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Fermionic long-range correlations realized by particles obeying deformed statistics

Andreas Osterloh

Published Jan 1, 2000• 10 citations
OpenAlex

Abstract

Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for electrons. The resulting models show up gauge-like modulations in the hopping processes, which induce long-range correlations in the lattice. The conditions for the Bethe ansatz solvability of the latter are interpreted as restrictions imposed on the statistics to be compatible with the Bethe ansatz solvability of the deformed models. It is found that solvable deformed models are not unitarily equivalent to fermionic models if the exchange of particles with the same spin orientations is deformed. Statistics deformations, where the exchange relation of two particles is influenced by the presence of other particles, cannot be realized by fermionic operators.

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Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for electrons. The resulting models show up gauge-like modulations in the hopping processes, which induce long-range correlations in the lattice. The conditions for the Bethe ansatz solvability of the latter are interpreted as restrictions imposed on the statistics to be compatible with the Bethe ansatz solvability of the deformed models. It is found that solvable deformed models are not unitarily equivalent to fermionic models if the exchange of particles with the same spin orientations is deformed. Statistics deformations, where the exchange relation of two particles is influenced by the presence of other particles, cannot be realized by fermionic operators.
Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for electrons. The resulting models show up gauge-like modulations in the hopping processes, which induce long-range correlations in the lattice. The conditions for the Bethe ansatz solvability of the latter are interpreted as restrictions imposed on the statistics to be compatible with the Bethe ansatz solvability of the deformed models. It is found that solvable deformed models are not unitarily equivalent to fermionic models if the exchange of particles with the same spin orientations is deformed. Statistics deformations, where the exchange relation of two particles is influenced by the presence of other particles, cannot be realized by fermionic operators.
We investigate the problem of constructing solvable models of nonrelativistic spin-1/2 interacting fermions on an infinite lattice. The extended Hubbard model, which includes the direct and exchange intersite interaction, is considered. The hopping term in the Hamiltonian is not restricted to nearest-neighbor sites (the ``overjumping'' model), but the short-range character of the standard Hubbard model is retained. The solutions in one- and two-particle sectors are obtained in an explicit form by using the theory of Weierstrass elliptic functions. The possibilities of further development of models of that type are also considered.
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.