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arXiv:1712.04279

Stochastic dressed wavefunction: a numerically exact solver for bosonic impurity model dynamics within wide time interval

Evgeny Polyakov, Alexey N. Rubtsov

Published Dec 12, 2017• 2 citations
arXivHTMLPDF

Abstract

In the dynamics of driven impurity models, there is a fundamental asymmetry between the processes of emission and absorption of environment excitations: most of the emitted excitations are rapidly and irreversibly scattered away, and only a small amount of them is reabsorbed back. We propose to use a stochastic simulation of the irreversible quantum emission processes in real-time dynamics, while taking into account the reabsorbed virtual excitations by the bath discretization. The resulting method delivers a fast convergence with respect to the number of bath sites, on a wide time interval, without the sign problem.

DOI
10.48550/arxiv.1712.04279

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In the dynamics of driven impurity models, there is a fundamental asymmetry between the processes of emission and absorption of environment excitations: most of the emitted excitations are rapidly and irreversibly scattered away, and only a small amount of them is reabsorbed back. We propose to use a stochastic simulation of the irreversible quantum emission processes in real-time dynamics, while taking into account the reabsorbed virtual excitations by the bath discretization. The resulting method delivers a fast convergence with respect to the number of bath sites, on a wide time interval, without the sign problem.
When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called “sign problem”. In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.
We present a very efficient solver for the general Anderson impurity problem. It is based on the perturbation around a solution obtained from exact diagonalization, using a small number of bath sites. We formulate a perturbation theory which is valid for both weak and strong coupling and interpolates between these limits. Good agreement with numerically exact quantum Monte Carlo results is found for a single bath site over a wide range of parameters. In particular, the Kondo resonance in the intermediate-coupling regime is well reproduced for a single bath site and the lowest-order correction. The method is particularly suited for low temperatures, alleviates analytical continuation of imaginary time data due to the absence of statistical noise and can be generalized to obtain dynamical quantities directly on the real axis.
We present a very efficient solver for the general Anderson impurity problem. It is based on the perturbation around a solution obtained from exact diagonalization, using a small number of bath sites. We formulate a perturbation theory which is valid for both weak and strong coupling and interpolates between these limits. Good agreement with numerically exact quantum Monte Carlo results is found for a single bath site over a wide range of parameters. In particular, the Kondo resonance in the intermediate-coupling regime is well reproduced for a single bath site and the lowest-order correction. The method is particularly suited for low temperatures, alleviates analytical continuation of imaginary time data due to the absence of statistical noise and can be generalized to obtain dynamical quantities directly on the real axis.
Abstract A new approach to theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly bounded on wide time intervals: the occupation of the virtual cloud of quanta. By ‘virtual’ we denote those bath excitations which were emitted by the open system, but eventually will be reabsorbed before any measurement of the bath state. A useful property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and virtual cloud (we call it dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be an arbitrarily large number of the observable quanta (which survive up to measurement), especially if the open system is under driving. However, it turns out that the statistics of the bath-measurement outcomes is classical (in a suitable measurement basis): one can employ a Monte Carlo sampling of these outcomes. Therefore, it is possible to efficiently simulate the dynamics of the observable quantum field. In this work we consider the bath measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The joint evolution of the dressed state and the corresponding outcome is called the dressed quantum trajectory. The Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.
We present a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.
We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.