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/0408374 · Physical Review B

Spinon-holon binding in t−J model

Tai Kai Ng

Published May 27, 2005• 25 citations
arXivHTMLPDF

Abstract

Using a phenomenological model, we discuss the consequences of spinon-holon binding in the $U(1)$ slave-boson approach to $t\text{\ensuremath{-}}J$ model in the weak-coupling limit. We find that spinon-holon binding produces a pseudogap normal state with a segmented Fermi surface and the superconducting state is formed by opening an ``additional'' $d$-wave gap on the segmented Fermi surface. The $d$-wave gap merges with the pseudogap smoothly as temperature $T\ensuremath{\rightarrow}0$. The quasiparticles in the superconducting state are coupled to external electromagnetic field with a coupling constant of order ${x}^{\ensuremath{\gamma}∕2}\phantom{\rule{0.3em}{0ex}}(x=\text{hole concentration})$, where $0\ensuremath{\leqslant}\ensuremath{\gamma}\ensuremath{\leqslant}1$.

DOI
10.1103/physrevb.71.172509

Related papers

Holon-pair boson theory based on the U(1) and SU(2) slave-boson approaches to the t-J Hamiltonian

Sung-Sik Lee, Sung‐Ho Suck Salk

To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high $T_c$ cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature $T_c$ and the pseudogap (spin gap) temperature $T^*$ tangential to $T_c$ in the overdoped region in the observed phase diagram of high $T_c$ cuprates. A universal parabolic scaling behavior of $T^*/T_c$ (or $T_c/T^*$) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of $T_c$ but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.

arXiv:cond-mat/0304293•Apr 12, 2003•0 citations

Slave-boson description of pseudogap metals in t−J models

Julia Brunkert, Matthias Punk

This work discusses a modified slave-boson representation of the t-J model, which accounts for spinon-holon bound states and gives rise to a metallic pseudogap phase with sharp, Fermi-arc like features in the electron spectral function.

arXiv:2002.04041•Physical Review Research•Oct 2, 2020•5 citations

Pairing and superconductivity in a spin-charge gauge approach to HTS cuprates

Michele Gambaccini

This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.

•Jan 31, 2011•0 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

Holon pair condensation and phase diagram of high- Tc cuprates

Tae-Hyoung Gimm, Sung-Sik Lee, Seung-Pyo Hong +1 more

A possibility of holon (boson) pair condensation is explored for hole-doped high-${T}_{c}$ cuprates, by using the $U(1)$ slave-boson representation of the $t\ensuremath{-}J$ Hamiltonian with the inclusion of hole-hole repulsion. A phase diagram of the hole doped high-${T}_{c}$ cuprates is deduced by allowing both the holon pairing and spinon pairing channels. It is shown that the spin gap size remains nearly unchanged below the holon pair condensation temperature. We find that the s-wave holon pairing under the condition of d-wave spin singlet pairing is preferred, thus allowing d-wave hole pairing.

arXiv:cond-mat/9812096•Physical review. B, Condensed matter•Sep 1, 1999•18 citations

Theoretical investigation of high-Tc cuprate superconductors using t-J model : transport properties

Xiangjun Xia

The U(1) slave-boson mean-field theory of the t - J model has been used by many authors as a starting point for the theoretical analysis of high - Tc cuprate superconductors. With suitable refinements, the theory can explain a lot of qualitative features of cuprates. However, the theory does not produce a correct description of the low-energy quasi-particle properties in the under-doped regime. There exist several possible schemes to resolve this difficulty, among them, one generalizes the U(1) theory to SU(2) formulation and the other introduces confinement between spinons and holons. In this thesis, we generalize the Landau transport equations of the U(1) slave-boson mean-field theory of the t - J model to the SU(2) formulation. We first generalize the SU(2) slave-boson mean-field theory to the time-dependent regime. After eliminating the boson and constraint fields exactly in the linear-response regime at zero-temperature, we obtain a set of transport equations for quasi-particles, which has a similar structure as the Landau transport equations for Fermi-liquid superconductors, with all the Landau parameters explicitly given except that besides the usual effective interaction in the particle-hole channel in Fermi-liquid theory, we find an effective interaction in the particle-particle channel, which reflects the SU(2) symmetry between particles and holes. The transport equation is SU(2) invariant at half-filling. Around q⃗ = 0, the electron density couples only to the transverse part of the external field and the quasi-particle charge is still of order x. Besides the SU(2) formulation approach, we also investigate spinon-holon confinement in the U(1) slave-boson theory. The optical and thermal conduc-tivities of U (1) slave-boson theory with confinement are calculated. For optical conductivity, we consider only the contributions from static impurities. The qualitative behavior of our results agrees with experimental results. However, to explain the experiments quantitatively, we need to study further the con-tributions from phonons. We found a phenomenological effective Hamiltonian for the quasi-particle Green's functions in the U(1) slave-boson theory with spinon-hoion confinement. Starting from this effective Hamiltonian, we exam-ine the thermal conductivity within the theory. In particular, we compare the thermal conductivity for four different situations: (i) the ordinary d-wave su-perconducting state with four Dirac Fermi points; (ii) the normal metal state with a half-pocket Fermi surface; (iii) the spinon-holon confinement supercon-ducting state with a half-pocket Fermi surface; (iv) BCS superconducting state with a half-pocket Fermi surface.

•Jan 1, 2005•0 citations
Using a phenomenological model, we discuss the consequences of spinon-holon binding in the U(1)U(1)U(1) slave-boson approach to t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model in the weak-coupling limit. We find that spinon-holon binding produces a pseudogap normal state with a segmented Fermi surface and the superconducting state is formed by opening an ``additional'' ddd-wave gap on the segmented Fermi surface. The ddd-wave gap merges with the pseudogap smoothly as temperature T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0. The quasiparticles in the superconducting state are coupled to external electromagnetic field with a coupling constant of order x\ensuremathγ∕2(x=hole concentration){x}^{\ensuremath{\gamma}∕2}\phantom{\rule{0.3em}{0ex}}(x=\text{hole concentration})x\ensuremathγ∕2(x=hole concentration), where 0\ensuremath⩽\ensuremathγ\ensuremath⩽10\ensuremath{\leqslant}\ensuremath{\gamma}\ensuremath{\leqslant}10\ensuremath⩽\ensuremathγ\ensuremath⩽1.
To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high TcT_cTc​ cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature TcT_cTc​ and the pseudogap (spin gap) temperature T∗T^*T∗ tangential to TcT_cTc​ in the overdoped region in the observed phase diagram of high TcT_cTc​ cuprates. A universal parabolic scaling behavior of T∗/TcT^*/T_cT∗/Tc​ (or Tc/T∗T_c/T^*Tc​/T∗) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of TcT_cTc​ but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.
This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.
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.
A possibility of holon (boson) pair condensation is explored for hole-doped high-Tc{T}_{c}Tc​ cuprates, by using the U(1)U(1)U(1) slave-boson representation of the $t\ensuremath{-}J$ Hamiltonian with the inclusion of hole-hole repulsion. A phase diagram of the hole doped high-Tc{T}_{c}Tc​ cuprates is deduced by allowing both the holon pairing and spinon pairing channels. It is shown that the spin gap size remains nearly unchanged below the holon pair condensation temperature. We find that the s-wave holon pairing under the condition of d-wave spin singlet pairing is preferred, thus allowing d-wave hole pairing.
The U(1) slave-boson mean-field theory of the t - J model has been used by many authors as a starting point for the theoretical analysis of high - Tc cuprate superconductors. With suitable refinements, the theory can explain a lot of qualitative features of cuprates. However, the theory does not produce a correct description of the low-energy quasi-particle properties in the under-doped regime. There exist several possible schemes to resolve this difficulty, among them, one generalizes the U(1) theory to SU(2) formulation and the other introduces confinement between spinons and holons. In this thesis, we generalize the Landau transport equations of the U(1) slave-boson mean-field theory of the t - J model to the SU(2) formulation. We first generalize the SU(2) slave-boson mean-field theory to the time-dependent regime. After eliminating the boson and constraint fields exactly in the linear-response regime at zero-temperature, we obtain a set of transport equations for quasi-particles, which has a similar structure as the Landau transport equations for Fermi-liquid superconductors, with all the Landau parameters explicitly given except that besides the usual effective interaction in the particle-hole channel in Fermi-liquid theory, we find an effective interaction in the particle-particle channel, which reflects the SU(2) symmetry between particles and holes. The transport equation is SU(2) invariant at half-filling. Around q⃗ = 0, the electron density couples only to the transverse part of the external field and the quasi-particle charge is still of order x. Besides the SU(2) formulation approach, we also investigate spinon-holon confinement in the U(1) slave-boson theory. The optical and thermal conduc-tivities of U (1) slave-boson theory with confinement are calculated. For optical conductivity, we consider only the contributions from static impurities. The qualitative behavior of our results agrees with experimental results. However, to explain the experiments quantitatively, we need to study further the con-tributions from phonons. We found a phenomenological effective Hamiltonian for the quasi-particle Green's functions in the U(1) slave-boson theory with spinon-hoion confinement. Starting from this effective Hamiltonian, we exam-ine the thermal conductivity within the theory. In particular, we compare the thermal conductivity for four different situations: (i) the ordinary d-wave su-perconducting state with four Dirac Fermi points; (ii) the normal metal state with a half-pocket Fermi surface; (iii) the spinon-holon confinement supercon-ducting state with a half-pocket Fermi surface; (iv) BCS superconducting state with a half-pocket Fermi surface.