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Physical review. B, Condensed matter

Numerical study of flux phases in the t-J model

Didier Poilblanc, Yukio Hasegawa, Thomas Maurice Rice

Published Feb 1, 1990• 51 citations
Publisher

Abstract

Commensurate flux states for the t-J model are investigated on a finite 4\ifmmode\times\else\texttimes\fi{}4 cluster with two holes. Qualitative agreement is found with a renormalized mean-field theory; in particular, the magnetic energy exhibits an absolute minimum when the flux exactly equals the filling. Competition with the kinetic energy favors a smaller commensurate flux at intermediate J/t values. We investigate the effect of a nearest-neighbor hole-hole repulsion V. Comparing the exact ground-state results shows that the V causes an effective reduction in the value of J/t. The commensurate flux phases (CFP's) do not exhibit hole-hole attraction in real space, contrary to the t-J model for J/t\ensuremath{\ge}0.4. Therefore, the stability of the CFP's would be enhanced by a short-range repulsion between the holes.

DOI
10.1103/physrevb.41.1949

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Generalized flux states and the quantum Hall effect (abstract)

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Journal of Applied Physics•Apr 15, 1991•0 citations
Commensurate flux states for the t-J model are investigated on a finite 4\ifmmode\times\else\texttimes\fi{}4 cluster with two holes. Qualitative agreement is found with a renormalized mean-field theory; in particular, the magnetic energy exhibits an absolute minimum when the flux exactly equals the filling. Competition with the kinetic energy favors a smaller commensurate flux at intermediate J/t values. We investigate the effect of a nearest-neighbor hole-hole repulsion V. Comparing the exact ground-state results shows that the V causes an effective reduction in the value of J/t. The commensurate flux phases (CFP's) do not exhibit hole-hole attraction in real space, contrary to the t-J model for J/t\ensuremath{\ge}0.4. Therefore, the stability of the CFP's would be enhanced by a short-range repulsion between the holes.
Strongly correlated 2D electrons described by the t–J model are investigated numerically. Exact ground state for one and two holes in a finite cluster with periodic boundary conditions are obtained by using the Lanczos algorithm. The effects of Coulomb repulsion of the holes on the nearest neighbor sites are taken into account. Commensurate flux phases are investigated for the same size of clusters. They are shown to be a good approximation for the ground state specially in the intermediate value of J/t.
A renormalized Hamiltonian approach is applied to construct commensurate flux phases for the t-J model. The assumption of nonuniform phases and modulus for the bond hopping amplitudes is necessary and (sufficient) condition of self-consistency. The supercell of the modulation is closely related to the filling. The self-consistent coupled equations are solved numerically on finite square clusters of sizes as large as 20\ifmmode\times\else\texttimes\fi{}20. The differences in kinetic energy and in spin-spin correlation with respect to the t=0 uniform commensurate flux state show \ensuremath{\sim}-(t/J)1/2{)}^{1/2})1/2 and \ensuremath{\sim}t/J behaviors, respectively. When t/J\ensuremath{\ge}1, time-reversal symmetry is only ``weakly broken'' and the Fermi level lies in a pseudogap with a depressed density of state.
Antiferromagnetic flux states for the t-J model are investigated on a finite 4\ifmmode\times\else\texttimes\fi{}4 cluster with 2 holes. These wave functions consist of projected Slater determinants of noninteracting wave functions of electrons moving on a lattice with alternating positive and negative magnetic fluxes flowing through the two sublattices of unit cells. Following a recent approach used for commensurate flux phases, we also evaluate the exchange energy and the kinetic energy in the thermodynamic limit. At small J/t ratio the commensurate flux phase is shown to be unstable against the metallic staggered flux phase.
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.