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arXiv:2301.11708

Classical Monte Carlo algorithm for simulation of a pseudospin model for cuprates

V. A. Ulitko, Yu. D. Panov, A. S. Moskvin

Published Jan 27, 2023• 0 citations
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Abstract

A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange interaction, single-particle and correlated two-particle transfer. We define the state selection rule that gives both the uniform distribution of states in the phase space and the doped charge conservation. The simulation results show a qualitative agreement of a phase diagrams with the experimental ones.

DOI
10.48550/arxiv.2301.11708

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A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange interaction, single-particle and correlated two-particle transfer. We define the state selection rule that gives both the uniform distribution of states in the phase space and the doped charge conservation. The simulation results show a qualitative agreement of a phase diagrams with the experimental ones.
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Abstract The results of numerical simulation using a modified Monte Carlo method with a heat bath algorithm for the pseudospin model of cuprates are presented. The temperature phase diagrams are constructed for various degrees of doping and for various parameters of the model, and the effect of local correlations on the critical temperatures of the model cuprate is investigated. It is shown that, in qualitative agreement with the results of the mean field approximaton, the heat bath algorithm leads to a significant decrease in the estimate of critical temperatures due to more complete accounting for fluctuations, and also makes it possible to detect phase inhomogeneous states. The possibility of using machine learning to accelerate the heat bath algorithm is discussed.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
The author reports on new high-fidelity simulations of charge carriers in the high-Tc_cc​ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this new application of this high accuracy technique, the doped ground state is found to be in the form of a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface in these materials. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.
The author reports on high-fidelity simulations of charge carriers in the high-Tc{T}_{c}Tc​ cuprate materials using quantum Monte Carlo techniques applied to the first-principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in x-ray, EELS, and neutron experiments.
We develop an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field theory.