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arXiv:1707.08823 · Physical Review Letters

Perfect Diode in Quantum Spin Chains

Vinitha Balachandran, Giuliano Benenti, Emmanuel Pereira, Giulio Casati, Dario Poletti

Published May 16, 2018• 75 citations
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Abstract

We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

DOI
10.1103/physrevlett.120.200603

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We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.
Balachandran et al. [Phys. Rev. Lett. 120, 200603 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200603] presented a segmented XXZ spin chain with zero anisotropy in one half and a large anisotropy on the other half that gave rise to a spin current rectification which is perfect in the thermodynamic limit. Here we extend the previous study to segmented chains with interacting integrable as well as nonintegrable halves, considering even cases in which no ballistic transport can emerge in either half. We demonstrate that, also in this more general case, it is possible to obtain giant rectification when the two interacting half chains are sufficiently different. We also show that the mechanism causing this effect is the emergence of an energy gap in the excitation spectrum of the out-of-equilibrium insulating steady state in one of the two biases. Finally, we demonstrate that in the thermodynamic limit there is no perfect rectification when each of the two half chains is interacting.
Transport and spectral properties of the XX+++XXZ diode and stability to dephasing
We study the transport and spectral property of a segmented diode formed by an XX+XXZ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has signatures pointing toward the existence of three different transport regimes depending on the value of the anisotropy: ballistic, diffusive, and insulating. In forward bias we observe two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging toward different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases, and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of quantum Zeno physics.
We study the transport and spectral property of a segmented diode formed by an XX+XXZXX+XXZXX+XXZ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has signatures pointing toward the existence of three different transport regimes depending on the value of the anisotropy: ballistic, diffusive, and insulating. In forward bias we observe two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging toward different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases, and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of quantum Zeno physics.
Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.
In XXZ chains with large enough interactions, spin transport can be significantly suppressed when the bias of the dissipative driving becomes large enough. This phenomenon of negative differential conductance is caused by the formation of two oppositely polarized ferromagnetic domains at the edges of the chain. Here, we show that this many-body effect, combined with a non-uniform magnetic field, can allow for a high degree of control of the spin current. In particular, by studying all of the possible shapes of local magnetic fields potentials, we find that a configuration in which the magnetic field points up for half of the chain and down for the other half, can result in giant spin-current rectification, for example, up to 108 for a system with only 8 spins. Our results show clear indications that the rectification can increase with the system size.
We study spin transport in nonitinerant one-dimensional quantum spin chains. Motivated by possible applications in spintronics, we consider rectification effects in both ferromagnetic and antiferromagnetic systems. We find that the crucial ingredients in designing a system that displays a nonzero rectification current are an anisotropy in the exchange interaction of the spin chain combined with an offset magnetic field. For both ferromagnetic and antiferromagnetic systems we can exploit the gap in the excitation spectrum that is created by a bulk anisotropy to obtain a measurable rectification effect at realistic magnetic fields. For antiferromagnetic systems we also find that we can achieve a similar effect by introducing a magnetic impurity, obtained by altering two neighboring bonds in the spin Hamiltonian.