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arXiv:1510.00031

Non--Equilibrium Transport in Open Quantum Systems via Dynamically Constrained non--Hermitian Boundary Domains

Justin E. Elenewski, Yanxiang Zhao, Hanning Chen

Published Sep 30, 2015• 0 citations
arXivHTMLPDF

Abstract

The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium steady states using non--Hermitian source and sink potentials alongside the application of dynamic density constraints during wavefunction propagation. This scheme adds negligible cost to existing computational methods while exhibiting exceptional stability and numerical accuracy.

DOI
10.48550/arxiv.1510.00031

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The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium steady states using non--Hermitian source and sink potentials alongside the application of dynamic density constraints during wavefunction propagation. This scheme adds negligible cost to existing computational methods while exhibiting exceptional stability and numerical accuracy.
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Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization or purification of the system density matrix, requiring large qubit resources and long-range coupling. In this work, we present a novel variational quantum algorithm that efficiently searches for non-equilibrium steady states by simulating the operator-sum form of the Lindblad equation. By introducing the technique of random measurement, we are able to estimate the nonlinear cost function while reducing the required qubit resources by half compared to previous methods. Additionally, we prove the existence of the parameter shift rule in our variational algorithm, enabling efficient updates of circuit parameters using gradient-based classical algorithms. To demonstrate the performance of our algorithm, we conduct simulations for dissipative quantum transverse Ising and Heisenberg models, achieving highly accurate results. Our approach offers a promising solution for effectively addressing non-equilibrium steady state problems while overcoming computational limitations and implementation challenges.
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral for the generating function of the nonequilibrium current. Self-energies due to the leads, being nonlocal in time, are fully taken into account within a finite memory time, thereby including non-Markovian effects, and numerical results are extrapolated both to vanishing (Trotter) time discretization and to infinite memory time. This extrapolation scheme converges except at very low temperatures, and the results are then numerically exact. The method is applied to nonequilibrium transport through an Anderson dot.
A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time evolution cannot be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, with the result that chains of length of the order of n≈100 spins are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. A previously conjectured relation between quantum chaos and normal transport is re-confirmed with high accuracy for much larger systems.
The study of quantum transport is important for understanding the propagation of electronic currents in matter on nanoscopic and mesoscopic scales. We discuss the use of a novel orthogonal wavepacket basis set for non-equilibrium many-electron transport problems. The basis is constructed from stroboscopic images of the continuous time evolution of an initial set of wavepackets. This built-in time-related feature of the basis makes it efficient for practical computational schemes and also suitable for providing physical insight into transport phenomena. We demonstrate how the wavepacket basis can be used to recover the exact non-interacting ground state density for systems with a localised potential barrier. Using a Hartree-like electron-electron interaction, we then implement the basis in two 1D transport problems: the establishment of a steady current and the abrupt switching on of a potential barrier in a system in its ground state. Finally, we discuss the effect of spurious self-interaction on the propagation of the wavepackets.
Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.