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arXiv:cond-mat/0204503 · Physical Review Letters

Stripe Phases in the Two-Dimensional Falicov-Kimball Model

R. Lemański, James K. Freericks, Grzegorz Banach

Published Oct 21, 2002• 74 citations
arXivHTMLPDF

Abstract

The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.

DOI
10.1103/physrevlett.89.196403

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The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.
Charge and spin orderings are studied on the simplest one-dimensional (1D) and the two-dimensional (2D) square lattices within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagram method (RPDM), a number of simple rules of formation of various sorts of ground-state phases have been detected. In particular, relationships between density of current carriers (electrons or holes) and type of charge and magnetic arrangement have been determined. In two dimensions in the mixed-valence regime, only axial stripes (vertical or horizontal) have been found for intermediate values of the coupling constants. They are composed of ferromagnetic or antiferromagnetic chains interchanged with nonmagnetic ones. For band fillings close to the half filling, stripe phases oriented along one of the main diagonal direction are formed. The results suggest the possibility of tuning modulations of charge and magnetic superstructures with a change in doping.
Abstract Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t′{t}^{{\prime} }t′ t′ or phonon energy Ω. Our results help elucidate how thee-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-Tccuprates.
A wide variety of experimental platforms, ranging from semiconductor quantum-dot arrays to moiré materials, have recently emerged as powerful quantum simulators for studying the Hubbard model and its variants. Motivated by these developments, here, we investigate a generalization of the Hubbard model which includes the effects of long-range Coulomb interactions. Working on finite-sized two-dimensional square and triangular lattices, we use exact diagonalization and density-matrix renormalization group calculations to probe the magnetic structure of the ground state in the strong-coupling regime, where UUU (the onsite repulsion) ≫\gg≫ ttt (the nearest-neighbor hopping). For small electron dopings above the half-filled antiferromagnet, we numerically uncover a rich variety of magnetically ordered states, and in conjunction with theoretical arguments, infer the phase diagram of the system as a function of doping and interaction strengths. In particular, we find that the inclusion of long-range Coulomb interactions induces an instability of high-spin states$\unicode{x2014}$such as the saturated Nagaoka ferromagnet$\unicode{x2014}$towards phase separation and stripe ordering. We also present proposals for the observation of some of our key findings in experiments that would shed further light on this paradigmatic strongly correlated system.
The ground-state phase diagram of two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings (characterized by t,t' constants, respectively) has been studied in perturbative regime, i.e. in the case when on-site Coulomb interaction constant U is much larger than t,t' ones. The fourth-order phase diagram exhibits a rich structure, more complicated than for the ordinary Falicov-Kimball model. Possible experimental implications of the presence of nnn term are shortly discussed.
Finite-temperature properties of the Falicov-Kimball model in two approximations were studied in the perturbative regime, i.e. for t/U 1, where t = 1 is the hopping constant and U = 10 denotes the Coulomb interaction strength.In our study, we determined the phase diagram of the model in the second order of the perturbation theory, where it reduces to the antiferromagnetic Ising model in the emergent magnetic field.In the fourth order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the phase diagram was established.The Monte Carlo method was employed to investigate the phase transition lines.The existence of stripe ordering at finite temperatures is proved.
We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest-neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature T * by a Landau free-energy analysis. While the magnetic order for filling factors n ≥ 1 is always of Néel type, for n ≤ 1 the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram. Published by the American Physical Society 2024