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Physical review. B, Condensed matter

Generalized flux states of thet-Jmodel

Franco Nori, Elihu Abrahams, Gergely T. Zimányi

Published Apr 1, 1990• 52 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.41.7277

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Physical review. B, Condensed matter•Nov 1, 1990•13 citations
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.
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 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 calculate the energy of flux states described by Slater determinants of single-particle levels in a uniform magnetic field with p/q flux quanta per plaquette and with no double occupancy. We find the exchange energy of flux states is lower than that of the Gutzwiller wave function by 10%--20%. The minimum kinetic energy is obtained by introducing phases associated with the holes. The phases are calculated by mapping onto a classical frustrated XY model. At 10% doping, the 1/2 flux state (\ensuremath{\pi} phase) is stabilized for the parameter regime J/t\ensuremath{\gtrsim}0.2. At about 20% doping, the time-reversal-breaking (1/3 flux state has the lowest energy for J/t\ensuremath{\gtrsim}1.0.
We study wave functions for generalized flux phases by the variational Monte Carlo method. Flux tubes are attached to the holes, which produce additional phase factors besides those due to the motion of electrons. The phase factors cancel each other when the electrons and holes interchange position at some special electron densities and, as a result, there are no orbital currents in these states. We investigate especially the one-third filled case and find a slightly lower kinetic energy than the original commensurate flux phase. We also calculate the chirality to confirm that time-reversal symmetry is also broken in these states. The analogy to the quantum-Hall-effect wave functions leads us to study modified forms of off-diagonal long-range order in the pair-correlation function. The existence of this long-range order is shown explicitly by variational Monte Carlo calculations and renormalized mean-field approximations. The flux phases do not have the usual off-diagonal long-range order but do have a modified form similar to that in the quantum Hall effect. The relationships to the slave-boson mean-field theories and anyon systems are also discussed.
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.