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arXiv:cond-mat/9405013 · Physical Review Letters

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

Bill Sutherland, Rudolf A. Römer, B. Sriram Shastry

Published Oct 17, 1994• 15 citations
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Abstract

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse sinh square of the distance. This interaction contains a variable range as a parameter and can thus interpolate between the known solutions for the nearest-neighbor chain and the inverse-square chain. The energy, susceptibility, charge stiffness, and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

DOI
10.1103/physrevlett.73.2154

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We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse sinh square of the distance. This interaction contains a variable range as a parameter and can thus interpolate between the known solutions for the nearest-neighbor chain and the inverse-square chain. The energy, susceptibility, charge stiffness, and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.
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A one-dimensional quantum N-body system of either fermions or bosons with SU (n) "spins" (or colors in particle physics language) interacting via inverse-square exchange is presented in this article.A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product type wave function.The class of states we construct in this paper corresponds to the ground state and the low energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian.By expanding the energy about the ground state we find the harmonic fluid parameters (i.e. the charge, spin velocities, etc.), explicitly.The correlation exponent and the compressibility are also found.As expected the general harmonic relation(i.e.v S = (v N v J ) 1/2 ) is satisfied among the charge and spin velocities.
We present exact wave functions for the ground state of a lattice gas of spinless one-dimensional fermions, at filling factors of 1/M1/M1/M. The one-body hopping operator decreases exponentially. The two-body interaction is Coulomb-like: A neutralizing background is required for the system to be extensive. There is a parameter in the problem, which can be taken to be the strength of the charge. All correlation functions are evaluated, and the system is shown to have long-ranged crystalline order. For filling factor 1/21/21/2, the momentum distribution and pair correlation function are explicitly evaluated. There is no Fermi surface. The crystalline order parameter is evaluated.
We study the S matrix of a spin- s quantum spin chain which can be interpreted as a multicomponent quantum lattice gas. We show that this system contains integrable subsystems where the Bethe ansatz method is applicable. We demonstrate that for some ranges of parameters of a spin-1 model, the ground states and low-lying excited states are exactly given by those of integrable subsystems; exact calculation is possible even if the system is not strictly integrable as a whole. We also analyze the magnetization curves for the spin chain, with exact saturation fields.
We study the S matrix of a spin- s quantum spin chain which can be interpreted as a multicomponent quantum lattice gas. We show that this system contains integrable subsystems where the Bethe ansatz method is applicable. We demonstrate that for some ranges of parameters of a spin-1 model, the ground states and low-lying excited states are exactly given by those of integrable subsystems; exact calculation is possible even if the system is not strictly integrable as a whole. We also analyze the magnetization curves for the spin chain, with exact saturation fields.