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Physical review. B, Condensed matter

Response function of thet-Jmodel calculated using anyon techniques

A. M. Tikofsky, R. B. Laughlin

Published Oct 1, 1994• 8 citations
Publisher

Abstract

We have computed zero-temperature properties of the t-J Hamiltonian using the formalism of anyon superconductivity. The results of these calculations agree quantitatively with exact-diagonalization studies. These properties include the optical conductivity, the ground-state kinetic energy, and the ground-state magnetic energy. Implicit in this calculational procedure is a Kosterlitz-Thouless transition temperature for the onset of superconductivity.

DOI
10.1103/physrevb.50.10165

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Physical review. B, Condensed matter•Jul 1, 1992•14 citations
We have computed zero-temperature properties of the t-J Hamiltonian using the formalism of anyon superconductivity. The results of these calculations agree quantitatively with exact-diagonalization studies. These properties include the optical conductivity, the ground-state kinetic energy, and the ground-state magnetic energy. Implicit in this calculational procedure is a Kosterlitz-Thouless transition temperature for the onset of superconductivity.
The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.
The finite-temperature phase diagram of the t-J model of electronic conduction is calculated in d dimensions, using the Migdal-Kadanoff renormalization-group procedure. No finite-temperature phase transition in d=1 and a finite-temperature first-order boundary ending at a critical point in d=2 are found. In d=3, a remarkably complex multicritical phase diagram is found, with a new phase, between hole dopings of 0.3 and 0.4 and temperatures 1/J below 0.4, in which the hopping strength t renormalizes to infinity under rescaling. Our results are confirmed by comparison of calculated electron densities, kinetic energies, and nearest-neighbor density-density and spin-spin correlation functions with exact finite-cluster results.
The t-J model is the simplest Hamiltonian for strongly correlated electrons, in which a superconducting phase may be present. This paper discusses superconducting correlation functions of the one-dimensional t-J model obtained from exact diagonalization of finite systems. Singlet and triplet channels are examined and compared with each other; the results are interpreted in terms of the Luttinger-liquid theory. A detailed study is made of the small-J limit, where the special form of the ground-state wave function allows a thorough study of correlation functions, including logarithmic corrections to the leading power-law decay. In addition, the effect of a magnetic field is also examined, since singlet and triplet superconducting correlations are competitive at zero field. It turns out that the magnetic field modifies the superconducting correlations in an interesting way. In particular, an analog of the Fulde-Ferrell state is found for some intermediate J.