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International Journal of Modern Physics B

One-dimensional quantum spin heterojunction as a thermal switch

Chuan-Jing Yang, Li-Hui Jin, Wei‐Jiang Gong

Published Mar 1, 2016• 1 citation
Publisher

Abstract

We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.

DOI
10.1142/s0217979216500272

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We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.
We study heat transport in a one-dimensional inhomogeneous quantum spin-1/2 system. It consists of a finite-size XXXXXX spin chain coupled at its ends to semi-infinite XXXXXX and XYXYXY chains at different temperatures, which play the role of heat and spin reservoirs. After using the Jordan-Wigner transformation we map the original spin Hamiltonian into a fermionic Hamiltonian, which contains normal and pairing terms. We find the expressions for the heat currents and solve the problem with a nonequilibrium Green's-function formalism. We analyze the behavior of the heat currents as functions of the model parameters. When finite magnetic fields are applied at the two reservoirs, the system exhibits rectifying effects in the heat flow.
The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps the system onto a non-interacting fermion gas. The exact excitation spectrum is determined by reducing the problem to a diagonalization of a block matrix, and it is shown that it is numerically identical to the one obtained by using the approximate transfer matrix method . The induced magnetization and the susceptibility χzzχ^{zz}χzz are determined as a function of the transverse field, and it is shown that, at T=0, the susceptibility presents multiple singularities. It is also shown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chain.
The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (SP) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize theSPtransition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.
We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.
The anisotropic quantum XY spin chain in a modulating magnetic field incommensurate with the periodicity of the chain is studied. Using Jordan-Wigner transformation, the model is mapped to a tight-binding model in fermions. In the absence of symmetry-breaking terms, the fermion model is identical with the well-known Harper equation exhibiting extended and localized phases with the onset of transition being a critical point with fractal spectrum and wave functions. The effect of O(2) symmetry breaking is to fatten the critical point resulting in a critical phase with power-law localization existing in a finite window of size determined by the anisotropy. In this three-phase spectral diagram, the transition from critical to localized phase is accompanied by the magnetic transition to long-range order. Furthermore, the scaling properties of the fractal spectrum vary in the critical phase. This leads to interesting consequences on the low-temperature thermodynamical properties of the system.
We study a one-dimensional anisotropic XXZ Heisenberg spin-12\frac{1}{2}21​ chain with weak random fields hizSiz{h}_{i}^{z}{S}_{i}^{z}hiz​Siz​ by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First, we reinvestigate the phase diagram of the system in terms of dimensionless disorder $\ensuremath{\gamma}=\ensuremath{\langle}{h}^{2}\ensuremath{\rangle}/{J}^{2}\ensuremath{\ll}1$ and anisotropy parameter $\mathrm{\ensuremath{\Delta}}={J}_{z}/{J}_{xy}$, we find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws, and compare it with previously obtained numerical and analytical results. Then we use the diagram technique in terms of plasmon excitations to study the low-temperature $(T\ensuremath{\ll}J)$ behavior of heat conductivity $\ensuremath{\kappa}$ and spin conductivity $\ensuremath{\sigma}$ in this power-law phase. The obtained Lorentz number $L\ensuremath{\equiv}\ensuremath{\kappa}/\ensuremath{\sigma}T$ differs from the value derived earlier by means of the memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.