔf​ and the Cooper pairing gap of the electrons ΔSC=ZΔfΔ_{SC} = ZΔ_fΔSC​=ZΔf​, where ZZZ is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by ZZZ but the its pairing term is not. As a result, if UUU exceeds the critical value for the Mott insulating state at half-filling, ZZZ develops a strong doping dependence, leading to a doping-driven crossover from strong to weak pairing states. In the strong pairing state, while ΔfΔ_fΔf​ is enhanced as x→0x\to 0x→0, ΔSC∼xΔ_{SC}\sim xΔSC​∼x due to the renormalization of ZZZ. In the weak pairing state, ZZZ does not change with xxx significantly. Therefore, ΔSCΔ_{SC}ΔSC​ is mainly controlled by ΔfΔ_fΔf​, and both of them go to zero at larger doping. The crossover from strong to weak pairing states is well captured by the slave spin formalism within reasonable range of parameters just at the mean-field level, indicating the slave spin formalism is a powerful tool to study correlated materials. For charge interactions, we find that the bandwidth of the spinon hopping term and its pairing term are renormalized by ZZZ and Z2Z^2Z2 respectively. Consequently, both ΔfΔ_fΔf​ and ΔSCΔ_{SC}ΔSC​ are suppressed at small xxx in large U, and no crossover will occur. The implication of our results for the superconducting states in correlated materials will be discussed.
Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral ttt equals the correlated hopping integral X.X.X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of XXX and any electron concentration n.n.n. At the half-filled band (n=1)(n=1)(n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for nnn close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral UUU close to the phase-transition point.
The cluster slave-spin method is introduced to systematically investigate the solutions of the Hubbard model including the symmetry-broken phases. In this method, the electron operator is factorized into a fermionic spinon describing the physical spin and a slave-spin describing the charge fluctuations. Following the U(1)U(1)U(1) formalism derived by Yu and Si [Phys. Rev. B 86, 085104 (2012)], it is shown that the self-consistent equations to explore various symmetry-broken density wave states can be constructed in general with a cluster of multiple slave-spin sites. We employ this method to study the antiferromagnetic (AFM) state in the single band Hubbard model with the two- and four-site clusters of slave spins. While the Hubbard gap, the charge gap due to the doubly occupied states, scales with the Hubbard interaction UUU as expected, the AFM gap $\mathrm{\ensuremath{\Delta}}$, the gap in the spinon dispersion in the AFM state, exhibits a crossover from the weak- to strong-coupling behaviors as UUU increases. Our cluster slave-spin method reproduces not only the traditional mean-field behavior of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}U$ in the weak-coupling limit, but also the behavior of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}{t}^{2}/U$ predicted by the superexchange mechanism in the strong-coupling limit. In addition, the holon-doublon correlator as functions of UUU and doping xxx is also computed, which exhibits a strong tendency toward the holon-doublon binding in the strong coupling regime. We further show that the quasiparticle weight obtained by the cluster slave-spin method is in a good agreement with the generalized Gutzwiller approximation in both AFM and paramagnetic states, and the results can be improved beyond the generalized Gutzwiller approximation as the cluster is enlarged from a single site to four sites. Our results demonstrate that the cluster slave-spin method can be a powerful tool to systematically investigate the strongly correlated system.
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half filling where the electron-phonon coupling ggg controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique to study the frequency dependence of phonon mediated interaction between electrons in a superconductive state. The frequency dependence induces distinct features such as the absence of the dispersion back bending of Bogoliubov quasiparticles, nonmonotonous coupling dependence of the pairing gap, and the critical temperature Tc{T}_{c}Tc​ being maximum at gc1{g}_{c1}gc1​, the lower critical coupling of the normal state insulator to metal transition. Some of these features have intriguing similarities with the recent observations in the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ and ${\mathrm{Fe}}_{1+y}{\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ iron chalcogenides in the BCS-BEC crossover.
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.
We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.
New interpretation of slave boson mean-field theory of the t−Jt-Jt−J model: short-range antiferromagnetic and d-wave pairing correlations
The t−Jt-Jt−J Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field approximation and the limitation of the t−Jt-Jt−J model near half-filling, we give a new interpretation to the slave boson mean-field theory of the t−Jt-Jt−J model. We argue that due to phase coherence-breaking antiferromagnetic fluctuations and quantum fluctuations, superconducting long-range order does not appear strictly in two dimensions. TcT_{c}Tc​ resulting from interlayer pairing hopping can lead to a universal relation, when TcT_{c}Tc​ is scaled by TcmaxT^{max}_{c}Tcmax​. Systematic reduction of superfluid density and increase of (Δd)max/KBTc(Δ_{d})_{max}/K_{B}T_{c}(Δd​)max​/KB​Tc​ ratio below and near optimal doping have their natural explanation in our picture. A crossover temperature T0T^{0}T0 found in some of magnetic experiments such as NMR is also easily understood in the present framework.