We obtain the exact ground state of N-particles in one dimension both on a line and on a circle in case the N particles are interacting via nearest and next-to-nearest neighbour interactions. Further, we establish a mapping between these N-body problems and short range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute one and two point functions of a related many-body theory in the thermodynamic limit and show the absence of long range order. Generalization of the model on the line to higher dimensions as well as to other root systems is also considered. Finally, we also consider a variant of the above model in two dimensions in which all the states exhibit novel correlations.We obtain the exact ground state of N-particles in one dimension both on a line and on a circle in case the N particles are interacting via nearest and next-to-nearest neighbour interactions. Further, we establish a mapping between these N-body problems and short range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute one and two point functions of a related many-body theory in the thermodynamic limit and show the absence of long range order. Generalization of the model on the line to higher dimensions as well as to other root systems is also considered. Finally, we also consider a variant of the above model in two dimensions in which all the states exhibit novel correlations.

International Journal of Modern Physics BAug 10, 20000 citations

An Exactly Solvable Many-Body Model

Nouredine Zettili, ABDELKRIM BOUKAHIL

Bulletin of the American Physical SocietyMar 31, 20120 citations

A class ofN-body problems with nearest- and next-to-nearest-neighbour interactions

Guy Auberson, Sudhir R. Jain, Avinash Khare

We obtain the exact ground state and part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in the case where the N particles are interacting via nearest- and next-to-nearest-neighbour interactions. Furthermore, using the exact ground state, we establish a mapping between these N -body problems and the short-range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute the one- and two-point functions of a related many-body theory in the thermodynamic limit and show the absence of long-range order. However, quite remarkably, we prove the existence of an off-diagonal long-range order in the symmetrized version of the related many-body theory. Generalization of the models to other root systems is also considered. Besides, we also generalize the model on the full line to higher dimensions. Finally, we consider a model in two dimensions in which all the states exhibit novel correlations.We obtain the exact ground state and part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in the case where the N particles are interacting via nearest- and next-to-nearest-neighbour interactions. Furthermore, using the exact ground state, we establish a mapping between these N -body problems and the short-range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute the one- and two-point functions of a related many-body theory in the thermodynamic limit and show the absence of long-range order. However, quite remarkably, we prove the existence of an off-diagonal long-range order in the symmetrized version of the related many-body theory. Generalization of the models to other root systems is also considered. Besides, we also generalize the model on the full line to higher dimensions. Finally, we consider a model in two dimensions in which all the states exhibit novel correlations.

arXiv:cond-mat/0004012Journal of Physics A Mathematical and GeneralJan 18, 200149 citations

Quantum many-body systems with nearest and next-to-nearest neighbor long-range interactions

Meripeni Ezung, Nakka Gurappa, Avinash Khare +1 more

The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is connected to decoupled oscillators. The analytically obtainable eigenstates are smaller in number as compared to the Calogero-Sutherland family, indicating the quasiexactly solvable nature of these models. The exactly found scattering states, a smaller set as compared to the Calogero case, can be realized as coherent states. The relation of the scattering Hamiltonian to free particles is also established algebraically. We analyze both ${A}_{N\ensuremath{-}1}$ and $B{C}_{N}$ models on a circle and construct a part of the excitation spectrum by making use of the symmetry arguments.The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is connected to decoupled oscillators. The analytically obtainable eigenstates are smaller in number as compared to the Calogero-Sutherland family, indicating the quasiexactly solvable nature of these models. The exactly found scattering states, a smaller set as compared to the Calogero case, can be realized as coherent states. The relation of the scattering Hamiltonian to free particles is also established algebraically. We analyze both ${A}_{N\ensuremath{-}1}$ and $B{C}_{N}$ models on a circle and construct a part of the excitation spectrum by making use of the symmetry arguments.

Physical Review BMar 22, 200515 citations

Exactly solvable two-dimensional many-body problems

Francesco Calogero

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoMay 1, 197612 citations

B{C}_{N}

models on a circle and construct a part of the excitation spectrum by making use of the symmetry arguments.