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.

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.

scholarly journals Unscreened Coulomb repulsion in the one-dimensional electron gas

1999 ◽  
Vol 60 (23) ◽  
pp. 15654-15659 ◽  
Author(s):  
G. Fano ◽  
F. Ortolani ◽  
A. Parola ◽  
L. Ziosi
Keyword(s):  
Electron Gas ◽  
Coulomb Repulsion ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Dimensional Electron Gas ◽  
The One

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.

Static and energy dependent nucleus–nucleus potential for description of near and sub-barrier fusion data

2015 ◽  
Vol 93 (11) ◽  
pp. 1343-1351 ◽  
Author(s):  
Manjeet Singh Gautam
Keyword(s):  
Degrees Of Freedom ◽  
Saxon Potential ◽  
Model Calculations ◽  
One Dimensional ◽  
A Value ◽  
Fusion Data ◽  
The One ◽  
Energy Dependent ◽  
Coupled Channel

This article analyzes the validity of static Woods–Saxon potential and the energy-dependent Woods–Saxon potential (EDWSP) to explore the specific features of fusion dynamics of [Formula: see text] and [Formula: see text] systems. The intrinsic degrees of freedom, such as inelastic surface excitations, play a crucial role in the enhancement of sub-barrier fusion excitation functions over the expectations of the one-dimensional barrier penetration model. Role of dominant intrinsic degrees of freedom of collision partners are entertained within the context of coupled channel calculations. Furthermore, the one-dimensional Wong formula using static Woods–Saxon potential fails miserably to describe the fusion enhancement of [Formula: see text] and [Formula: see text] systems. However, the Wong formula along with the EDWSP model accurately explains the observed fusion enhancement of [Formula: see text] reactions. In the fusion of [Formula: see text] reaction, the above-barrier fusion data are suppressed by a factor of 0.66 with reference to the EDWSP model calculations while the below-barrier fusion data are adequately addressed by the EDWSP model and the coupled channel calculations. Therefore, the coupled channel calculations and the EDWSP model calculations reasonably describe the observed fusion mechanism of [Formula: see text] and [Formula: see text] reactions. This suggests that the energy dependence in the Woods–Saxon potential model introduces similar kinds of barrier modification effects (barrier height, barrier position, and barrier curvature) as reflected from the coupled channel calculations. In the EDWSP model calculations, significantly larger values of diffuseness ranging from a = 0.86 to 0.94 fm, which is much larger than a value extracted from the elastic scattering analysis, are needed to address the sub-barrier fusion data.

scholarly journals One-Dimensional Alternating Extended Hubbard Model at Quarter-Filling and Its Applications to Structural Instabilities of Organic Conductors

Crystals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 942
Author(s):  
M. Ménard ◽  
C. Bourbonnais
Keyword(s):  
Hubbard Model ◽  
Degrees Of Freedom ◽  
Organic Conductors ◽  
Group Method ◽  
Extended Hubbard Model ◽  
Bechgaard Salts ◽  
One Dimensional ◽  
Ordered Alloys ◽  
The One ◽  
Structural Instabilities

The one-dimensional extended Hubbard model with lattice dimerization and alternated site potentials is analyzed using the renormalization group method. The coupling of electrons to structural degrees of freedom such as the anion lattice and acoustic phonons is investigated to obtain the possible instabilities against the formation of lattice superstructures. Applications of the theory to anionic and spin-Peierls instabilities in the Fabre and Bechgaard salts series of organic conductors and ordered alloys are presented and discussed.

Sign in / Sign up

Export Citation Format

Share Document