Solvability of a class of
                    PT
                    -symmetric non-Hermitian Hamiltonians: Bethe ansatz method

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

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Quantum sine-Gordon thermodynamics: The Bethe ansatz method

Physical Review B ◽

10.1103/physrevb.24.2634 ◽

1981 ◽

Vol 24 (5) ◽

pp. 2634-2639 ◽

Cited By ~ 72

Author(s):

Michael Fowler ◽

Xenophon Zotos

Keyword(s):

Bethe Ansatz ◽

Ansatz Method

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Numerical and Monte Carlo Bethe ansatz method: 1D Heisenberg model

The European Physical Journal B ◽

10.1140/epjb/e2005-00390-1 ◽

2005 ◽

Vol 48 (2) ◽

pp. 157-165 ◽

Cited By ~ 7

Author(s):

S.-J. Gu ◽

N. M.R. Peres ◽

Y.-Q. Li

Keyword(s):

Monte Carlo ◽

Bethe Ansatz ◽

Heisenberg Model ◽

Ansatz Method

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Finite Heisenberg Quantum Spin Chain

Models of Quantum Matter ◽

10.1093/oso/9780199678839.003.0020 ◽

2019 ◽

pp. 667-686

Author(s):

Hans-Peter Eckle

Keyword(s):

Bethe Ansatz ◽

Conformal Symmetry ◽

Finite Size ◽

Quantum Spin ◽

Ansatz Method ◽

Finite Sums ◽

Mathematical Techniques ◽

Higher Order Corrections ◽

Finite Size Corrections ◽

Maclaurin Formula

The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.

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A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

Advances in High Energy Physics ◽

10.1155/2019/3423198 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

ZiLong Zhao ◽

ZhengWen Long ◽

MengYao Zhang

Keyword(s):

Exact Solution ◽

Quantum Mechanics ◽

Dirac Equation ◽

Exact Solutions ◽

Bethe Ansatz ◽

Dirac Oscillator ◽

Solvable Models ◽

Ansatz Method ◽

Radial Dirac Equation

The generalized Dirac oscillator as one of the exact solvable models in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic, and sixth power potentials in radial Dirac equation were further given by means of the Bethe ansatz method. And finally, the corresponding exact solutions in this paper were further discussed.

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A NEW INTEGRABLE MODEL OF STRONGLY CORRELATED ELECTRONS WITH HUBBARD-LIKE INTERACTION

Modern Physics Letters B ◽

10.1142/s0217984901001574 ◽

2001 ◽

Vol 15 (06n07) ◽

pp. 213-218

Author(s):

XIANG-YU GE

Keyword(s):

Bethe Ansatz ◽

Integrable Model ◽

Strongly Correlated Electrons ◽

The Other ◽

Competitive Interactions ◽

Correlated Electrons ◽

Strongly Correlated ◽

Transfer Matrices ◽

Ansatz Method ◽

Commuting Transfer Matrices

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.

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Exact Solutions of a Class of Double-Well Potentials: Algebraic Bethe Ansatz

Advances in High Energy Physics ◽

10.1155/2017/8429863 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

M. Baradaran ◽

H. Panahi

Keyword(s):

Bethe Ansatz ◽

Numerical Evaluation ◽

Energy Levels ◽

Algebraic Approach ◽

Wave Functions ◽

Algebraic Equations ◽

Ansatz Method ◽

Exact Solvability ◽

Exactly Solvable ◽

Bistable Potential

Applying the Bethe ansatz method, we investigate the Schrödinger equation for the three quasi-exactly solvable double-well potentials, namely, the generalized Manning potential, the Razavy bistable potential, and the hyperbolic Shifman potential. General exact expressions for the energies and the associated wave functions are obtained in terms of the roots of a set of algebraic equations. Also, we solve the same problems using the Lie algebraic approach of quasi-exact solvability through the sl(2) algebraization and show that the results are the same. The numerical evaluation of the energy spectrum is reported to display explicitly the energy levels splitting.

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