scholarly journals Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

2008 ◽  
Vol 78 (11) ◽  
Author(s):  
Benjamin Tayo ◽  
Sandro Sorella
Keyword(s):  
Wave Function ◽  
One Dimensional ◽  
Luttinger Model ◽  
The One

The W. K. B. approximation for Bloch electrons with an application to interband tunnelling

1964 ◽  
Vol 280 (1381) ◽  
pp. 185-197 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Effective Mass ◽  
Periodic Term ◽  
One Dimensional ◽  
Auxiliary Functions ◽  
Varying Coefficients ◽  
Exponential Behaviour ◽  
The One ◽  
Bloch Electrons

The W. K. B. technique for solving the one-dimensional wave equation is extended to the case when the potential field includes a rapidly varying periodic term as well as a slowly varying term. A pair of auxiliary functions are introduced which are identical to the wave function and its derivative respectively at the edges of the periodic cells, but which have a simple exponential behaviour within the cells. The auxiliary functions satisfy a pair of auxiliary (related) differential equations, with slowly varying coefficients, which are valid for all energy values. Solution of the auxiliary equations by the well-known W. K. B. technique yields approximations to the wave function. These approximations break down in the neighbourhood of the band edges, which are the turning points of the problem. Connexion formulae are established across the band edges and employed to calculate the interband tunnelling probability. In the immediate neighbourhood of a band edge the analysis yields an effective-mass wave equation and a closed form for the wave function. The auxiliary functions are closely related to the effective-mass modulating wave function and the results of this paper may be regarded as an extension of effective-mass theory for the one-diinensional case, throughout the whole of the energy ranges of allowed bands and forbidden gaps.

scholarly journals Spectral functions of the one-dimensional Hubbard model in the U→+∞ limit:How to use the factorized wave function

1997 ◽  
Vol 55 (23) ◽  
pp. 15475-15488 ◽  
Author(s):  
Karlo Penc ◽  
Karen Hallberg ◽  
Frédéric Mila ◽  
Hiroyuki Shiba
Keyword(s):  
Wave Function ◽  
Hubbard Model ◽  
Spectral Functions ◽  
One Dimensional ◽  
The One

CORRELATION FUNCTIONS IN ONE-DIMENSIONAL LARGE-U HUBBARD MODEL: ZERO-FIELD AND FINITE-FIELD CASES

1991 ◽  
Vol 05 (01n02) ◽  
pp. 31-44 ◽  
Author(s):  
Hiroyuki SHIBA ◽  
Masao OGATA
Keyword(s):  
Wave Function ◽  
Finite Field ◽  
Hubbard Model ◽  
Slater Determinant ◽  
Direct Calculation ◽  
Spin Correlation ◽  
Zero Field ◽  
Property A ◽  
One Dimensional ◽  
The One

A recent study of the large-U limit of the one-dimensional (1D) Hubbard model is presented and discussed. It is pointed out first that the wave function has a simple structure in this limit. Namely, it is a product of Slater determinant of noninteracting spinless fermions and the wave function of 1D S=1/2 Heisenberg antiferromagnet. Secondly, by using this property, a direct calculation of momentum distribution and spin correlation function is carried out for the ground state at zero-field and finite-field cases. The results show various singularities exactly at the same position where one expects for the small-U case in both zero-field and finite-field cases. The critical exponents estimated from the size dependence are in reasonable agreement with those predicted by the Tomonaga-Luttinger-liquid and the conformal field theory.

GENERALIZED GUTZWILLER ANSATZ FOR THE HALF-FILLED HUBBARD CHAIN

1988 ◽  
Vol 02 (05) ◽  
pp. 1021-1034 ◽  
Author(s):  
Patrik Fazekas ◽  
Karlo Penc
Keyword(s):  
Wave Function ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Occupation Number ◽  
Step Function ◽  
Spin Correlations ◽  
One Dimensional ◽  
Leading Term ◽  
The One

The well-known Gutzwiller wave function is generalized by including new variational parameters to control nearest-neighbour charge-charge, charge-spin, and spin-spin correlations. The non-magnetic state of the one-dimensional, half-filled Hubbard model is studied. Within the Gutzwiller approximation, the expression for the ground state energy can be worked out analytically. The correlation between empty and doubly occupied sites is found to play the most essential role. Minimization in the large-U limit shows that the Brinkman-Rice transition has been pushed to U → ∞, and the leading term of the ground state energy density is of order −t2/ U . In contrast to results obtained with the Gutzwiller wave function, we find that the band occupation number nk is monotonically decreasing both above and below kF. The dominant k–dependence is given by ~(t/U) cos k, in agreement with t/U–expansion results. nk has also a weak step-function component, with the discontinuity at kF vanishing as (t/U)2 in the limit U/t ≫ 1.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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