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We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach is based on the structure of entanglement in the NESS. With reasonable physical assumptions, we show that a NESS close to local equilibrium is lightly entangled and can be represented via a computationally efficient tensor network. We further argue that the NESS may be found by dynamically evolving the system within a manifold of appropriate low entanglement states. A physically realistic law of dynamical evolution is Markovian open system dynamics, or the Lindblad equation. We explore this approach in a well-studied free fermion model where comparisons with the literature are possible. We study both electrical and thermal currents with and without disorder, and compute entropic quantities such as mutual information and conditional mutual information. We conclude with a discussion of the prospects of this approach for the challenging problem of transport in strongly interacting systems, especially those with disorder.
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We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. We present evidence that the eigenstates of non-equilibrium steady state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is non-integrable, just as eigenstates of Gibbs density matrices are conjectured to do in equilibrium. This generalized ETH, which we call NESS-ETH, can be used to obtain representative pure states that reproduce the expectation values of few-body operators in the NESS. The density matrices of these representative pure states can be further interpreted as weak solutions of the GKLS Master Equation. Additionally, we explore the validity and breakdown of NESS-ETH in the presence of symmetries, integrability and many-body localization in the bulk Hamiltonian.
This Article investigates dissipative preparation of entangled non-equilibrium steady states (NESS). We construct a collision model where the open system consists of two qubits which are coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of qubits interacting with the open system. The model can be studied in different dynamical regimes: with and without environmental memory effects. We report that only a certain bath temperature range allows for entangled NESS. Furthermore, we obtain minimal and maximal critical values for the heat current through the system. Surprisingly, quantum memory effects play a crucial role in the long time limit. First, memory effects broaden the parameter region where quantum correlated NESS may be dissipatively prepared and, secondly, they increase the attainable concurrence. Most remarkably, we find a heat current range that does not only allow but guarantees that the NESS is entangled. Thus, the heat current can witness entanglement of non-equilibrium steady states.
We examine how systems in non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.
Modern methods for sampling rugged landscapes in state space mainly rely on knowledge of the relative probabilities of microstates, which is given by the Boltzmann factor for equilibrium systems. In principle, trajectory reweighting provides an elegant way to extend these algorithms to non-equilibrium systems, by numerically calculating the relative weights that can be directly substituted for the Boltzmann factor. We show that trajectory reweighting has many commonalities with Rosenbluth sampling for chain macromolecules, including practical problems which stem from the fact that both are iterated importance sampling schemes: for long trajectories the distribution of trajectory weights becomes very broad and trajectories carrying high weights are infrequently sampled, yet long trajectories are unavoidable in rugged landscapes. For probing the probability landscapes of genetic switches and similar systems, these issues preclude the straightforward use of trajectory reweighting. The analogy to Rosenbluth sampling suggests though that path ensemble methods such as PERM (pruned-enriched Rosenbluth method) could provide a way forward.
We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological quantum field theories (TQFTs). By formulating the order parameters in the Hilbert space of state sum TQFT, we establish the connection between the quantized non-local order parameters and the underlying field theory, clarifying the nature of the order parameters as topological invariants. We also formulate several entanglement measures including the entanglement negativity on state sum spin TQFT, and describe the exact correspondence of the entanglement measures to path integrals on a closed surface equipped with a specific spin structure.
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