Thermofield-based chain-mapping approach for open quantum systems

Vega, Inés de; Bañuls, Mari Carmen

doi:10.1103/physreva.92.052116

Cited by 85 publications

(97 citation statements)

References 57 publications

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“…To further simplify the MPS calculation, the leads are described in the form suggested by the thermofield approach [36][37][38], in which the thermal state Wñ | is a pure quantum state, and, even more advantageously, a simple product state on the MPS chain. This implies that the time evolution of the tDMRG quench is started with a product state and, hence, with lowest possible entanglement.…”

Section: Comparison To Nrg-tdmrg Quench Calculationsmentioning

confidence: 99%

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

et al. 2018

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We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage f and a magnetic field B. We investigate the interplay between the shift ( B w ) of the Kondo peak in the spin-resolved density of states (DOS) and the one ( B f ) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as. Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

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Section: Comparison To Nrg-tdmrg Quench Calculationsmentioning

confidence: 99%

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

et al. 2018

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“…A very effective technique to solve low-dimensional correlated systems are matrix product states (MPS), and great progress has been made in recent years to apply MPS techniques to interacting Lindblad equations [72][73][74][75][76][77][78][79][80][81][82][83][84][85]. With this, rather large systems are within reach even though the numerical effort for Hubbard-type problems is rather high due to an extensive entanglement growth with system size [77,85].…”

Section: Markovian Approximations and Beyondmentioning

confidence: 99%

Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation

et al. 2017

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We present a general scheme to map correlated nonequilibrium quantum impurity problems onto an auxiliary open quantum system of small size. The infinite fermionic reservoirs of the original system are thereby replaced by a small number NB of noninteracting auxiliary bath sites whose dynamics is described by a Lindblad equation. Due to the presence of the intermediate bath sites, the overall dynamics acting on the impurity site is non-Markovian.With the help of an optimization scheme for the auxiliary Lindblad parameters, an accurate mapping is achieved, which becomes exponentially exact upon increasing NB. The basic idea for this scheme was presented previously in the context of nonequilibrium dynamical mean field theory. In successive works on improved manybody solution strategies for the auxiliary Lindblad equation, such as Lanczos exact diagonalization or matrix product states, we applied the approach to study the nonequilibrium Kondo regime.In the present paper, we address in detail the mapping procedure itself, rather than the manybody solution. In particular, we investigate the effects of the geometry of the auxiliary system on the accuracy of the mapping for given NB. Specifically, we present a detailed convergence study for five different geometries which, besides being of practical utility, reveals important insights into the underlying mechanisms of the mapping. For setups with onsite or nearest-neighbor Lindblad parameters we find that a representation adopting two separate bath chains is by far more accurate with respect to other choices based on a single chain or a commonly used star geometry. A significant improvement is obtained by allowing for long-ranged and complex Lindblad parameters. These results can be of great value when studying Lindblad-type approaches to correlated systems.

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“…Fig. 3 provides a thorough comparison of the results of the three simulation schemes, thermalized fTEDOPA (TT), thermofield (TF) 38 and standard matrix product operator evolution (MPO) for different inverse temperatures β. The figure is split into three main parts.…”

Section: B Modified Resonant Level Modelmentioning

confidence: 99%

Efficient simulation of open quantum systems coupled to a fermionic bath

et al. 2020

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We present and analyze the fermionic time evolving density matrix using orthogonal polynomials algorithm (fTEDOPA), which enables the numerically exact simulation of open quantum systems coupled to a fermionic environment. The method allows for simulating the time evolution of open quantum systems with arbitrary spectral densities at zero or finite temperatures with controllable and certified error. We demonstrate the efficacy of the method towards the simulation of quintessential fermionic open quantum systems including the resonant level model and quantum dot coupled to an impurity and towards simulating hitherto intractable problems in quantum transport. Furthermore, we demonstrate significant efficiency gains in the computational costs by performing simulations in the Heisenberg picture. Finally, we compare different approaches for simulating finite-temperature situations and provide guidelines for choosing between these approaches. arXiv:1909.09589v1 [quant-ph]

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Thermofield-based chain-mapping approach for open quantum systems

Cited by 85 publications

References 57 publications

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation

Efficient simulation of open quantum systems coupled to a fermionic bath

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