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/9908161 · Europhysics Letters (EPL)

Supersymmetric mean-field theory of the t - J model

Chi-Ho Cheng, Tai Kai Ng

Published Oct 1, 2000• 3 citations
arXivHTMLPDF

Abstract

The supersymmetric formulation of the t - J model is studied in this paper at the mean-field level where the δ- T phase diagram is determined. We found that the slave-fermion–like spiral phase is stable at low doping concentration, and the slave-boson–like d -wave fermionic spin pairing state becomes energetically favourable when δ ⩾ 0.23. An improvement in free energy using Gutzwiller's method lowers the transition doping concentration to δ ≃ 0.06. We also point out the existence of new branches of excitations in the supersymmetric theory.

DOI
10.1209/epl/i2000-00408-4

Related papers

Supersymmetric formulation of t-J model

Chi-Ho Cheng

A new kind of symmetry, called Supersymmetry, is introduced in t-J model and its corresponding Supersymmetric Formulation is constructed. The new formulation unifies the so-called slave-fermion and slave-boson formulations to the model in a single framework and is able to incorporate the advantage of the two approaches. The formulation is analysed at mean-field level where we found that antiferromagnetism described by slave-fermion-like state is stable at low doping regime, and the slave-boson-like d-wave RVB superconducting state becomes favorable at optimal doping. The global phase diagram is determined. To remedy the relaxation of non-double-occupancy constraint in a simple mean-field theory, the Gutzwiller's approximation is applied. Surprisingly the resulting phase diagram is in rather close agreement with experiment. Several physical quantities such as spin-spin correlation lengths, electron spectral functions, magnetic dynamical structure factors and spin susceptibilities are also calculated at the mean-field level where the new effect coming from finite spin and charge excitations of opposite statistics allowed by supersymmetry is pointed out. Finally, future research direction of the formulation is discussed.

•Jan 1, 2000•1 citation

Phase separation in the slave-fermion mean-field theory of thet-Jmodel

Tzanko Ivanov

The stability of the spiral phase is studied in the context of the slave-fermion mean-field theory of the t-J model. For J/t small enough the spiral phase is unstable against phase separation. For larger values of J/t there exists a critical concentration of holes below which this phase is stable, while for larger doping a phase separation occurs. The phase diagram of the t-J model is presented and discussed.

Physical review. B, Condensed matter•Dec 1, 1991•9 citations

Flux phases in thet-Jmodel

Menke U. Ubbens, Patrick A. Lee

We analyze a class of mean-field flux phases of the slave boson t-J model, and present a finite-temperature phase diagram. The mean-field theory arises from a decomposition of the four-fermion terms into exchange, pairing, and direct terms, using Hubbard-Stratonovich fields. We find numerically that at low doping staggered flux phases are energetically favorable over the d-wave-pairing state. Very close to half filling a \ensuremath{\pi}-flux phase becomes stable. The occurrence of flux phases suppresses the pairing gap transition temperature.

Physical review. B, Condensed matter•Oct 1, 1992•138 citations

Susy atomic model

John M. Hopkinson, Piers Coleman

We present the simplest model to which one can apply the supersymmetric Hubbard operators recently introduced. For the atomic model, $H=-E_d X_{00}$, where $X_{00} = |0><0|$ is a Hubbard operator and $E_d$ is the energy of the localized spin level, we show how one can develop exact solutions for the entropy and heat capacity as a function of temperature. With this gold standard we are able to develop a controlled approximation scheme to field theoretically treat the susy approximation at the level of mean field + gaussian corrections and test its accuracy against the widely used slave boson and slave fermion approximations. We find that in addition to slave boson and slave fermion solutions, a new class of solutions exists in the physical case Q = 1, N = 2 which can be properly treated by neither previously existing approach. The phase diagram generated by the mean field saddle-point bears a superficial resemblance to the V-shaped phase diagram common to systems close to a quantum critical point and may provide a natural starting point for investigations of strongly correlated models capturing this physics.

arXiv:cond-mat/0207111•Jul 3, 2002•0 citations

SU(2) formulation of the t−J model: Application to underdoped cuprates

Patrick A. Lee, Naoto Nagaosa, Tai Kai Ng +1 more

We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain $d$-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.

arXiv:cond-mat/9701168•Physical review. B, Condensed matter•Mar 1, 1998•213 citations

Phase Diagram and Pairing Symmetry of the Two-Dimensionalt-JModel by a Variation Theory

Hisatoshi Yokoyama, Masao Ogata

Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).

arXiv:cond-mat/9607050•Journal of the Physical Society of Japan•Nov 15, 1996•148 citations
The supersymmetric formulation of the t - J model is studied in this paper at the mean-field level where the δ- T phase diagram is determined. We found that the slave-fermion–like spiral phase is stable at low doping concentration, and the slave-boson–like d -wave fermionic spin pairing state becomes energetically favourable when δ ⩾ 0.23. An improvement in free energy using Gutzwiller's method lowers the transition doping concentration to δ ≃ 0.06. We also point out the existence of new branches of excitations in the supersymmetric theory.
A new kind of symmetry, called Supersymmetry, is introduced in t-J model and its corresponding Supersymmetric Formulation is constructed. The new formulation unifies the so-called slave-fermion and slave-boson formulations to the model in a single framework and is able to incorporate the advantage of the two approaches. The formulation is analysed at mean-field level where we found that antiferromagnetism described by slave-fermion-like state is stable at low doping regime, and the slave-boson-like d-wave RVB superconducting state becomes favorable at optimal doping. The global phase diagram is determined. To remedy the relaxation of non-double-occupancy constraint in a simple mean-field theory, the Gutzwiller's approximation is applied. Surprisingly the resulting phase diagram is in rather close agreement with experiment. Several physical quantities such as spin-spin correlation lengths, electron spectral functions, magnetic dynamical structure factors and spin susceptibilities are also calculated at the mean-field level where the new effect coming from finite spin and charge excitations of opposite statistics allowed by supersymmetry is pointed out. Finally, future research direction of the formulation is discussed.
We analyze a class of mean-field flux phases of the slave boson t-J model, and present a finite-temperature phase diagram. The mean-field theory arises from a decomposition of the four-fermion terms into exchange, pairing, and direct terms, using Hubbard-Stratonovich fields. We find numerically that at low doping staggered flux phases are energetically favorable over the d-wave-pairing state. Very close to half filling a \ensuremath{\pi}-flux phase becomes stable. The occurrence of flux phases suppresses the pairing gap transition temperature.
We present the simplest model to which one can apply the supersymmetric Hubbard operators recently introduced. For the atomic model, H=−EdX00H=-E_d X_{00}H=−Ed​X00​, where X00=∣0><0∣X_{00} = |0><0|X00​=∣0><0∣ is a Hubbard operator and EdE_dEd​ is the energy of the localized spin level, we show how one can develop exact solutions for the entropy and heat capacity as a function of temperature. With this gold standard we are able to develop a controlled approximation scheme to field theoretically treat the susy approximation at the level of mean field + gaussian corrections and test its accuracy against the widely used slave boson and slave fermion approximations. We find that in addition to slave boson and slave fermion solutions, a new class of solutions exists in the physical case Q = 1, N = 2 which can be properly treated by neither previously existing approach. The phase diagram generated by the mean field saddle-point bears a superficial resemblance to the V-shaped phase diagram common to systems close to a quantum critical point and may provide a natural starting point for investigations of strongly correlated models capturing this physics.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).