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arXiv:1509.02914 · Physical Review Letters

Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

A. L. Chernyshev, A. V. Rozhkov

Published Jan 8, 2016• 23 citations
arXivHTMLPDF

Abstract

The heat transport in a system of S=1/2 large-J Heisenberg spin chains, describing closely Sr(2)CuO(3) and SrCuO(2) cuprates, is studied theoretically at T≪J by considering interactions of the bosonized spin excitations with optical phonons and defects. Treating rigorously the multiboson processes, we derive a microscopic spin-phonon scattering rate that adheres to an intuitive picture of phonons acting as thermally populated defects for the fast spin excitations. The mean-free path of the latter exhibits a distinctive T dependence reflecting a critical nature of spin chains and gives a close description of experiments. By the naturalness criterion of realistically small spin-phonon interaction, our approach stands out from previous considerations that require large coupling constants to explain the data and thus imply a spin-Peierls transition, absent in real materials.

DOI
10.1103/physrevlett.116.017204

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The heat transport in a system of S=1/2 large-J Heisenberg spin chains, describing closely Sr(2)CuO(3) and SrCuO(2) cuprates, is studied theoretically at T≪J by considering interactions of the bosonized spin excitations with optical phonons and defects. Treating rigorously the multiboson processes, we derive a microscopic spin-phonon scattering rate that adheres to an intuitive picture of phonons acting as thermally populated defects for the fast spin excitations. The mean-free path of the latter exhibits a distinctive T dependence reflecting a critical nature of spin chains and gives a close description of experiments. By the naturalness criterion of realistically small spin-phonon interaction, our approach stands out from previous considerations that require large coupling constants to explain the data and thus imply a spin-Peierls transition, absent in real materials.
We study the low-temperature transport properties of clean one-dimensional spin-12\frac{1}{2}21​ chains coupled to phonons. Due to the presence of approximate conservation laws, the heat current decays very slowly giving rise to an exponentially large heat conductivity, $\ensuremath{\kappa}\ensuremath{\sim}{e}^{{T}^{*}/T}.$ As a result of an interplay of umklapp scattering and spinon-phonon coupling, the characteristic energy scale T∗{T}^{*}T∗ turns out to be of order ${\ensuremath{\Theta}}_{D}/2,$ where ${\ensuremath{\Theta}}_{D}$ is the Debye energy, rather than the magnetic exchange interaction JJJ---in agreement with recent measurements in SrCuO compounds. A large magnetic field h strongly affects the heat transport by two distinct mechanisms. First, it induces a linear spinon-phonon coupling, which alters the nature of the $\stackrel{\ensuremath{\rightarrow}}{T}0$ fixed point: the elementary excitations of the system are composite spinon-phonon objects. Second, the change of the magnetization and the corresponding change of the wave vector of the spinons strongly affects the way in which various umklapp processes can relax the heat current, leading to a characteristic fractal-like spiky behavior of $\ensuremath{\kappa}(T,h)$ as a function of h.
Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tDMRG) can be used to simulate isolated spin chains, the coupling with phonons make simulations significantly more challenging. The recently developed multisite tensor network path integral (MS-TNPI) method builds a framework for simulating the dynamics in extended open quantum systems by combining ideas from tDMRG and Feynman-Vernon influence functional. This MS-TNPI is used to characterize dynamics in open, extended quantum systems. Simulations are done with the commonly used sub-Ohmic, Ohmic and super-Ohmic spectral densities describing the phononic bath. We show that while the transport in presence of impurities eventually becomes diffusive, the exact details are dependent on the specifics of the interactions and amount of impurities. In contrast, the presence of a bath makes the transport diffusive irrespective of the parameters characterizing the bath.
We revisit the problem of the spin-Peierls instability in a one-dimensional spin-12\frac{1}{2}21​ chain coupled to phonons. The phonons are treated within the mean-field approximation. We use bosonization techniques to describe the gapped spin chain and then use the thermodynamic Bethe ansatz to obtain quantitative results for the thermodynamics of the spin-Peierls system in a whole range of temperature. This allows us to predict the behavior of the specific heat and the magnetic susceptibility in the entire dimerized phase. We study the effect of small magnetic fields on the transition. Moreover, we obtain the parameters of the Landau-Ginzburg theory describing this continuous phase transition near the critical point.
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We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}256N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling $\ensuremath{\alpha}$ exceeds a critical value ${\ensuremath{\alpha}}_{c}$. Using sum rules, we show that the phonon spectral function has divergent (for $N\ensuremath{\rightarrow}\ensuremath{\infty}$) weight extending to zero frequency for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$. The phonon correlations decay with distance rrr as 1/r1/r1/r. This behavior is characteristic for all $0<\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ and the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$ phonon does not soften (to zero frequency) at $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\alpha}}_{c}$.
The one-dimensional spin-1/2 Heisenberg model with nearest-neighbour interaction coupled to Einstein phonons is of interest for the understanding of materials which show the spin-Peierls phase transition. I examined this model by performing a finite-temperature quantum Monte Carlo simulation by using the very efficient loop algorithm. I studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-spin correlation function of this model for various spin-phonon couplings and phonon frequencies. In particular I gave evidence for a global effective spin-spin coupling and for the transition from a gapless to the massive phase by studying the finite-size behavior of the magnetic susceptibility.