Many-Body Quantum State Diffusion for Non-Markovian Dynamics in Strongly Interacting Systems

Flannigan, Stuart; Damanet, François; Daley, Andrew J.

doi:10.1103/physrevlett.128.063601

Cited by 33 publications

(27 citation statements)

References 55 publications

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“…If, for instance in the case of strong coupling, a larger hierarchy is required to obtain accurate results, one could employ MPS techniques in order to keep the state dimension under control. Recently, such strategies have been successfully applied within the hierarchical expansion of Gaussian NMQSD [43,44]. As a future perspective, it would be interesting to benchmark whether the proposed hierarchical scheme is useful from a numerical perspective, compared to other methods such as ML-MCTDH or ACE.…”

Section: Discussionmentioning

confidence: 99%

Non-Markovian Quantum State Diffusion for Spin Environments

Link¹,

Luoma²,

Strunz³

2022

Preprint

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We introduce a theory of non-Markovian quantum state diffusion (NMQSD) for quantum systems coupled to a class of non-Gaussian environments consisting of spins. This allows us to express the time evolved reduced state of the system as the average of an ensemble of stochastically evolving pure states. We develop the theory for arbitrary linear spin environments at zero and also at finite temperature. Moreover, we introduce a hierarchical expansion which constitutes a method to numerically compute the time evolution of the stochastic pure states, and thus to solve the open system problem.

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Section: Discussionmentioning

confidence: 99%

Non-Markovian Quantum State Diffusion for Spin Environments

Link¹,

Luoma²,

Strunz³

2022

Preprint

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“…( 5) is exceptionally challenging because of the last term of the right-hand side, which is non-local in time [103]. This problem can be solved efficiently by the HOPS method [93,99], where one defines:…”

Section: Hierarchy Of Pure Statesmentioning

confidence: 99%

“…This becomes even more relevant given the remarkable development of experimental platforms such as ultracold quantum gases [71][72][73][74][75], high-quality electromagnetic cavities [76][77][78][79][80][81], time-resolved pumpprobe experiments on photosynthetic complexes [82], and large arrays of superconducting qubits [83][84][85][86][87][88][89]. These platforms make it possible to study the effects of dissipation in cleaner environments but also to investigate the possibility to exploit them as a resource to engineer new phenomena in OQS [90][91][92][93][94]. This work aims to close the gap between the necessity of unbiased descriptions of OQS on the one hand, and numerically efficient lattice representations, operating on the required large local Hilbert spaces on the other hand.…”

mentioning

confidence: 99%

“…This work aims to close the gap between the necessity of unbiased descriptions of OQS on the one hand, and numerically efficient lattice representations, operating on the required large local Hilbert spaces on the other hand. For that purpose, we combine a recently introduced mapping of bosonic Hilbert spaces [97,98] with well-known techniques to describe lattice OQS [93,94,99,100], obtaining powerful, MPS-based tools. We test and benchmark the obtained methods at the example of the dissipative Hubbard-Holstein model in a large parameter space and explore their applicabilities as a function of the electron-phonon coupling and dissipation strength.…”

mentioning

confidence: 99%

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Metallicity in the Dissipative Hubbard-Holstein Model: Markovian and Non-Markovian Tensor-Network Methods for Open Quantum Many-Body Systems

Moroder¹,

Grundner²,

Damanet³

et al. 2022

Preprint

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The Hubbard-Holstein Hamiltonian describes a prototypical model to study the transport properties of a large class of materials characterized by strong electron-phonon coupling. Even in the one-dimensional case, simulating the quantum dynamics of such a system with high accuracy is very challenging due to the infinite-dimensionality of the phononic Hilbert spaces. The difficulties tend to become even more severe when considering the incoherent coupling of the phonon-system to a practically inevitable environment. For this reason, the effects of dissipation on the metallicity of such systems have not been investigated systematically so far. In this article, we close this gap by combining the non-Markovian hierarchy of pure states method and the Markovian quantum jumps method with the newly introduced projected purified density-matrix renormalization group, creating powerful tensor network methods for dissipative quantum many-body systems. Investigating their numerical properties, we find a significant speedup up to a factor ∼ 30 compared to conventional tensor-network techniques. We apply these methods to study quenches of the Hubbard-Holstein model, aiming for an indepth understanding of the formation, stability, and quasi-particle properties of bipolarons. Our results show that in the metallic phase, dissipation localizes the bipolarons. However, the bipolaronic binding energy remains mainly unaffected, even in the presence of strong dissipation, exhibiting remarkable bipolaron stability. These findings shed new light on the problem of designing real materials exhibiting phonon-mediated high-T C superconductivity.

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“…We use NMQSD approach to investigate the non-Markovian dynamical evolution of the system [26][27][28][29]. It determines the quantum dynamics of open systems by solving the diffusive stochastic Schrödinger equation or the non-Markovian master equation [30,31]. The effects of the environmental (temperature T b , non-Markovinity γ, interaction strength Γ) and system (DM interaction strength D z , magnetic field intensity B z ) parameters are analyzed in warm and cold baths, respectively.…”

Section: Introductionmentioning

confidence: 99%

Quantum energy current and quantum coherence of a spin chain in a non-Markovian environment

Ablimit,

He,

Xie

et al. 2022

Preprint

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We investigate the behavior in time of the energy current between a quantum spin chain and its surrounding non-Markovian, finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are assumed to be initially in thermal equilibrium at temperature Ts and T b , respectively. This model plays a fundamental role for the study of quantum system evolution towards thermal equilibrium in an open system. The non-Markovian quantum state diffusion (NMQSD) equation approach is used to calculate the dynamics of the spin chain. The effects of bath non-Markovinity, temperature difference and system-bath interaction strength on the energy current and the coherence in warm and cold baths are analyzed, respectively. For both cases, our calculation results show that strong non-Markovianity, weak system-bath interaction and low temperature difference will be helpful to maintain the coherence of the system and correspond to a small energy current. Interestingly, the warm baths destroy the coherence while the cold baths help to generate coherence. Furthermore, the effects of the Dzyaloshinskii-Moriya (DM ) interaction and the external magnetic field on the energy current and coherence are analyzed. Both energy current and coherence will change due to the improvement of the system energy induced by the DM interaction and magnetic field. Significantly, the lowest coherence corresponds to the critical magnetic field which causes the first order phase transition.

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Many-Body Quantum State Diffusion for Non-Markovian Dynamics in Strongly Interacting Systems

Cited by 33 publications

References 55 publications

Non-Markovian Quantum State Diffusion for Spin Environments

Non-Markovian Quantum State Diffusion for Spin Environments

Metallicity in the Dissipative Hubbard-Holstein Model: Markovian and Non-Markovian Tensor-Network Methods for Open Quantum Many-Body Systems

Quantum energy current and quantum coherence of a spin chain in a non-Markovian environment

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