Thermal transport in one-dimensional spin gap systems

Orignac, Edmond; Читра, Р.; Citro, Roberta

doi:10.1103/physrevb.67.134426

Cited by 79 publications

(96 citation statements)

References 55 publications

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“…This universal behavior was also found in gen- * E-mail address: sakai@stat.phys.titech.ac.jp † E-mail address: kluemper@physik.uni-wuppertal.de eral systems in which the low-energy excitations are described by a c = 1 conformal field theory. 13,14) In the massive regime, we find that D th (T ) ∼ exp(−δ/T )/ √ T where δ is the one-spinon (respectively one-magnon) excitation gap for the antiferromagnetic (respectively ferromagnetic) regime. …”

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confidence: 92%

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Sakai

Klümper

2005

J. Phys. Soc. Jpn.

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Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg chain. The energy current is related to one of the non-trivial conserved quantities underlying integrability and therefore both the diagonal and off diagonal dynamical correlations of spin and energy current diverge. The energy-energy and spin-energy current correlations at finite temperatures are exactly calculated by a lattice path integral formulation. The low-temperature behavior of the thermomagnetic (magnetic Seebeck) coefficient is also discussed. Due to effects of strong correlations, we observe the magnetic Seebeck coefficient changes sign at certain interaction strengths and magnetic fields.KEYWORDS: transport properties, thermal conductivity, magnetothermal effect, Seebeck coefficient, Heisenberg chainIn the last two decades, 1D strongly correlated systems have attracted immense theoretical and experimental interest. One of the reasons stems from their unusual static and dynamical properties peculiar to 1D systems. The spin-1/2 Heisenberg chain is one of the most fundamental solvable models for 1D magnetic insulators and has served as a testing ground for many approaches.Recently, transport properties of low-dimensional strongly correlated quantum systems have been extensively studied from both theoretical and experimental sides.1) Among them anomalously enhanced thermal conductivity 2-4) and unconventional large spin diffusion constants 5) have been reported in experiments on one-or quasi 1D materials with weak interchain interactions. These observations indicate the existence of nondissipative transport properties in 1D quantum systems. Theoretically, the existence of such anomalous properties has also been pointed out especially in quantum integrable systems. 6) One of the criteria for anomalous transport is the existence of a non-zero Drude weight.In particular for the spin-1/2 XXZ chain, the Drude weight for the spin transport has been obtained by Zotos for finite temperature at zero magnetic field.7) In the massless regime, the Drude weight is non-zero and hence the spin transport is non-dissipative. In the massive regime without magnetic field a similar treatment yields zero Drude weight at any temperature implying dissipative spin transport. This feature, however, contradicts with numerical or field theoretical approaches and is still debated. 8-10)On the other hand, the thermal Drude weight D th (T ) for zero magnetic field has been recently obtained by the Bethe ansatz showing that the thermal transport is non-dissipative in both massless and massive regimes.11, 12) At low-temperature D th (T ) behaves as D th (T ) = πv F T /3 where v F is the velocity of excitations. This universal behavior was also found in gen- * E-mail address: sakai@stat.phys.titech.ac.jp † E-mail address: kluemper@physik.uni-wuppertal.de eral systems in which the low-energy excitations are described by a c = 1 conformal field theory. 13,14) In the massive regime, we find that D th (T ) ∼ exp(−δ/T )/ √ T where δ is the one-spinon (respectively one...

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confidence: 92%

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Sakai

Klümper

2005

J. Phys. Soc. Jpn.

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“…[7][8][9][10][11] . Very high purity Sr 2 CuO 3 , SrCuO 2 compounds, which are very good realizations of this model as the interchain coupling is very weak, have confirmed this expectation.…”

Section: Introductionmentioning

confidence: 99%

“…This is in strong contrast to the two orders of magnitude smaller conductivity along the rung direction which only shows the low temperature phonon related peak 18 . The thermal conductivity of spin ladders systems, including phonons and impurities, has been approached theoretically mostly by low energy effective models 10,20 and numerical simulations 21 . The goal of this work is to sort out the effect of triplon-triplon scattering in limiting the thermal conduction along the leg direction.…”

Section: Introductionmentioning

confidence: 99%

Thermal conductivity of anisotropic spin-1/2 two leg ladder: Green’s function approach

et al. 2014

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We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of legs. The possible effect of spin-orbit coupling and crystalline electric field are investigated in terms of anisotropies in the Heisenberg interactions on both leg and rung couplings. The original spin ladder is mapped to a bosonic model via a bond-operator transformation where an infinite hard-core repulsion is imposed to constrain one boson occupation per site. The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. The thermal conductivity is found to be monotonically decreasing with temperature due to increased scattering among triplet excitations at higher temperatures. A tiny dependence of thermal transport on the anisotropy in the leg direction at low temperatures is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Our results reach asymptotically the ballistic regime of the spin -1/2 Heisenberg chain and compare favorably well with exact diagonalization data.

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“…[4]. For recent studies of transport in spin ladders see [6][7][8][9][10][11]. With rapidly progressing experimental cold atoms techniques [12], transport properties of Fermi gases [13] as well as of the Hubbard model [14] have actually been measured.…”

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Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder

Žnidarič

2013

Phys. Rev. Lett.

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We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is found to be diffusive. This shows that (i) quantum chaotic systems can possess ballistic subspaces, and (ii) diffusive and ballistic transport modes can coexist in a rather simple nonintegrable model. In the limit of an infinite anisotropy in rungs the system studied is equivalent to the one-dimensional Hubbard model.Transport properties of simple spin ladders are interesting for two reasons. On one hand they are realized in a number of materials [1][2][3], on the other they serve as model systems on which theoretical ideas can be tested. For instance, the Hubbard model -a paradigmatic model of strongly correlated electrons -is equivalent to a ladder system. One of the most actively investigated areas of statistical physics in recent years is nonequilibrium properties of strongly correlated systems. In particular, there is a long quest to understand transport properties of systems from first principles, e.g. [4]. For recent studies of transport in spin ladders see [6][7][8][9][10][11]. With rapidly progressing experimental cold atoms techniques [12], transport properties of Fermi gases [13] as well as of the Hubbard model [14] have actually been measured. Perhaps the simplest question, is a given model diffusive or ballistic, seems to be for most models too difficult to rigorously answer, even if the system is integrable, an example being for instance the gapped one-dimensional Heisenberg model, see, e.g. [5]. A powerful method to prove ballistic transport is by bounding the time-averaged current autocorrelation function using constants of motion, the so-called Mazur's inequality [15,16]. Because quantum integrability is usually defined [17] by the existence of an infinite set of local conserved quantities it often leads to ballistic transport. In fact, all proved ballistic systems are integrable and possess either local [16] or quasilocal [18] conserved quantities that have nonzero overlap with the current. Based on this one is tempted to conclude that ballistic transport is possible only in integrable systems and that chaotic ones display diffusion. However, as we shall show, this widely held belief is not correct. Studying a class of spin ladder systems, which includes nonintegrable as well as integrable instances (the Hubbard model), we explicitly show the existence of ballistic transport. This provides a new mechanism of ballistic transport, different from the so-far known ballistic transport in integrable systems.XX-ladder.-We shall study the so-called XX spin ladder composed of two coupled spin-1/2 chains in which the nearest-neighbor coupling along two chains (legs) is of the XX type, while the interchain coupling (rungs) is of the XXZ type. We shall show that the XX ladder, regardless of the value of two parameters J and ∆, possesses a number of ballistic...

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Thermal transport in one-dimensional spin gap systems

Cited by 79 publications

References 55 publications

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Thermal conductivity of anisotropic spin-1/2 two leg ladder: Green’s function approach

Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder

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