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Physics of the Solid State

Вариационная модель низкоразмерного магнетика

Yu. B. Kudasov, R. V. Kozabaranov

Published Jan 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.21883/ftt.2020.09.49779.21h

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Abstract The method of nonlocal trial variation function for quantum one-dimensional systems is developed on an example of a spin-1/2 XXZ chain with an alternating magnetic field. A four-site trial wave function for a fermionic representation of the model is constructed. The results obtained using the model with the extended trial wave function show a considerable improvement of accuracy of the ground state energy calculation in the field of critical behavior in comparison with the solutions obtained earlier. The methods for calculating the experimentally observed spin correlation function are considered.
A scheme of optimization of a trial wave function in the variational Monte Carlo calculation is developed. It provides a more precise description of the ground state for strongly correlated electronic systems with highly improved trial wave function. A general type of variational wave function constructed from a linear combination of Slater determinants multiplied by Jastrow correlation factors is proposed. They can explicitly contain low-energy fluctuations and long-range correlations. Using this optimization method, we examine the properties of these wave functions by applying them to a one-dimensional Hubbard model for which the exact solution is available for comparison. It is found that these wave functions prove to be substantial improvements compared to the conventional Jastrow-type wave functions.
A new variational scheme based on a modified Bethe–Peierls method is used to study the ground state properties of the one-dimensional t–J model. Expectation values are evaluated by cutting out a four-site cluster from a correlated Fermi sea, the ground state of which is described by a variational trial wave function. We study a generalized Gutzwiller state where nearest-neighbour hole–hole correlations are controlled variationally. From the electron concentration dependence of the ground state energy, we determine the true thermodynamic boundary where segregation into an electron-rich, and purely hole phase sets in. We also determine the spinodal line and pair susceptibilities. The variational method is applied also to an extended t–J–V model, where V is the coupling constant of the charge interaction term.
The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe-ansatz solution is proposed, where the spin-charge separation is realized and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; both the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery-liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived. \textcopyright{} 1996 The American Physical Society.
We introduce an alternative approach to highly correlated systems that generalizes the Fermi hypernetted chain and correlated basis function techniques. While the latter approaches can be applied only to systems for which a nonrelativistic wave function can be defined, the present approach is based on the variation of a trial Hamiltonian within a path-integral framework and thus can be applied also to relativistic and field theoretical problems. We derive a diagrammatic scheme for the present approach and show how a particular choice of trial Hamiltonian corresponds exactly to the use of a Jastrow correlated ansatz for the wave function in the Fermi hypernetted chain approach. We show how our approach can be used to find upper bounds to ground-state energies in systems that the Fermi hypernetted chain approach cannot handle, including those described by an energy-dependent effective Hamiltonian. We demonstrate our approach by applying it to a quantum field theoretical system of interacting pions and nucleons. \textcopyright{} 1996 The American Physical Society.