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ENERGY-LEVEL ORDERING IN THE ONE-DIMENSIONAL T-J MODEL - A RIGOROUS RESULT

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Published Sep 10, 2026• 0 citations
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Abstract

Two theorems about the spin properties of the ground state and the ordering of the energy levels for different spins of the one-dimensional t-J model are stated and proved. It is shown that when the number of electrons N=4n + 2 (n an integer) with periodic boundary conditions or N=4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet.

DOI
10.82444/warw.33552853

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Two theorems about the spin properties of the ground state and the ordering of the energy levels for different spins of the one-dimensional t-J model are stated and proved. It is shown that when the number of electrons N=4n + 2 (n an integer) with periodic boundary conditions or N=4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet.
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A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N=4n+2 (n an integer) with periodic boundary conditions or N=4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.
Ground states of the two-dimensional t - t '- J model with one and two holes in 4×4 sites (with periodic boundary conditions) are studied numerically. Using a Lanczos algorithm, we calculate the ground-state energy and momentum distribution, and the phase diagram in the plane of J / t and t '/ t is presented. The momentum distribution for J / t =0.25 is compared with the Fermi surface obtained in the mean-field theory. It is shown that the t '/ t dependences of the momentum distribution are consistent with the mean-field approximation, although there are quantitative differences between them.
We present a generalization of the Sutherland multicomponent model. Our extension includes both the ferromagnetic and the antiferromagnetic $t\ensuremath{-}J$ model for any value of the exchange coupling JJJ and the hopping parameter ttt. We prove rigorously that for one-dimensional chains the ground state of the generalized model is nondegenerate. As a consequence, the ordering of energy levels of the antiferromagnetic $t\ensuremath{-}J$ model is determined. Our result rigorously proves and extends the analysis carried out by Sutherland in establishing the phase diagram of the model as a function of the number of components.