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Physical review. B, Condensed matter

Singlet wave functions for thet-Jmodel

Didier Poilblanc

Published Oct 1, 1989• 16 citations
Publisher

Abstract

We investigate T=0 properties of the commensurate flux phases, a class of variational wave functions for the t-J model proposed recently by Anderson, Shastry, and Hristopoulos and which generalize the (1/2-flux state of Affleck and Marston away from half-filling. These states can be formally written in the quantum spin liquid form, the singlet bond amplitudes of which break the lattice translational symmetry. The supercell of the electromagnetic gauge (defining the fictitious flux) imposes the actual periodicities of the correlated wave function. Their order of commensurability with the lattice unit length is closely related to the hole density.

DOI
10.1103/physrevb.40.7376

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Physical review. B, Condensed matter•Apr 1, 1990•25 citations
We investigate T=0 properties of the commensurate flux phases, a class of variational wave functions for the t-J model proposed recently by Anderson, Shastry, and Hristopoulos and which generalize the (1/2-flux state of Affleck and Marston away from half-filling. These states can be formally written in the quantum spin liquid form, the singlet bond amplitudes of which break the lattice translational symmetry. The supercell of the electromagnetic gauge (defining the fictitious flux) imposes the actual periodicities of the correlated wave function. Their order of commensurability with the lattice unit length is closely related to the hole density.
We propose a variational approach for the study of chiral flux-phase states. We present a class of variational wave functions of the generalized Laughlin-type. The generalization consists of the introduction of Gutzwiller projections and of a fictitious magnetic field. We classify antiferromagnetic chiral flux-phase states and evaluate analytically the corresponding expectation values of the t-J Hamiltonian at any value of filling. There are two types of chiral flux-phase states: commensurate and fractional. We have found that the minimal energy has a commensurate-flux-phase state for which the value of the flux of the orbital magnetic field equals the filling.
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.
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.
We use a renormalized mean-field theory of the t-J model to show that flux states closely related to those recently proposed by Anderson, Shastry, and Hristopoulos are stabilized, at values of J/t\ensuremath{\gtrsim}1, when the flux per plaquette is commensurate with the electron density in a way similar to that found recently for noninteracting electrons. These states (in the interacting t-J model) are characterized by a collective gauge variable which leads to superconductivity. At not too small values of J/t the state with half a flux quantum per plaquette is stable at low doping.
We investigate flux phases of the three-dimensional (3D) t-J model for a layer structure. For some range of parameters, the system is stabilized by a uniform fictitious flux, which is commensurate to the electron number density. This state corresponds in 2D lattices to the commensurate flux phase, although in the 3D system we have the flux orientation as another variational parameter to lower the energy. Exchange of two carriers gives an extra phase factor to the wave function; this is not allowed in a continuous space but is in a lattice structure. The system exhibits 2D superconductivity confined in a plane perpendicular to the commensurate flux.
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.