arXiv:cond-mat/0106385 · Physical review. B, Condensed matter

Redistribution of spectral weight in Haldane chains doped with spin- 12 moments

Stefan Weßel, Stephan Haas

Published Mar 8, 2002• 3 citations

Abstract

We study the evolution of the dynamical spin structure factor in a spin-1 antiferromagnetic Heisenberg chain which is randomly doped with spin-1/2 moments. Using stochastic series expansion quantum Monte Carlo simulations combined with the maximum entropy method, we monitor the crossover from the spin-1 chain, dominated by a single resonance at the Haldane energy, to the spin-1/2 chain with a continuum of spinon states which diverges at zero frequency. Upon increasing the doping level, spectral weight is rapidly transferred from the Haldane peak to lower energies. If the exchange couplings between the spin-1/2 substituents and the spin-1 sites of the host are sufficiently small, finite-frequency bound states are observed below the spin gap for small doping concentrations.

DOI: 10.1103/physrevb.65.132402

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arXiv:cond-mat/0106385 · Physical review. B, Condensed matter

Redistribution of spectral weight in Haldane chains doped with spin- 12 moments

Stefan Weßel, Stephan Haas

Published Mar 8, 2002• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.65.132402

Related papers

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We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings

J

and

-|λ|J

as a power series in

λ

. For small

|λ|

, the gapped one-particle spectrum has a maximum at

k=0

and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As

|λ|

is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from

k=0

, the one particle states merge with the bottom of the continuum near

k=0

, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large

|λ|

confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

We present a study of the dynamic structure factor of the antiferromagnetic spin-

\frac{1}{2}

Heisenberg chain at finite temperatures and finite magnetic fields. Using quantum Monte Carlo based on the stochastic series expansion and maximum entropy methods, we evaluate the longitudinal and the transverse dynamic structure factors from vanishing magnetic fields up to and above the threshold

{B}_{c}

for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero-temperature Bethe ansatz. The crossover between the field-induced ferromagnet above

{B}_{c}

and the Luttinger liquid below

{B}_{c}

is analyzed in terms of the transverse spin dynamics. Evaluating sum rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the maximum entropy results.

Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor

S(k,ω)

of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point,

S(k,ω)

develops broad non-spinon excitations as well as the random-singlet peak near

(k, ω) = (π, 0)

, consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu

_2

(Si

_x

_{1-x}

)

_2

_7

{\mathrm{T}}_{1}

from the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit, and compare with recent experimental results for

{\mathrm{Sr}}_{2}

{\mathrm{CuO}}_{3}

and

{\mathrm{CuGeO}}_{3}

. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility \ensuremath{\chi}(k). We confirm the asymptotic low-temperature forms S(\ensuremath{\pi})\ensuremath{\sim}[ln (T)

{]}^{3\mathrm{/}2}

and \ensuremath{\chi}(\ensuremath{\pi})\ensuremath{\sim}${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$[ln (T)

{]}^{1\mathrm{/}2}

, expected from previous theoretical studies.