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

TL;DR

This work develops a classical Monte Carlo study of a real-space $S=1$ pseudospin Hamiltonian for cuprates, incorporating local and nonlocal charge correlations, single- and two-particle transport, and Heisenberg exchange. A quasi-classical energy functional is derived and used to guide Monte Carlo sampling, together with a charge-conserving state-selection algorithm that enables pair updates while preserving total charge. Comparing Monte Carlo results with mean-field theory shows substantial suppression of critical temperatures due to fluctuations and reveals regions of no ordering at low temperature, yielding phase diagrams that qualitatively align with experimental cuprate behavior. The framework provides a tractable route to investigate the interplay among antiferromagnetism, charge order, and Bose-like pairing tendencies in doped cuprates across doping levels.

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.

Figures (7)

• Figure 1: (a) The constant value lines for the on-site charge density $n$ defined by Eq. \ref{['eq:neq']}; (b) the probability density function $f(n)$; (c) the probability distribution function $F(n)$.
• Figure 2: The normalized probability density function $f_1(t;2n)$ for values of the pair charge (a) $2|n| = 0.0$, $0.3$, $0.6$, $0.9$; (b) $2|n| = 0.9$, $1.0$, $1.1$, $1.9$; (c) the cumulative distribution function $F_1(t;2n)$ for $2|n| = 0.0$, $0.3$, $0.6$, $1.0$, $1.9$.
• Figure 3: (a) The shaded area is the domain of functions in variables $(n_1 , m )$; (b) the conditional density function $p_2$ for given values of $n_1$; (c) the conditional distribution function $F_2$ for given values of $n_1$.
• Figure 4: Critical temperature of CO ordering. The nonzero model parameters are $\Delta=0.1$, $V=0.25$. The dotted line shows the MFA value obtained from Eq. \ref{['eq:TCO']}. The solid line corresponds to results of MC simulation.
• Figure 5: Critical temperature of AFM ordering. The nonzero model parameters are $\Delta=0.1$, $J=1$. The dotted line shows the MFA value obtained from Eq. \ref{['eq:TAFM']}. The solid line corresponds to results of MC simulation.