Bethe ansatz for the Toda lattice: Ground state and excitations

1984 ◽  
Vol 55 (4) ◽  
pp. 353-360 ◽  
Author(s):  
Franz G. Mertens
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
Toda Lattice

scholarly journals THE SINE-GORDON MODEL AS $\mathcal{SO}(2n)_{1} \times \mathcal{SO}(2n)_{1} \over \mathcal{SO}(2n)_{2}$-PERTURBED COSET THEORY AND GENERALIZATIONS

1995 ◽  
Vol 10 (09) ◽  
pp. 1357-1376 ◽  
Author(s):  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
Coupling Constant ◽  
Special Values ◽  
The Third ◽  
Algebraic Bethe Ansatz ◽  
Sine Gordon Model ◽  
Special Points ◽  
Coset Models ◽  
Ground State Energies

The ground state energies of the [Formula: see text] coset theories, perturbed by the [Formula: see text] operator, and those of the sine-Gordon theory, for special values of the coupling constant in the attracting regime, are the same. In the first part of this paper we extend these results to the [Formula: see text] cases. In the second part, we analyze the algebraic Bethe ansatz procedure for special points in the repulsive region. We find a one-to-one “duality” correspondence between these theories and those studied in the first part of the paper. We use the gluing procedure at the massive node proposed by Fendley and Intriligator in order to obtain the TBA systems for the generalized parafermionic supersymmetric sine-Gordon model. In the third part we propose the TBA equations for the whole class of perturbed coset models [Formula: see text] with the operator [Formula: see text] and G a nonsimplylaced group generated by one of the [Formula: see text], ℱ4, ℬn, [Formula: see text] algebras.

Bose Gas in One Dimension: Lieb–Liniger Model

2019 ◽  
pp. 545-582
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Boundary Condition ◽  
Bethe Ansatz ◽  
Ground State ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Bose Gas ◽  
Quantum Model ◽  
Ultracold Gases ◽  
Infinite Line ◽  
Limiting Case

The coordinate Bethe ansatz can be extended to a model, the Lieb–Liniger model, of a one-dimensional gas of Bosons interacting with repulsive δ‎-function potentials. It has attracted attention due to its relevance for experimental developments in the fields of ultracold gases and optical lattices. This chapter provides an exposition of the related classical nonlinear Schrödinger equation, followed by its generalization to the quantum model. It explores a limiting case, the Tonks-Girardeau gas. The δ‎-function potentials supply a kind of boundary condition on the wave functions allowing us to analyze the eigenfunctions of the Bethe ansatz, which are examined on the infinite line and for periodic boundary conditions. The latter leads to the Bethe ansatz equations. The solution of these equations is achieved in the thermodynamic limit for the ground state and for low-lying excited states.

ULTRAVIOLET BEHAVIOR OF THE INTEGRABLE OFF-CRITICAL NON-UNITARY SERIES M3/q

1990 ◽  
Vol 05 (26) ◽  
pp. 2189-2195 ◽  
Author(s):  
P. CHRISTE ◽  
M. J. MARTINS
Keyword(s):  
High Temperature ◽  
Bethe Ansatz ◽  
Ground State ◽  
State Energy ◽  
Central Charge ◽  
Minimal Models ◽  
Perfect Agreement ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Higher Order Corrections

We discuss the ultraviolet behavior of the non-unitary M3/q (q = 5, 7) minimal models perturbed by the operator ϕ13. The Thermodynamic Bethe Ansatz is used to compute the central charge and the next higher order corrections in the high temperature expansion of the finite volume ground state energy. The results are in perfect agreement with perturbative calculations. Generalizations of these results are commented on.

INTEGRABLE TWO-PARAMETER MODEL OF THE FERMI GAS

1996 ◽  
Vol 10 (07) ◽  
pp. 287-292
Author(s):  
IGOR N. KARNAUKHOV
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
State Energy ◽  
Fermi Gas ◽  
Band Model ◽  
Conduction Electrons ◽  
Interband Interaction ◽  
Two Band Model ◽  
Two Parameter ◽  
Local Pairs

We present a two-band model of the gas of fermions consisting of a parabolic band of conduction electrons and a band of local pairs interacting via a δ-function interband interaction. The model is integrable and its solution has been obtained by means of the Bethe ansatz. The ground state energy and the density of conduction electrons have been calculated numerically.

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