arXiv:cond-mat/0402366 · Physical Review B

Bond-impurity-induced bound states in disordered spin- 12 ladders

Marcelo Arlego, W. Brenig, D. C. Cabra, Fabian Heidrich‐Meisner, A. Honecker, G. L. Rossini

Published Jul 30, 2004• 6 citations

Abstract

We discuss the effect of weak bond disorder in two-leg spin ladders on the dispersion relation of the elementary triplet excitations with a particular focus on the appearance of bound states in the spin gap. Both the cases of modified exchange couplings on the rungs and the legs of the ladder are analyzed. Based on a projection on the single-triplet subspace, the single-impurity and small cluster problems are treated analytically in the strong-coupling limit. Numerically, we study the problem of a single impurity in a spin ladder by exact diagonalization to obtain the low-lying excitations. At finite concentrations and to leading order in the inter-rung coupling, we compare the spectra obtained from numerical diagonalization of large systems within the single-triplet subspace with the results of diagrammatic techniques, namely, low-concentration and coherent-potential approximations. The contribution of small impurity clusters to the density of states is also discussed.

DOI: 10.1103/physrevb.70.014436

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arXiv:cond-mat/0402366 · Physical Review B

Bond-impurity-induced bound states in disordered spin- 12 ladders

Marcelo Arlego, W. Brenig, D. C. Cabra, Fabian Heidrich‐Meisner, A. Honecker, G. L. Rossini

Published Jul 30, 2004• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.70.014436

Related papers

Spin gaps in coupledt-Jladders

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Spin gaps in coupled t-J ladders are investigated by exact diagonalization of small clusters up to 4\ifmmode\times\else\texttimes\fi{}8 sites. At half-filling, the numerical results for the triplet excitation spectrum are in very good agreement with a second-order perturbation expansion in terms of small interladder and intraladder exchange couplings between rungs (J/J'0.25). The band of local triplet excitations moving coherently along the ladder (with momenta close to \ensuremath{\pi}) is split by the interladder coupling. For intermediate couplings, finite-size scaling is used to estimate the spin gap. In the isotropic infinite four-chain system (two coupled ladders) we find a spin gap of 0.245J, roughly half of the single-ladder spin gap. When the system is hole doped, bonding and antibonding bound pairs of holes can propagate coherently along the chains and the spin gap remains finite.Spin gaps in coupled t-J ladders are investigated by exact diagonalization of small clusters up to 4\ifmmode\times\else\texttimes\fi{}8 sites. At half-filling, the numerical results for the triplet excitation spectrum are in very good agreement with a second-order perturbation expansion in terms of small interladder and intraladder exchange couplings between rungs (J/J'0.25). The band of local triplet excitations moving coherently along the ladder (with momenta close to \ensuremath{\pi}) is split by the interladder coupling. For intermediate couplings, finite-size scaling is used to estimate the spin gap. In the isotropic infinite four-chain system (two coupled ladders) we find a spin gap of 0.245J, roughly half of the single-ladder spin gap. When the system is hole doped, bonding and antibonding bound pairs of holes can propagate coherently along the chains and the spin gap remains finite.

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H.-J. Mikeska, U. Neugebauer, Ulrich Schollwöck

We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical [Lanczos and density matrix renormalization group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction ${\mathrm{J}}_{\mathrm{eff}}$ , the magnitude of which depends on the impurity distance. The magnitude of ${\mathrm{J}}_{\mathrm{eff}}$ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical [Lanczos and density matrix renormalization group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction ${\mathrm{J}}_{\mathrm{eff}}$, the magnitude of which depends on the impurity distance. The magnitude of ${\mathrm{J}}_{\mathrm{eff}}$ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.

arXiv:cond-mat/9608100Physical review. B, Condensed matterFeb 1, 199739 citations

We investigate the influence of biquadratic exchange interactions on the low-lying excitations of a

S=\frac{1}{2}

ladder using perturbation theory, numerical diagonalization of finite systems, and exact results for ladders with matrix product ground states. We consider in particular the combination of biquadratic exchange interactions corresponding to ring exchange on the basic ladder plaquette. We find that a moderate amount of ring exchange reduces the spin gap substantially and makes equal bilinear exchange on legs and rungs consistent with experimentally observed spectra.

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding

t_{1,2}-J_{1,2}

Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.

Using the conventional

T

-matrix approach, we discuss gapped phases in one-, two-, and three-dimensional (3D) spin systems (both with and without a long-range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-

\frac{1}{2}

systems and in integer-spin magnets with large single-ion easy-plane anisotropy

\mathcal{D}

with disorder in exchange coupling constants (and/or

\mathcal{D}

). The elementary excitation spectrum and the density of states are calculated in the first order in defects concentration $c\ensuremath{\ll}1$. In 2D and 3D systems, the scattering on defects leads to a finite damping of all propagating excitations in the band except for states lying near its edges. We demonstrate that the analytical approach is inapplicable for states near the band edges and our numerical calculations reveal their localized nature. We find that the damping of propagating excitations can be much more pronounced in considered systems than in magnetically ordered gapless magnets with impurities. In 1D systems, the disorder leads to localization of all states in the band, while those lying far from the band edges (short-wavelength excitations) can look like conventional wave packets.

{\mathrm{J}}_{\mathrm{eff}}

, the magnitude of which depends on the impurity distance. The magnitude of

{\mathrm{J}}_{\mathrm{eff}}

is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.