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Charge density correlations in t-J ladders investigated by the CORE method

Sylvain Capponi, Didier Poilblanc

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Using 4-site plaquette or rung basis decomposition, the CORE method is applied to 2-leg and 4-leg t-J ladders and cylinders. Resulting range-2 effective hamiltonians are studied numerically on periodic rings taking full advantage of the translation symmetry as well as the drastic reduction of the Hilbert space. We investigate the role of magnetic and fermionic degrees of freedom to obtain the most reliable representation of the underlying model. Spin gaps, pair binding energies and charge correlations are computed and compared to available ED and DMRG data for the full Hamiltonian. Strong evidences for short-range diagonal stripe correlations are found in periodic 4-leg t-J ladders.

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arXiv:cond-mat/0007196•Physical review. B, Condensed matter•Dec 12, 2000•28 citations
Using 4-site plaquette or rung basis decomposition, the CORE method is applied to 2-leg and 4-leg t-J ladders and cylinders. Resulting range-2 effective hamiltonians are studied numerically on periodic rings taking full advantage of the translation symmetry as well as the drastic reduction of the Hilbert space. We investigate the role of magnetic and fermionic degrees of freedom to obtain the most reliable representation of the underlying model. Spin gaps, pair binding energies and charge correlations are computed and compared to available ED and DMRG data for the full Hamiltonian. Strong evidences for short-range diagonal stripe correlations are found in periodic 4-leg t-J ladders.
Using four-site plaquette or rung basis decomposition, the contractor-renormalization method is applied to two-leg and four-leg $t\ensuremath{-}J$ ladders and cylinders. Resulting range-2 effective Hamiltonians are studied numerically on periodic rings taking full advantage of the translation symmetry as well as the drastic reduction of the Hilbert space. We investigate the role of magnetic and fermionic degrees of freedom. Spin gaps, pair-binding energies, and charge correlations are computed and compared to available exact-diagonalization and density-matrix renormalization-group data for the full Hamiltonian. Strong evidence for short-range diagonal stripe correlations are found in periodic four-leg $t\ensuremath{-}J$ ladders.
We study the ground state properties of the t–J model on two and three leg ladders. The phase diagram of the anisotropic couplings along the rungs and legs is investigated to find the opening of a charge transfer gap which appears as a charge density plateau. In a perturbative approach we start from isolated rungs at zero leg couplings. Then the stability of the charge density plateau is examined by first order perturbation theory in terms of an effective Hamiltonian using the numerical Lanczos method on finite size ladders. The results of this approach are compared with the exact diagonalization of finite systems. We have found that an improvement of our results depends on the initial clusters for zeroth order perturbation which cannot be recovered by higher order perturbation in rung clusters. For the two leg ladder case the application of 4-site (2 × 2) plaquettes helped us to overcome earlier flaws when the charge density is greater than one-half. We have also addressed the generalization of our method to trace phase separation in this model, where a linear dependence of ground state energy versus charge density gives evidence of a phase separated state.
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with non-equal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin densities as well as their correlation functions at half-filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.
Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix renormalization group (DMRG) method and its time-dependent extension. By analyzing ground-state correlations and single-particle removal spectra, we systematically examine the effects of plaquette diagonal hopping, spin exchange, and hole doping. Within appropriate parameter regimes, these factors drive the system from the well-known Luther Emery phase, with gapped spin and gapless charge modes, into a Luttinger liquid phase characterized by gapless spin and charge excitations, where signatures of spin-charge separation emerge. In combination with previous studies using exact diagonalization, our results provide evidence that spin-charge separation may persist in wider ladder systems.
The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.
The recently discussed tendency of holes to generate nontrivial spin environments in the extended two-dimensional $t\ensuremath{-}J$ model [G. Martins, R. Eder, and E. Dagotto, Phys. Rev. B 60, R3716 (1999)] is here investigated using computational techniques applied to ladders with several number of legs. This tendency is studied also with the help of analytic spin-polaron approaches directly in two dimensions. Our main result is that the presence of robust antiferromagnetic correlations between spins located at both sides of a hole either along the x or y axis, observed before numerically on square clusters, is also found using ladders, as well as applying techniques based on a string-basis expansion. This so-called ``across-the-hole'' nontrivial structure exists even in the two-leg spin-gapped ladder system, and leads to an effective reduction in dimensionality and spin-charge separation at short-distances, with a concomitant drastic reduction in the quasiparticle weight Z. In general, it appears that holes tend to induce one-dimensional-like spin arrangements to improve their mobility. Using ladders it is also shown that the very small $J/t\ensuremath{\sim}0.1$ regime of the standard $t\ensuremath{-}J$ model may be more realistic than anticipated in previous investigations, since such regime shares several properties with those found in the extended model at realistic couplings. Another goal of the present paper is to provide additional information on the recently discussed tendencies to stripe formation and spin incommensurability reported for the extended $t\ensuremath{-}J$ model. These tendencies are illustrated with several examples.