Two-component δ-function fermions and bethe ansatz eigenstates

Shuichi Murakami, Miki Wadati

We study the one-dimensional repulsive δ-function fermion system on an infinite interval. We construct a basis set of the Bethe ansatz eigenstates and show the completeness and the orthonormality of this basis set. We discuss the correspondence between these Bethe ansatz states and the states made by the quantum inverse scattering method. It justifies the method to study thermodynamics by the quantum Gel'fand-Levitan equations. In addition, we evaluate thermodynamic quantities by using the complete set of the Bethe ansatz states and obtain the first two terms of the virial expansions.

Ram K. Tripathi

P. Schlottmann

The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.

Ladislav Šamaj, Zoltán Bajnok

Feng Pan, L. R. Dai

It is shown that the two component Fermi or Bose many-body Hamiltonian, such as the two-orbit fermion pairing and two-site Bose-Hubbard model with arbitrary finite higher order terms can always be solved exactly by using Bethe ansatz vector construction based on the permutation of two components of bosons or fermions involved. As examples of the solution, the extended one-dimensional dimer Bose -Hubbard model with multi-body interactions and the mean-fifield plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits are demonstrated with the eigenstates and the eigen-energy and the related Bethe ansatz equations. It is shown that the main feature of the solutions lies in the fact that the Bethe ansatz vectors can be expressed in terms of binomials of the boson or fermion operators times the related symmetric functions. As the consequence, two-component quantum many-body systems , such as the extended Lipkin-Meshkov-Glick model with higher-order interactions, can be solved in a similar way.

Никита Андреевич Славнов