Electronic Systems

2019 ◽  
pp. 585-630
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Degrees Of Freedom ◽  
Electronic Systems ◽  
One Dimensional ◽  
Kondo Resonance ◽  
Nested Bethe Ansatz ◽  
Component Systems ◽  
Metallic Ring ◽  
The One ◽  
Internal Degrees Of Freedom

The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ‎-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.

ON THE TRANSLATIONAL SYMMETRY OF INFINITE U HUBBARD MODEL

2012 ◽  
Vol 26 (02) ◽  
pp. 1150005 ◽  
Author(s):  
D. JAKUBCZYK
Keyword(s):  
Degrees Of Freedom ◽  
High Temperature Superconductors ◽  
Coulomb Repulsion ◽  
Finite System ◽  
Translational Symmetry ◽  
Operator Approach ◽  
One Dimensional ◽  
Closed Chain ◽  
Nested Bethe Ansatz ◽  
The One

We investigate two commonly used methods of obtaining the solution of the one-dimensional Hubard model, in the regime of infinite intrasite Coulomb repulsion U, that is the nested Bethe ansatz and the Gutzwiller projection operator approach. These two formalisms give rise to different kinds of the wavefunctions, received via the additional operator and as a general feature, in Gutzwiller and Bethe methods, respectively. We consider the finite system consisting of three particles on a four site closed chain. We investigate the consequences of the dissimilarities in the translational symmetry of the representations of the Hamiltonian for these two approaches. We look for the proof of the decoupling of the spin and charge degrees of freedom, known in context of high-temperature superconductors, in this case.

Phonons in one-dimensional Peierls systems with internal degrees of freedom

1995 ◽  
Vol 51 (9) ◽  
pp. 5790-5799 ◽  
Author(s):  
M. Yu. Lavrentiev ◽  
H. Köppel ◽  
L. S. Cederbaum
Keyword(s):  
Degrees Of Freedom ◽  
One Dimensional ◽  
Internal Degrees Of Freedom

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

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