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Commensurate-flux-phase state of the t-J model

Fedor Vasilievich Kusmartsev

Published Aug 9, 2019• 0 citations
OpenAlex

Abstract

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.

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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.

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Fedor Vasilievich Kusmartsev

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Modern Physics Letters B•Apr 10, 1991•1 citation
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 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 present a variational approach different from that based on Gutzwiller's ansatz by investigating chiral flux-phase states of the Hubbard Hamiltonian in analogy to the treatment of the fractional quantum Hall effect. The proposed class of generalized Laughlin trial functions is specialized to permit detailed consideration of a set of states that includes a ferromagnetic ground state generated by a spontaneous gauge field in conjunction with a fictitious magnetic field having a flux commensurate with the filling. We evaluate the trial energy expectation values and demonstrate that the treatment is, at least, appropriate for the Hubbard model with sufficiently large on-site Coulomb repulsion and low electron densities. The members of the special set of trial states may be suitably classified by the flux quanta of the associated field and may be characterized either by integer or fractional quantum numbers. The excitations designated by fractional quantum numbers, which are not commensurate with the filling, are identified as flux-phase states breaking the symmetries of the lattice.
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.
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 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.