Spin and energy correlations in the one dimensional spin- Heisenberg model
TL;DR: In this paper, the spin and energy dynamic correlations of the one-dimensional spin-heisenberg model were studied using exact diagonalization numerical techniques, and it was shown that the energy currents decay to finite values at long times.
Abstract: In this paper, we study the spin and energy dynamic correlations of the one-dimensional spin- Heisenberg model, using mostly exact diagonalization numerical techniques. In particular, observing that the uniform spin and energy currents decay to finite values at long times, we argue for the absence of spin and energy diffusion in the easy plane anisotropic Heisenberg model.
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TL;DR: In this article, the authors studied the thermal transport through a quantum spin-1/2 chain heterostructure, which consists of a finite-size chain with two-site isotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite chain.
Abstract: We study the thermal transport through a quantum spin-1/2 chain heterostructure, which consists of a finite-size chain with two-site isotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. After performing Jordan-Wigner transformation, we map the original spin Hamiltonian into a fermion Hamiltonian and express the heat current with a nonequilibrium Green’s function formalism. Then, the heat current as functions of the structure parameters are studied in detail. As a result, we observe that a finite magnetic field applied at the finite-size chain can efficiently induce the heat current asymmetry with ΔΩ (ΔΩ is the magnetic field difference between the finite-size chain and the semi-infinite chains). Accordingly, such a magnetic field can be viewed as a switch in manipulating the heat current.
233 citations
TL;DR: In this paper, a review of the current understanding of transport in one-dimensional lattice models, in particular in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-theart theoretical methods, including both analytical and computational approaches.
Abstract: Over the last decade impressive progress has been made in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable, including the anisotropic spin-1/2 Heisenberg (also called the spin-1/2 XXZ chain) and the Fermi-Hubbard model. Nevertheless, practical computations of correlation functions and transport coefficients pose hard problems from both the conceptual and technical points of view. Only because of recent progress in the theory of integrable systems, on the one hand, and the development of numerical methods, on the other hand, has it become possible to compute their finite-temperature and nonequilibrium transport properties quantitatively. Owing to the discovery of a novel class of quasilocal conserved quantities, there is now a qualitative understanding of the origin of ballistic finite-temperature transport, and even diffusive or superdiffusive subleading corrections, in integrable lattice models. The current understanding of transport in one-dimensional lattice models, in particular, in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-the-art theoretical methods, including both analytical and computational approaches. Among other novel techniques, matrix-product-state-based simulation methods, dynamical typicality, and, in particular, generalized hydrodynamics are covered. The close and fruitful connection between theoretical models and recent experiments is discussed, with examples given from the realms of both quantum magnets and ultracold quantum gases in optical lattices.
213 citations
TL;DR: The thermal conductivity of the spin-1/2 XXZ chain is ballistic at finite temperatures, while in non-integrable models, this quantity is argued to vanish.
Abstract: We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.
120 citations
TL;DR: In this paper, the authors discuss the recent progress and the current status of experimental investigations of spin-mediated energy transport in spin-chain and spin-ladder materials with antiferromagnetic coupling.
Abstract: We discuss the recent progress and the current status of experimental investigations of spin-mediated energy transport in spin-chain and spin-ladder materials with antiferromagnetic coupling. We briefly outline the central results of theoretical studies on the subject but focus mainly on recent experimental results that were obtained on materials which may be regarded as adequate physical realizations of the idealized theoretical model systems. Some open questions and unsettled issues are also addressed.
110 citations
TL;DR: In this article, thermal transport in anisotropic Heisenberg spin chains using the quantum master equation was studied and it was found that thermal rectification changes sign when the external homogeneous magnetic field is varied.
Abstract: We study thermal transport in anisotropic Heisenberg spin chains using the quantum master equation It is found that thermal rectification changes sign when the external homogeneous magnetic field is varied This reversal also occurs when the magnetic field becomes inhomogeneous Moreover, we can tune the reversal of rectification by temperatures of the heat baths, the anisotropy, and size of the spin chains
58 citations
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TL;DR: In this paper, the response of a system to an external disturbance can always be expressed in terms of time dependent correlation functions of the undisturbed system, and the complicated structure the correlation functions must have in order that these descriptions coincide.
871 citations
TL;DR: In this article, the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems was studied and the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous.
Abstract: We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.
440 citations
TL;DR: The boundary energy of a many-body system of fermions on a lattice under twisted boundary conditions is identified as the inverse of the effective charge-carrying mass, or the stiffness, renormalizing nontrivially under interactions due to the absence of Galilean invariance.
Abstract: We identify the boundary energy of a many-body system of fermions on a lattice under twisted boundary conditions as the inverse of the effective charge-carrying mass, or the stiffness, renormalizing nontrivially under interactions due to the absence of Galilean invariance. We point out that this quantity is a sensitive and direct probe of the metal-insulator transitions possible in these systems, i.e., the Mott-Hubbard transition or Density-wave formation. We calculate exactly the stiffness, or the effective mass, in the 1D Heisenberg-Ising ring and the 1D Hubbard model by using the ansatz of Bethe. For the Hubbard ring we also calculate a spin stiffness by extending the nested ansatz of Bethe-Yang to this case.
361 citations
TL;DR: In this article, the thermodynamics of the one-dimensional Heisenberg-Ising model for I.JI < 1 as well as of the X-Y-Z model is reduced to a set of non-linear integral equations under some plausible assumptions.
Abstract: The thermodynamics of the one-dimensional Heisenberg-Ising model for I.JI<1 as well as of the X-Y-Z model is reduced to a set of non-linear integral equations under some plausible assumptions. It is remarkable that the number of unknown functions involved in them becomes finite when rr/cos-1.J is a rational number for the Heisenberg-Ising model and when Kz/t; is a rational number for the X-Y-Z model (where coupling constants J"', Ju and J. are parametrized by f;, l, and J. as J:c=J. en (2t;,l) and Jy=J. dn (2t;,l); 12l20, K!22C20, and K 1 is the complete elliptic integral· of the first kind of modulus l). The validity of our theory has been confirmed by the high-temperature expansion of the free energy through the second term for a general value of .J and through the fourth term for .J=!.
360 citations
TL;DR: In this article, the authors studied the X-Y model of a linear chain of spins in the presence of a magnetic field h along the z axis and derived an expression for the time-dependent correlation function ϱ z R (β, t) of the z -components of spins separated by an arbitrary number R of lattice sites.
278 citations