A new trial wave function for the one dimensional t−J model

1992 ◽  
Author(s):  
T. K. Lee
Keyword(s):  
Wave Function ◽  
Trial Wave Function ◽  
One Dimensional ◽  
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

Variational Solution of Steady-Structure in Exciton-Polariton Condensates with a Modified Lagrangian Approach

2018 ◽  
Vol 787 ◽  
pp. 113-122
Author(s):  
Jian Wei Zhang ◽  
Hai Jun Chen ◽  
Sheng Jun Wang ◽  
Yuan Ren
Keyword(s):  
Wave Function ◽  
Steady State ◽  
Lagrangian Method ◽  
Trial Wave Function ◽  
Pitaevskii Equation ◽  
Quantum Dissipation ◽  
State Structure ◽  
Static Version ◽  
The One ◽  
First Time

Exciton-polariton condensate is a new kind of system exhibiting spontaneous coherence, which is a new quantum dissipation system. Numerical simulation and analytical methods can be used to study the static and dynamical properties of exciton-polariton condensate. In this paper, A modified Lagrangian method is developed for exciton-polariton system to find the steady-state structure and regimes among the parameters of the system, and two new forms of trial wave function are proposed. The modified Lagrangian method is successfully applied to the exciton-polariton system described by the open-dissipative Gross-Pitaevskii equation for the first time. Furthermore, static version of the modified Lagrangian method provides stationary shape of the steady-state structure, while the time-dependent version can be used to study small amplitude oscillations around stationary states. On the one hand, comparison of the profiles for steady-state structure, predicted by the modified Lagrangian and those found from numerical solution of the open-dissipative Gross-Pitaevskii(dGP) equation shows good agreement, thereby proving the accuracy of the trial wave function and validating the proposed approach. Particularly, this new method promotes the deeper cognition and understanding for the dissipative exciton-polariton system and is helpful to explore the mechanism of the gain and dissipation effect on the steady-state structure of the system.

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.

scholarly journals Вариационная модель низкоразмерного магнетика

2020 ◽  
Vol 62 (9) ◽  
pp. 1514
Author(s):  
Ю.Б. Кудасов ◽  
Р.В. Козабаранов
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Ground State ◽  
State Energy ◽  
Spin Correlation ◽  
Trial Wave Function ◽  
Spin Correlation Function ◽  
One Dimensional ◽  
Fermionic Representation ◽  
Extended Trial

A variational method with nonlocal trial function is developed for quantum one-dimensional systems. It is applied to the XXZ spin-1/2 chain with an alternating magnetic field. A four-node trial wave function for the fermionic representation of the model is constructed. The results obtained in the model with an extended trial wave function demonstrate a significant increase in the accuracy of the ground state energy in the region of critical behavior compared with the solutions obtained previously. A method for calculation of the spin correlation function are discussed.

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