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arXiv:2009.00838 · Physical Review Research

Rectification in nonequilibrium steady states of open many-body systems

Kazuki Yamamoto, Yuto Ashida, Norio Kawakami

Published Dec 8, 2020• 27 citations
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Abstract

We study how translationally invariant couplings between many-particle systems and nonequilibrium baths can be used to rectify particle currents, for which we consider minimal setups to realize bath-induced currents in nonequilibrium steady states of one-dimensional open fermionic systems.We first analyze dissipative dynamics associated with a nonreciprocal Lindblad operator and identify a class of Lindblad operators that are sufficient to acquire a unidirectional current.We show that unidirectional particle transport can, in general, occur when a Lindblad operator is reciprocal provided that the inversion symmetry and the time-reversal symmetry of the microscopic Hamiltonian are broken.We demonstrate this mechanism on the basis of both analytical and numerical approaches, including the Rashba spin-orbit coupling and the Zeeman magnetic field.

DOI
10.1103/physrevresearch.2.043343

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We study how translationally invariant couplings between many-particle systems and nonequilibrium baths can be used to rectify particle currents, for which we consider minimal setups to realize bath-induced currents in nonequilibrium steady states of one-dimensional open fermionic systems.We first analyze dissipative dynamics associated with a nonreciprocal Lindblad operator and identify a class of Lindblad operators that are sufficient to acquire a unidirectional current.We show that unidirectional particle transport can, in general, occur when a Lindblad operator is reciprocal provided that the inversion symmetry and the time-reversal symmetry of the microscopic Hamiltonian are broken.We demonstrate this mechanism on the basis of both analytical and numerical approaches, including the Rashba spin-orbit coupling and the Zeeman magnetic field.
We investigate the generation and control of both charge and spin currents via nonreciprocal dissipative mechanisms in a two-dimensional spinful fermionic atom quantum system with broken inversion and time-reversal symmetries. Within the Gorini-Kossakowski-Sudarshan-Lindblad master equation formalism and using an approach based on the time-dependent generalized Gibbs ensemble, we identify in the weak dissipative coupling regime the minimal set of nonreciprocal jump operators required to induce charge and spin currents and to control both their direction and magnitude. We find that in the presence of finite tunneling, Rashba coupling and magnetic field, the combine application of two jump operators nonreciprocally coupling each spin species to a different spatial direction of motion is sufficient to generate both types of current. Furthermore, by tuning the degree of nonreciprocity of the jump operators we modify the dominant transport mechanism from spin to charge. Finally, we checked that this nonreciprocal current generation mechanism is robust to the application of dephasing noise as even in the presence of this additional dissipative process the steady-state occupation distributions for the quasiparticle modes of the Hamiltonian remains non-trivial, an essential requirement to obtain non-zero currents.
State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/21/21/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.
Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent condition for an open quantum many-body system governed by the Gorini-Kossakowski-Sudarshan-Lindblad dynamics under local drive and/or dissipation to have a quantum independent and identically distributed (i.i.d.) steady state. We present a sufficient condition for a system to have a quantum i.i.d. steady state by identifying a set of operators that commute with arbitrary quantum i.i.d. states. In particular, a set of quantum i.i.d. states is found to be an invariant subset of time evolution superoperators for systems that satisfy the sufficient condition. These findings not only identify a class of models with exactly solvable steady states but also lead to a no-go theorem that precludes quantum entanglement and spatial correlations in a broad class of quantum many-body steady states in a dissipative environment.
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of nonreciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk, Phys. Rev. X 5, 021025 (2015): Nonreciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, so as to make the total interactions directional. Specifically, we consider an interacting spin- (or boson-) model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization, and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms.
Using the Lindblad master equation approach, we investigate the structure of steady-state solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We identify a class of boundary dissipation processes which permits to derive exact steady-state density matrices in the form of graded matrix-product operators. All the solutions factorize in terms of vacuum analogues of Baxter’s Q-operators which are realized in terms of non-unitary representations of certain finite dimensional subalgebras of graded Yangians. We present a unifying framework which allows to solve fermionic models and naturally incorporates higher-rank symmetries. This enables to explain underlying algebraic content behind most of the previously-found solutions.