The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

Klümper, Andreas; Sakai, Kazumitsu

doi:10.1088/0305-4470/35/9/307

Cited by 177 publications

(284 citation statements)

References 29 publications

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“…Following Ref. [49] we constructed quantum transfer matrix description of this ensemble, and derived a set of nonlinear integral equations that describe the largest eigenvalue of the quantum transfer matrix. We emphasize that there is an important difference between our description of the stationary state after a quench and thermal ensembles for generalized integrable Hamiltonians of the kind considered in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…We emphasize that there is an important difference between our description of the stationary state after a quench and thermal ensembles for generalized integrable Hamiltonians of the kind considered in Ref. [49]: in our case the "input data" are not given by the Lagrange multipliers (inverse temperature, chemical potential, etc. ), but instead fixed implicitly through the expectation values of local conservation laws.…”

Section: Discussionmentioning

confidence: 99%

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Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Fagotti¹,

Eßler²

2013

J. Stat. Mech.

153

257

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We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values, that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Fagotti¹,

Eßler²

2013

J. Stat. Mech.

153

257

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“…7,18 It can be verified that J E is conserved in the strong sense that [J E , H] = 0. The thermal conductivity therefore only has a Drude part which can be calculated exactly by BA.…”

Section: The Spin Current In the Spin-1/2 Xxz Modelmentioning

confidence: 99%

Conservation laws, integrability, and transport in one-dimensional quantum systems

2011

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In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where the current operator is also orthogonal to the set of conserved quantities associated with integrability but becomes itself conserved in the thermodynamic limit.

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“…It can be approached in two ways. One is by treating the low temperature spinon transport in the framework of a semi-classical kinetic model [1,2,[4][5][6]35], and the other is to use the more microscopic Drude weight approach [12,13,20,25]. In theory, intergrability of the spin-1/2 Heisenberg model results in a divergent κ mag and is described by the product of the thermal Drude weight and a delta function at zero frequency.…”

Section: Resultsmentioning

confidence: 99%

Bond disorder and spinon heat transport in theS=12Heisenberg spin chain compound Sr2CuO3: From

et al. 2014

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We investigate the effect of disorder on the heat transport properties of the S = 1 2 Heisenberg chain compound Sr2CuO3 upon chemically substituting Sr by increasing concentrations of Ca. As Ca occupies sites outside but near the Cu-O-Cu spin chains, bond disorder, i.e. a spatial variation of the exchange interaction J, is expected to be realized in these chains. We observe that the magnetic heat conductivity (κmag) due to spinons propagating in the chains is gradually but strongly suppressed with increasing amount of Ca, where the doping dependence can be understood in terms of increased scattering of spinons due to Ca-induced disorder. This is also reflected in the spinon mean free path which can be separated in a doping independent but temperature dependent scattering length due to spinon-phonon scattering, and a temperature independent but doping dependent spinon-defect scattering length. The latter spans from very large (> 1300 lattice spacings) to very short (∼ 12 lattice spacings) and scales with the average distance between two neighboring Ca atoms. Thus, the Ca-induced disorder acts as an effective defect within the spin chain, and the doping scheme allows to cover the whole doping regime between the clean and the dirty limits. Interestingly, at maximum impurity level we observe, in Ca-doped Sr2CuO3, an almost linear increase of κmag at temperatures above 100 K which reflects the intrinsic low temperature behavior of heat transport in a Heisenberg spin chain. These findings are quite different from that observed for the Ca-doped double spin chain compound, SrCuO2, where the effect of Ca seems to saturate already at intermediate doping levels.

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The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

Cited by 177 publications

References 29 publications

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Conservation laws, integrability, and transport in one-dimensional quantum systems

Bond disorder and spinon heat transport in theS=12Heisenberg spin chain compound Sr2CuO3: From

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