scholarly journals Quantum group and magnetic translations. Bethe-Ansatz solution for bloch electrons in a magnetic field

2008 ◽  
pp. 49-58
Author(s):  
P. B. Wiegmann ◽  
A. V. Zabrodin
Keyword(s):  
Magnetic Field ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Bethe Ansatz Solution ◽  
Bloch Electrons

scholarly journals QUANTUM GROUP AND MAGNETIC TRANSLATIONS: BETHE ANSATZ SOLUTION FOR THE HARPER’S EQUATION

1994 ◽  
Vol 08 (05) ◽  
pp. 311-318 ◽  
Author(s):  
P.B. WIEGMANN ◽  
A.V. ZABRODIN
Keyword(s):  
Magnetic Field ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Critical Value ◽  
Bloch Function ◽  
Present Solution ◽  
Bethe Ansatz Solution ◽  
Bloch Electrons ◽  
Natural Relation

We present the Bethe ansatz solution for the problem of Bloch electrons in magnetic field described by the Harper’s equation [Formula: see text] We made explicit a natural relation between magnetic translations and the quantum group Uq(sl2) and express the midband spectrum and the Bloch function in terms of solutions of the Bethe ansatz equations. In this letter we present solution for the critical value λ=1.

scholarly journals Spin chains with boundary inhomogeneities

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Rafael I. Nepomechie ◽  
Ana L. Retore
Keyword(s):  
Quantum Group ◽  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Spin Chains ◽  
Group Symmetry ◽  
Quantum Spin Chain ◽  
Open Quantum ◽  
Bethe Ansatz Solution

Abstract We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.

scholarly journals Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field

1994 ◽  
Vol 73 (8) ◽  
pp. 1134-1137 ◽  
Author(s):  
Yasuhiro Hatsugai ◽  
Mahito Kohmoto ◽  
Yong-Shi Wu
Keyword(s):  
Magnetic Field ◽  
Bethe Ansatz ◽  
Explicit Solutions ◽  
Bloch Electrons

Nonlinear electromagnetic response of bloch electrons in a magnetic field

1968 ◽  
Vol 58 (1) ◽  
pp. 93-106 ◽  
Author(s):  
K. C. Rustagi ◽  
C. S. Warke ◽  
S. S. Jha
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Response ◽  
Bloch Electrons

Exact S-Matrices

2020 ◽  
pp. 676-743
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Quantum Group ◽  
Scattering Theory ◽  
Integrable Model ◽  
Group Symmetry ◽  
Fusion Rules ◽  
Lee Model ◽  
Sine Gordon Model ◽  
Multiple Poles

The Ising model in a magnetic field is one of the most beautiful examples of an integrable model. This chapter presents its exact S-matrix and the exact spectrum of its excitations, which consist of eight particles of different masses. Similarly, it discusses the exact scattering theory behind the thermal deformation of the tricritical Ising model and the unusual features of the exact S-matrix of the non-unitary Yang–Lee model. Other examples are provided by O(n) invariant models, including the important Sine–Gordon model. It also discusses multiple poles, magnetic deformation, the E 8 Toda theory, bootstrap fusion rules, non-relativistic limits and quantum group symmetry of the Sine–Gordon model.

Exact Bethe ansatz solution of O(2N) symmetric theories

1987 ◽  
Vol 280 ◽  
pp. 225-254 ◽  
Author(s):  
H.J. De Vega ◽  
M. Karowski
Keyword(s):  
Bethe Ansatz ◽  
Bethe Ansatz Solution
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