Simulating generic spin-boson models with matrix product states

Wall, Michael L.; Safavi-Naini, Arghavan; Rey, Ana María

doi:10.1103/physreva.94.053637

Cited by 56 publications

(40 citation statements)

References 107 publications

(125 reference statements)

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“…[100][101][102][103] for examples of recent developments). References [60,[104][105][106] discuss MPS methods that are specifically designed for electron-phonon coupled systems. These questions are left for future work.…”

Section: Discussionmentioning

confidence: 99%

Eigenstate thermalization and quantum chaos in the Holstein polaron model

et al. 2019

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The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.

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Section: Discussionmentioning

confidence: 99%

Eigenstate thermalization and quantum chaos in the Holstein polaron model

et al. 2019

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“…[23]. This correspondence proves to be useful for our purposes, since many analytical and numerical techniques have been developed for the spin-boson model including the generalized master equation 31 , stochastic Schrödinger equation description 3 , Bethe-ansatz 32 solution, numerical renormalization group 7,33 , exact mapping between the spin-boson and the Kondo model 10 , and most recently tensor network methods 34,35 .…”

Section: Introductionmentioning

confidence: 95%

Driven quantum dot coupled to a fractional quantum Hall edge

Wagner¹,

Nguyen²,

Kovrizhin

et al. 2019

Phys. Rev. B

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In relation to recent electron quantum optics experiments we study a model of a quantum dot coupled to a fractional quantum Hall edge driven out of equilibrium by a time-dependent bias voltage. In this setup we take into account short-range interactions between the dot and the edge and calculate the time evolution of the current through the dot using a mapping to a spin-boson problem. Here we present the details of this mapping together with the discussion of numerical results, and their comparison with the perturbative calculations.

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“…While the spin-boson model has been extensively studied both in the presence [6,8,[22][23][24][25][26][27][28][29][30][31] and absence [2,8,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] of external driving, the spin-fermion model is less well understood. In particular, the interplay of external driving on the system and the system-environment coupling strength is less explored due to the limitations of both theoretical and numerical tools.…”

Section: Introductionmentioning

confidence: 99%

Dissipative features of the driven spin-fermion system

Chen

2019

Phys. Rev. B

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We study a generic spin-fermion model, where a two-level system (spin) is coupled to two metallic leads with different chemical potentials, in the presence of monochromatic driving fields. The real-time dynamics of the system is simulated beyond the Markovian limit by an iterative numerically exact influence functional path integral method. Our results show that although both system-bath coupling and chemical potential difference contribute to dissipation, their effects are distinct. In particular, under certain drivings the asymptotic Floquet states of the system exhibit robustness against a range of system-bath coupling strength: the asymptotic behaviors of the system are insensitive to different system-bath coupling strength, while they are highly tunable by the chemical potential difference of baths. Further simulations show that such robustness may be essentially a result of the interplay between driving, bath electronic structure and system-bath coupling. Therefore the robustness could break down depending on the characteristics of the interplay. In addition, under fast linearly polarized driving the quantum stochastic resonance is demonstrated that stronger system-bath coupling (stronger dissipation) enhances rather than suppresses the amplitude of coherent oscillations of the system. arXiv:1909.13276v2 [cond-mat.mes-hall]

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Simulating generic spin-boson models with matrix product states

Cited by 56 publications

References 107 publications

Eigenstate thermalization and quantum chaos in the Holstein polaron model

Eigenstate thermalization and quantum chaos in the Holstein polaron model

Driven quantum dot coupled to a fractional quantum Hall edge

Dissipative features of the driven spin-fermion system

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