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Europhysics Letters (EPL)

Generalized Flux Phases in the t - J Model Via a Large- N Slave-Boson Mean-Field Theory

J. P. Rodriguez, Benoît Douçot

Published Mar 1, 1990• 33 citations
Publisher

Abstract

Via a large-N slave-boson formulation of the t-J model on the square lattice, we study the stability of generalized flux phases as a function of electronic filling fraction in the mean-field approximation. At zero temperature we find that there exists a critical hopping parameter, below which a phase with flux quanta per plaquette given by the filling fraction is stable, and above which a fluxless uniform phase is stable.

DOI
10.1209/0295-5075/11/5/011

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Physical review. B, Condensed matter•Mar 1, 1990•20 citations
Via a large-N slave-boson formulation of the t-J model on the square lattice, we study the stability of generalized flux phases as a function of electronic filling fraction in the mean-field approximation. At zero temperature we find that there exists a critical hopping parameter, below which a phase with flux quanta per plaquette given by the filling fraction is stable, and above which a fluxless uniform phase is stable.
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 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 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 have studied the stability of the Fermi-liquid phase of a square-lattice tight-binding model with respect to the spontaneous generation of magnetic flux and orbital magnetization. An energy density of the form 1/2KB2{\mathit{KB}}^{2}KB2 is associated with the magnetic field B, and the phase diagram is investigated as a function of K, temperature T, and density or chemical potential \ensuremath{\mu}. For K\ensuremath{\ne}0 and density near half filling, the system condenses below a critical temperature into a \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 antiferromagnetic flux phase in which the spontaneously generated flux alternates in sign in a checkerboard pattern. Farther from half filling and for K\ensuremath{\ne}0, the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 pattern is replaced by an incommensurate flux phase in which the spatial periodicity of the spatially modulated flux is in general an irrational multiple of the lattice constant. At zero temperature for densities off half filling, the commensurate flux phase with uniform flux density equal to the particle density is the lowest-energy state of those considered at sufficiently small values of K. We also relate the Fermi-liquid instabilities of this gauge-invariant tight-binding (t-\ensuremath{\varphi}) model at nonzero K/t to those of the large-N t-J model at nonzero t/J, and thereby predict the existence of similar flux-phase instabilities in the latter model.
We present a mean-field theory of the t-J model on a square lattice that becomes exact in a particular large-N limit. A detailed study of the free-energy manifold is carried out for the case of filling fraction \ensuremath{\nu}=(1/4 as a function of t/J. Over the manifold examined, the ground state is either an insulating crystal of an N-hole bound state (for small t/J) or a normal Fermi liquid (for large t/J). For (1/4\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le} 1) / 2 , and t=0+{0}^{+}0+, states with the localized holes, and nonzero spin correlations restricted to clusters of 4 or smaller, are global free-energy minima; in particular they are lower in energy than the state with uniform flux \ensuremath{\Phi}=\ensuremath{\nu}, with staggered flux or a normal Fermi liquid.