Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation

• URL: http://arxiv.org/abs/2401.12460v2
• Date: Tue, 2 Jul 2024 16:34:36 GMT
• Title: Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Authors: Gunhee Park, Nathan Ng, David R. Reichman, Garnet Kin-Lic Chan,
• Abstract summary: We implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. We show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.
• Score: 2.368662284133926
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe two developments of tensor network influence functionals (in particular, influence functional matrix product states (IF-MPS)) for quantum impurity dynamics within the fermionic setting of the Anderson impurity model. The first provides the correct extension of the IF-MPS to continuous time by introducing a related mathematical object, the boundary influence functional MPS. The second connects the dynamics described by a compressed IF-MPS to that of a quantum embedding method with a time-dependent effective bath undergoing nonunitary dynamics. Using these concepts, we implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. The calculations illustrate the ability of the current formulation to efficiently remove the time step error in standard discrete-time IF-MPS implementations as well as to interface with state vector propagation techniques. They also show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.

Related papers

• Emergence of fluctuating hydrodynamics in chaotic quantum systems [47.187609203210705]
  macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in boson ladders. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior.
  arXiv  Detail & Related papers  (2023-06-20T11:26:30Z)
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain [0.0]
  We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF) We obtain explicit expressions of the wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. The approach can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.
  arXiv  Detail & Related papers  (2022-05-10T16:05:25Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• A Multisite Decomposition of the Tensor Network Path Integrals [0.0]
  We extend the tensor network path integral (TNPI) framework to efficiently simulate quantum systems with local dissipative environments. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.
  arXiv  Detail & Related papers  (2021-09-20T17:55:53Z)
• Value Iteration in Continuous Actions, States and Time [99.00362538261972]
  We propose a continuous fitted value iteration (cFVI) algorithm for continuous states and actions. The optimal policy can be derived for non-linear control-affine dynamics. Videos of the physical system are available at urlhttps://sites.google.com/view/value-iteration.
  arXiv  Detail & Related papers  (2021-05-10T21:40:56Z)
• Scaling of temporal entanglement in proximity to integrability [0.0]
  We analytically compute the exact IM for a family of integrable Floquet models. We show that the IM exhibits area-law temporal entanglement scaling for all parameter values. Near criticality, a non-trivial scaling behavior of temporal entanglement is found.
  arXiv  Detail & Related papers  (2021-04-15T17:16:57Z)
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics [0.0]
  We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes. As one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.
  arXiv  Detail & Related papers  (2021-01-14T05:42:25Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• Dynamically Evolving Bond-Dimensions within the one-site Time-Dependent-Variational-Principle method for Matrix Product States: Towards efficient simulation of non-equilibrium open quantum dynamics [0.0]
  We show that an MPS can restructure itself as the complexity of the dynamics grows across time and space. This naturally leads to more efficient simulations, oviates the need for multiple convergence runs, and, as we demonstrate, is ideally suited to the typical, finite-temperature 'impurity' problems.
  arXiv  Detail & Related papers  (2020-07-27T13:07:05Z)
• Feedback-induced instabilities and dynamics in the Jaynes-Cummings model [62.997667081978825]
  We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system.
  arXiv  Detail & Related papers  (2020-06-20T10:07:01Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.