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Physical review. B, Condensed matter

Exactly solvable multichain supersymmetrict-Jmodel

Andrei A. Zvyagin

Published Dec 1, 1995• 13 citations
Publisher

Abstract

We have constructed a Bethe ansatz solution for the multichain quantum supersymmetric frustrated t-J model. The system is in the antichiral state for both spin and charge degrees of freedom. Elementary spin and charge excitations carry nonzero chiralities (topological charges) but they are confined into pairs with opposite signs of their chiralities, so the state of the system remains antichiral. Topological terms of Wess-Zumino nature in the Hamiltonian cause such chiral behavior. We conjecture that a multichain supersymmetric frustrated t-J model without topological terms in the Hamiltonian has charge and spin excitations with gaps.

DOI
10.1103/physrevb.52.15050

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We have constructed a Bethe ansatz solution for the multichain quantum supersymmetric frustrated t-J model. The system is in the antichiral state for both spin and charge degrees of freedom. Elementary spin and charge excitations carry nonzero chiralities (topological charges) but they are confined into pairs with opposite signs of their chiralities, so the state of the system remains antichiral. Topological terms of Wess-Zumino nature in the Hamiltonian cause such chiral behavior. We conjecture that a multichain supersymmetric frustrated t-J model without topological terms in the Hamiltonian has charge and spin excitations with gaps.
The equations of the thermodynamic Bethe ansatz for two-chain and multichain quantum spin 1/2 systems are constructed. It is shown that the system is in the antichiral state for any temperature range and for any value of the external magnetic field (except for the ferromagnetic ground-state case). The elementary spin excitations carry nonzero chirality and are gapless. Those excitations are confined into pairs (singlets and triplets), with opposite sign of chiralities, so the state of the system remains antichiral at any temperature. The reason for such chiral behavior is the existence of the topological term of the Wess-Zumino nature in the Hamiltonian. We conjecture that the quantum spin (1/2) multichain system with the Hamiltonian without the topological terms has excitations with gaps.
Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​ which we identify with the holon and the spinon excitations near half filling.
We obtain an integrable two-leg supersymmetric t - J model through the algebraic Bethe ansatz scheme in the BFF grading. In this model, the two t - J chains interact with each other via a coupling constant κ. The model reduces to a two-chain Heisenberg spin model when the bosonic degrees of freedom are turned off and to two decoupled t - J chains when κ = 0. The construction of the diagonalized Hamiltonian yields the Bethe ansatz equations. We also obtain thermodynamic Bethe ansatz equations and calculate the magnetic susceptibility at a weak magnetic field and at zero temperature.
In this article we review recent developments in the one-dimensional Bethe ansatz solvable multi-chain quantum models. The algebraic version of the Bethe ansatz (the quantum inverse scattering method) permits us to construct new families of integrable Hamiltonians using simple generalizations of the well known constructions of the single-chain model. First we consider the easiest example (`basic' model) of this class of models: the antiferromagnetic two-chain spin-1/2 model with the nearest-neighbour and next-nearest-neighbour spin-frustrating interactions (zigzag chain). We show how the algebra of the quantum inverse scattering method works for this model, and what are the important features of the Hamiltonian (which reveal the topological properties of two dimensions together with the one-dimensional properties). We consider the solution of the Bethe ansatz for the ground state (in particular, commensurate-incommensurate quantum phase transitions present due to competing spin-frustrating interactions are discussed) and construct the thermal Bethe ansatz (in the form of the `quantum transfer matrix') for this model. Then possible generalizations of the basic model are considered: an inclusion of a magnetic anisotropy, higher-spin representations (including the important case of a quantum ferrimagnet), the multi-chain case, internal degrees of freedom of particles at each site, etc. We observe the similarities and differences between this class of models and related exactly solvable models: other groups of multi-chain lattice models, quantum field theory models and magnetic impurity (Kondo-like) models. Finally, the behaviour of non-integrable (less constrained) multi-chain quantum models is discussed.
Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​ which we identify with the holon and the spinon excitations near half filling.