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Orthofermions versus Gutzwiller projection operator approach for the infinite U Hubbard model

A.K. Mishra, Rishabh Kishore

Physics Letters AAug 4, 20083 citations

ON THE TRANSLATIONAL SYMMETRY OF INFINITE U HUBBARD MODEL

Dorota Jakubczyk

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.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.

Modern Physics Letters BDec 13, 20115 citations

Supersymmetric approach to the infinite U Hubbard model

P. Coleman, C. Pépin

arXiv:cond-mat/0110099Physica B Condensed MatterMar 1, 20026 citations

Spin-charge decoupling and orthofermi quantum statistics

A. K. Mishra

Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the U infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a form of quantum statistics, viz., orthofermi statistics. In these statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the U infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a form of quantum statistics, viz., orthofermi statistics. In these statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.

arXiv:cond-mat/0105012Physical review. B, Condensed matterMar 12, 200112 citations

Large N expansion of the infinite U two-dimensional Hubbard model

Arti Tandon

Jan 1, 20000 citations

On form factors in nested Bethe Ansatz systems

Balázs Pozsgay, Willem-Victor van Gerven Oei, Márton Kormos

We investigate form factors of local operators in the multi-component Quantum Non-linear Schrödinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.We investigate form factors of local operators in the multi-component Quantum Non-linear Schrödinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.

arXiv:1204.4037Journal of Physics A Mathematical and TheoreticalOct 31, 201241 citations

Distinct solutions of infinite U Hubbard model through nested Bethe ansatz and Gutzwiller projection operator approach

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Distinct solutions of infinite U Hubbard model through nested Bethe ansatz and Gutzwiller projection operator approach

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