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International Journal of Modern Physics B

HARD-CORE SLAVE-BOSON DESCRIPTION OF GENERALIZED FLUX PHASES

Franco Nori, Gergely T. Zimányi, Elihu Abrahams

Published Jan 1, 1991• 3 citations
Publisher

Abstract

Through a hard-core slave-boson mean-field approach to the t-J model, which describes the dynamics of holes moving in a quantum antiferromagnet, we investigate its generalized flux phases. We first study the motion of an electron gas for arbitrary fillings and fields and establish the linear proportionality between the filling factor and the optimal flux with high accuracy. Using this result, we show that if the hard-core nature of the hole bosons is taken into account, then the slave-boson mean-field approximation for the t-J Hamiltonian allows for a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. This enables them to achieve the lowest possible energy within the manifold of spatially-uniform flux states. In the case of the continuum model, this is possible only for certain fractional fillings and we suggest that the system may react to this frustration effect by phase separation.

DOI
10.1142/s0217979291000080

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Physical review. B, Condensed matter•Nov 1, 1990•13 citations
Through a hard-core slave-boson mean-field approach to the t-J model, which describes the dynamics of holes moving in a quantum antiferromagnet, we investigate its generalized flux phases. We first study the motion of an electron gas for arbitrary fillings and fields and establish the linear proportionality between the filling factor and the optimal flux with high accuracy. Using this result, we show that if the hard-core nature of the hole bosons is taken into account, then the slave-boson mean-field approximation for the t-J Hamiltonian allows for a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. This enables them to achieve the lowest possible energy within the manifold of spatially-uniform flux states. In the case of the continuum model, this is possible only for certain fractional fillings and we suggest that the system may react to this frustration effect by phase separation.
We investigate certain generalized flux phases arising in a mean-field approach to the t-J model. First, we establish that the energy of noninteracting electrons moving in a uniform magnetic field has an absolute minimum as a function of the flux at exactly one flux quantum per particle. Using this result, we show that if the hard-core nature of the hole bosons is taken into account, then the slave-boson mean-field approximation for the t-J Hamiltonian allows for a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. This enables them to achieve the lowest possible energy within the manifold of spatially uniform flux states. In the case of the continuum model, this is possible only for certain fractional fillings and we speculate that the system may react to this frustration effect by phase separation.
We investigate certain generalized flux phases arising in a mean-field approach to the t-J model. First we establish that the energy of noninteracting electrons moving in a uniform magnetic field has an absolute minimum as a function of the flux at exactly one flux quantum per particle. Using this result we show that if the hard-core nature of the hole bosons is taken into account, then the generalized flux states in the mean-field approximation constitute a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. We elaborate the relation to the integer and fractional quantum Hall effect. Based on this analogy one expects that only states with certain fractional fillings (ν=1/odd integer) are stable against the fluctuations of the (gauge) field. We speculate that at arbitrary fillings the system minimizes its energy by phase separating into these stable states. Finally we work out the ground state energy for nonuniform (staggered) flux phases and establish that the often claimed equivalence of frustration and doping does not hold for these states.
We study the three-dimensional bosonic ttt-JJJ model, that is, the ttt-JJJ model of ``bosonic electrons'' at finite temperatures. This model describes a system of an isotropic antiferromagnet with doped bosonic holes and is closely related to systems of two-component bosons in an optical lattice. The bosonic ``electron'' operator ${B}_{x\ensuremath{\sigma}}$ at the site xxx with a two-component spin $\ensuremath{\sigma}(=$1,2)1,2)1,2) is treated as a hard-core boson operator and represented by a composite of two slave particles: a spinon described by a Schwinger boson (CP1{}^{1}1 boson) ${z}_{x\ensuremath{\sigma}}$ and a holon described by a hard-core-boson field ${\ensuremath{\phi}}_{x}$ as ${B}_{x\ensuremath{\sigma}}={\ensuremath{\phi}}_{x}^{\ifmmode\dagger\else\textdagger\fi{}}{z}_{x\ensuremath{\sigma}}$. By means of Monte Carlo simulations of this bosonic ttt-JJJ model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. Obtained results show that the bosonic ttt-JJJ model has a phase diagram that suggests some interesting implications for high-temperature superconducting materials.
We study the system of hard-core bosons (HCB) with two species in the three-dimensional lattice at finite temperatures. In the strong-correlation limit, the system becomes the t-J model, that is, the t-J model of bosonic electrons. The electron operator Bxσ at the site x with a two-component spin σ(= 1, 2***) is treated as a HCB operator, and represented by a composite of two slave particles; a spinon described by a Schwinger boson (CP1 boson) zxσ and a holon described by a HCB field x as Bxσ = †xzxσ.*** This x is again represented by another CP1 quasi-spinon operator ωxa*** (a = 1, 2***). The phase diagrams of the resulting double CP1 system obtained by Monte Carlo simulations involve first-order and second-order phase boundaries. We present in detail the techniques and algorithm to reduce the hysteresis and locate the first-order transition points.
The competition and possible coexistence of the flux phase and pairing states are considered within the slave-boson approach. In addition to the gauge field, coupling holons, and spinons, a statistical gauge field is introduced to account for the hard-core nature of holons. Using the equivalence of \ensuremath{\pi}-uniform and -staggered fluxes, we show the possibility of reducing the staggered flux and guaranteeing the commensurability condition of the uniform flux for holons at the same time. For certain dopings the frustration of the spinon gauge field to holon motion can be compensated by the holon's own statistical gauge field. Contrary to earlier conclusions of other authors, we find that the flux phase can coexist with the resonating-valence-bond (RVB) states below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, beyond which the d-wave RVB state takes over.