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Physics of the Solid State

Variational Model for Low-Dimensional Magnets

Yu. B. Kudasov, R. V. Kozabaranov

Published Sep 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1063783420090176

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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 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.
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.
In this thesis the quantum Monte Carlo loop algorithm is applied to study the properties of correlation functions in low-dimensional quantum antiferromagnets. Two different types of lattice models are investigated. The first system is the quantum critical XXZ chain. The second class of models emerges when coupling the square lattice Heisenberg model to phonons. In case of the quantum critical XXZ chain, the loop algorithm is used to compute the two-point spin and dimer correlation functions at low temperatures. Starting from the well-known asymptotic expressions from conformal field theory for the decay of the correlations, the crossover from the finite-temperature to the ground state behavior is investigated. In addtion, the Monte Carlo data are used to extract numerical estimates for the correlation amplitudes. The deviations from asymptotic scaling at low finite temperatures and intermediate distances are examined. The results are also used to study the algebraic and logarithmic corrections in the ground state. The method is further applied to compute the low-temperature spin correlations of the square lattice Heisenberg model coupled to dispersionless Einstein phonons. Also, statically dimerized Heisenberg models in two dimensions are investigated. Here the quantum Monte Carlo technique is used to determine the specific pattern of dimerized bonds which has the largest gain in the magnetic energy. A direct comparison of ground state energies is only possible for a small number of dimerized systems. For this reason an alternative approach is developed, which allows to study a significantly larger class of models. Starting from a Landau expansion of the free energy, this amounts to a computation of specific structure factors of the dimer correlations of the uniform Heisenberg model. As a consequence, a Landau theory for the two-dimensional counterpart of the spin-Peierls transition is established. This adiabatic approach also applies to the Heisenberg model coupled to dispersive phonons. In this case the data for the dimer correlations are used to study the impact of the spin-phonon coupling on the phonon dispersion relations. In particular, the softening of phonon modes is investigated, which is relevant for experimental studies on substances with a quasi two-dimensional magnetic structure.
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model (S=1/2S=1/2S=1/2 and S=5/2S=5/2S=5/2) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.