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arXiv:2510.08289 · The Physics of Metals and Metallography

Modified Monte Carlo Method with the Heat Bath Algorithm for a Model Cuprate

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

Published Oct 1, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1134/s0031918x25600976

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Europhysics Letters (EPL)•Apr 1, 2021•4 citations
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.
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.
We develop a classical Monte Carlo algorithm based on a quasi-classical approximation for a pseudospin S = 1 Hamiltonian in real space to construct a phase diagram of a model cuprate with a high T c . A model description takes into account both local and nonlocal correlations, Heisenberg spin-exchange interaction, correlated single-particle, and two-particle transport. We formulate a state selection algorithm for a given parameterization of the wave function in order to ensure a uniform distribution of states in the phase space. The simulation results show a qualitative agreement with the experimental phase diagrams.
The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference ΔdpΔ_{dp}Δdp​ between ddd and ppp electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when ΔdpΔ_{dp}Δdp​ decreases and the pure ddd-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate xxx contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.
High-temperature superconductivity in copper oxides (cuprates, e.g. La2−xSrxCuO4, YBa2Cu3O6+δ or Bi2Sr2CaCu2O8+δ) remains among the most spectacular phenomena in condensed matter physics. Since its discovery in 1986, an enormous number (∼ 105) of papers on the subject have appeared. So far, there is no single, commonly accepted theory of high-temperature superconductivity. However, it is widely believed that a basic description of this phenomenon can be provided by a single-band Hubbard model or its derivative, the t-J model. The latter model is regarded as a minimal microscopic model, capable of describing the essential aspects of the complex physics of the cuprates. Unfortunately, in general case, neither of those two models can be solved exactly and therefore various approximate methods are used. Among them, the so-called mean-field methods provide a simple, yet fairly reasonable description of the cuprates. In particular, some of the main qualitative features of the phase diagram and the essential features of electronic spectrum are roughly reproduced. A standard mean-field approach to the t-J model, known under the name of renormalized mean-field theory (RMFT) goes beyond the Hartree-Fock approximation. Consequently, its fully consistent treatment requires a novel theoretical approach. This has been our original motivation to develop a general approach to the mean-field models, which is based on the maximum entropy (MaxEnt) principle. The method is presented in detail in Part II of this Thesis, and in Part III it is applied to study RMFT of the t-J model. First, we compare the results obtained within our formalism with those of the frequently used non-variational approach based entirely on the self-consistent equations. Also, various versions of RMFT are compared, and the most satisfactory of them is selected. This optimal version is subsequently used to study different versions of the original t-J Hamiltonian. As a result, upper critical concentration and doping dependence of the selected physical quantities (e.g. the superconducting gap and the Fermi velocity) is determined at low temperatures and in the absence of external magnetic field. We compare our findings both with theoretical results obtained from the Variational Monte Carlo (VMC) methods, as well as with the experimental data for selected cuprates. We show that the version of RMFT approach formulated in this Thesis provides a reasonable qualitative and in some cases semiquantitative rationalization of the principal characteristics of the hole-doped high-temperature superconductors at the optimal doping and in the overdoped regime. Possible extensions of the proposed analysis are mentioned at the end.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d − p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of the antiferromagnetic state by changing the band parameters such as the hole number, level difference Δ d p between d and p electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when Δ d p decreases and the pure d -wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate x contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.