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arXiv:2112.15549 · Physical Review Letters

Vertex-Based Diagrammatic Treatment of Light-Matter-Coupled Systems

Aaram J. Kim, Katharina Lenk, Jiajun Li, Philipp Werner, Martin Eckstein

Published Jan 19, 2023• 7 citations
arXivHTMLPDF

Abstract

We propose a diagrammatic Monte Carlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.

DOI
10.1103/physrevlett.130.036901

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We propose a diagrammatic Monte Carlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.
We present a quantum impurity solver based on a pseudoparticle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach (A. J. Kim et al., arXiv:2112.15549) is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign-oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.
We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the Grassmannian Hubbard-Stratonovich transformation, our construction is based on Wick's theorem and a recursive procedure to group contractions into effective connected vertices that are nonperturbative in all local physics and can be calculated exactly. The resulting expansion is described by simple diagrammatic rules that make it suitable for systematic treatment via stochastic sampling. Benchmarks against numerical linked cluster expansion display excellent agreement.
We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative quantum impurity models. These are small open quantum systems with interaction and local Markovian dissipation, coupled to a large quantum bath. Our algorithm samples the hybridization expansion formulated on a single real-time contour, rather than on the double Keldysh one, as it naturally arises in the thermofield/vectorized representation of the Lindblad dynamics. We show that local Markovian dissipation generally helps the convergence of the diagrammatic Monte Carlo sampling by reducing the sign problem, thus allowing to reach longer timescales as compared to the conventional unitary case. We apply our method to an Anderson impurity model in the presence of local dephasing and discuss its effect on the charge and spin dynamics of the impurity.
We develop a method to study quantum impurity models, small interacting quantum systems bilinearly coupled to an environment, in the presence of an additional Markovian quantum bath, with a generic nonlinear coupling to the impurity. We aim at computing the evolution operator of the reduced density matrix of the impurity, obtained after tracing out all the environmental degrees of freedom. First, we derive an exact real-time hybridization expansion for this quantity, which generalizes the result obtained in the absence of the additional Markovian dissipation and which could be amenable to stochastic sampling through diagrammatic Monte Carlo. Then, we obtain a Dyson equation for this quantity and we evaluate its self-energy with a resummation technique known as the noncrossing approximation. We apply this novel approach to a simple fermionic impurity coupled to a zero temperature fermionic bath and in the presence of Markovian pump, losses, and dephasing.
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We describe a controllable and unbiased strong coupling technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous works that generally rely on the Grassmannian Hubbard-Stratonovich transformation, our construction is based on Wicks theorem and a recursive procedure to group contractions into effective irreducible vertices that are non-perturbative in all local physics and can be calculated exactly. The resulting expansion is described by simple diagrammatic rules that make it suitable for systematic treatment, and is independent of model parameters or doping. Comparison to approaches based on fermionization techniques indicates a dramatic advantage in terms of computational complexity, which will result in access to completely new parameter regimes and phenomena.