On the Phase Diagram of the Zero-Bandwidth Extended Hubbard Model with Intersite Magnetic Interactions for Strong On-Site Repulsion Limit

Abstract

In this report we have analyzed a simple eective model for a description of magnetically ordered insulators.The Hamiltonian considered consists of the eective on-site interaction (U ) and the intersite Ising-like magnetic exchange interaction (J ) between nearest neighbors. For the rst time the phase diagrams of this model have been determined within Monte Carlo simulation on 2D-square lattice. They have been compared with results obtained within variational approach, which treats the on-site term exactly and the intersite interactions within mean-eld approximation. We show within both approaches that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: FNO).

Monte Carlo Study of Phase Separation in Magnetic Insulators

“…Notice that the results presented are in good qualitative agreement with mean field calculations using variational approach presented in [13,[21][22][23][24][25]. When comparing these results one should keep in mind differences between these two methods, as the VA is exact only for infinite dimensions d → ∞.…”

“…chemical potential dependence of electron concentration curvesn(µ). The Monte Carlo algorithm used in this analysis consists of three steps: (i) creation, (ii) destruction, and (iii) moving of particle, all of them with appropriate probability P ∼ exp (∆E/(k B T )) [11][12][13][14]. It is worth noting, that for constant values of concentration a simpler algorithm with only step (iii) -"move" would be sufficient.…”

“…Unfortunately, addition of chemical potential term in the Hamiltonian prevents us from implementing cluster updates algorithm, so only local updates [15] are used here. The details of the algorithm used can be found in [11][12][13][14].…”

“…Within the variational approach (with on-site U term treated exactly and mean field decoupling of intersite term J) the model has been analyzed for half-filing (n = 1) [21,22] as well as for arbitrary electron concentration 0 ≤ n ≤ 2 [23] (these results are rigorous in the limit of infinite dimensions d → +∞). Our preliminary Monte Carlo (MC) results have been presented in [13,14] for L = 10 and onsite repulsion: U/(4J) = 1, 10 (corresponding to rather weak and strong coupling, respectively) [13] as well as for L = 20 and U/(4J) = 1 [14].…”

Some Properties of Two-Dimensional Extended Repulsive Hubbard Model with Intersite Magnetic Interactions - A~Monte Carlo Study

“…Within the variational approach the model has been analyzed for half-filing (n = 1) [6,7] as well as for arbitrary electron concentration 0 ≤ n ≤ 2 [8,9] (these results are rigorous in the limit of infinite dimensions d → +∞). Our preliminary Monte Carlo (MC) results have been presented in [10] for strong on-site repulsion (U/4J = 1, 10 and L = 10). In this paper we investigate in details the phase diagram and thermodynamic properties of the model for arbitrary electron concentration n ≤ 1 and arbitrary chemical potentialμ ≤ 0 (μ = µ − U/2) in the whole range of temperatures for a specific repulsive value of the on-site interaction parameter U/(4J) = 1 (and L = 20).…”