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arXiv:cond-mat/0207065 · Physical review. B, Condensed matter

Phase separation in effective hard-core boson and triplet models in one and two dimensions

José A. Riera

Published Oct 29, 2002• 4 citations
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Abstract

Effective models of hard-core hole pair bosons and triplets are derived from the $t\ensuremath{-}J$ model in ladders and on the square lattice by performing a change from site to dimer basis. The Hilbert space is truncated by projecting out single-occupied electron states and only nearest-neighbor interactions are retained. The resulting effective models in one and two dimensions are studied by numerical techniques. In both spatial dimensions, the main result is that each hole pair is surrounded by a singlet cloud expelling triplet excitations from its vicinity. It is suggested an interpretation of this feature as a phase-separated state between a hole-pair-rich singlet phase and an undoped triplet phase with antiferromagnetic correlations. The possible relevance of this result to other theoretical scenarios and experimental results is discussed.

DOI
10.1103/physrevb.66.134523

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Effective models of hard-core hole pair bosons and triplets are derived from the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model in ladders and on the square lattice by performing a change from site to dimer basis. The Hilbert space is truncated by projecting out single-occupied electron states and only nearest-neighbor interactions are retained. The resulting effective models in one and two dimensions are studied by numerical techniques. In both spatial dimensions, the main result is that each hole pair is surrounded by a singlet cloud expelling triplet excitations from its vicinity. It is suggested an interpretation of this feature as a phase-separated state between a hole-pair-rich singlet phase and an undoped triplet phase with antiferromagnetic correlations. The possible relevance of this result to other theoretical scenarios and experimental results is discussed.
A model of hard-core bosons and spin-1 sites with single-ion anisotropy is proposed to approximately describe hole pairs moving in a background of singlets and triplets with the aim of exploring the relationship between superconductivity and antiferromagnetism. The properties of this model at zero temperature were investigated using quantum Monte Carlo techniques. The most important feature found is the suppression of superconductivity, as long range coherence of preformed pairs, due to the presence of both antiferromagnetism and ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1$ excitations. Indications of charge ordered and other phases are also discussed.
We consider a Hubbard-like model of strongly interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half filling. The problem of a single stripe can be mapped to fermions in one dimension, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of a few stripes, finding that they repel and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into a particle-rich phase and a hole-rich liquid, we evaluate the liquid's equation of state, finding that the stripe-array is not stable for bosons but is possibly stable for fermions.
A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t< or =1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation; in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).
We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the XXZXXZXXZ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter KKK obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.
The formation of density modulations observed in cuprates by means of scanning tunneling microscopy is analyzed in the framework of an effective model for hole-doped short-range two-dimensional antiferromagnets. That model has been derived from the $t\text{\ensuremath{-}}J$ model on the square lattice. It is defined in terms of hard-core bosons. The latter objects represent tightly bound hole pairs. Long-range Coulomb repulsion between them is assumed. The nature of the ground state for the effective model is determined by analyzing the density correlation function and the density structure factor. The exact diagonalization for four hard-core bosons in the 128-site cluster, which corresponds to eight holes in the $8\ifmmode\times\else\texttimes\fi{}8$ cluster of sites in the initial square lattice, is performed to derive these quantities. Signatures of the density modulations with the periodicity 4 spacings between nearest-neighbor sites in the initial square lattice in horizontal and vertical directions and with the full symmetry of that lattice may be seen both in the density correlation function and in the density structure factor. On the other hand, a strong tendency to form smectic order may be noticed in the results of the calculation. It turns out that the ground state is a symmetric combination of states representing stripes running either in the vertical or in the horizontal directions. In a real system, the same effect may have the formation of regions with short-range fluctuating stripe order oriented either vertically or horizontally.
We show that a nearest-neighbor singlet phase results (from an effective Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of strong electron-electron and electron-phonon interactions and under nonadiabatic conditions ($t/{\ensuremath{\omega}}_{0}\ensuremath{\leqslant}1$). By mapping the system of nearest-neighbor singlets at a filling Np/N{N}_{p}/NNp​/N onto a hard-core-boson (HCB) ttt-VVV model at a filling ${N}_{p}/(N\ensuremath{-}{N}_{p})$, we demonstrate explicitly that superfluidity and charge density wave (CDW) occur mutually exclusively with the diagonal long range order manifesting itself only at one-third filling. Furthermore, we also show that the Bose-Einstein condensate (BEC) occupation number n0{n}_{0}n0​ for the singlet phase, similar to the n0{n}_{0}n0​ for a HCB tight binding model, scales as N\sqrt{N}N​; however, the coefficient of N\sqrt{N}N​ in the n0{n}_{0}n0​ for the interacting singlet phase is numerically demonstrated to be smaller.