Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State

• URL: http://arxiv.org/abs/2403.16700v2
• Date: Sun, 31 Mar 2024 15:25:09 GMT
• Title: Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Authors: Chu Guo, Ruofan Chen,
• Abstract summary: We present an infinite Grassmann time-evolving matrix product operator method for quantum impurity problems, which directly works in the steady state. We benchmark the method on the finite-temperature equilibrium Green's function in the noninteracting limit against exact solutions. We also study the zero-temperature non-equilibrium steady state of an impurity coupled to two baths with a voltage bias, obtaining consistent particle currents with existing calculations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an infinite Grassmann time-evolving matrix product operator method for quantum impurity problems, which directly works in the steady state. The method embraces the well-established infinite matrix product state algorithms with the recently developed GTEMPO method, and benefits from both sides: it obtains numerically exact real-time Green's functions without sampling noises and bath discretization error, it is applicable for any temperature without the sign problem, its computational cost is independent of the transient dynamics and does not scale with the number of baths. We benchmark the method on the finite-temperature equilibrium Green's function in the noninteracting limit against exact solutions and in the single-orbital Anderson impurity model against GTEMPO calculations. We also study the zero-temperature non-equilibrium steady state of an impurity coupled to two baths with a voltage bias, obtaining consistent particle currents with existing calculations. The method is ideal for studying steady-state quantum transport, and can be readily used as an efficient real-time impurity solver in the dynamical mean field theory and its non-equilibrium extension.

Related papers

• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour [0.0]
  We extend the recently developed Grassmann time-evolving matrix product operator (GTEMPO) method to solve quantum impurity problems directly on the Kadanoff-Baym contour. The accuracy of this method is numerically demonstrated against exact solutions in the noninteracting case, and against existing calculations on the real- and imaginary-time axes.
  arXiv  Detail & Related papers  (2024-04-08T11:21:06Z)
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems [0.0]
  We use the Grassmann time-evolving matrix product operator (GTEMPO) method for zero-temperature imaginary-time calculations. We devise a very efficient infinite GTEMPO algorithm targeted at zero-temperature equilibrium quantum impurity problems.
  arXiv  Detail & Related papers  (2024-04-06T23:42:46Z)
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators [0.0]
  We present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method.
  arXiv  Detail & Related papers  (2024-01-10T02:20:29Z)
• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action [0.0]
  In this Article, we explore the computational power of representing the retarded action as matrix product state (RAMPS) We demonstrate that the RAMPS approach reliably reaches the Kondo regime for a range of interaction strengths $U$, with a numerical error scaling as a weak power law with inverse temperature. Our results show that the RAMPS approach offers promise as an alternative tool for studying quantum impurity problems in regimes that challenge established methods.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium [62.51015395213579]
  We consider the non-AL equilibrium nonconptotic objective function in two-player zero-sum continuous games. The proposed algorithm employs the movements of particles to represent the updates of random strategies for the $ilon$-mixed Nash equilibrium.
  arXiv  Detail & Related papers  (2023-03-02T05:08:15Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Sampling with Mollified Interaction Energy Descent [57.00583139477843]
  We present a new optimization-based method for sampling called mollified interaction energy descent (MIED) MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs) We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
  arXiv  Detail & Related papers  (2022-10-24T16:54:18Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem [27.09339991866556]
  We show that ODE searches for optimal control for an unknown computation system by directly searching over the corresponding space of controllers. We take a step towards demystifying the performance and efficiency of such methods by focusing on the gradient-flow dynamics set of stabilizing feedback gains and a similar result holds for the forward disctization of the ODE.
  arXiv  Detail & Related papers  (2019-12-26T16:56:59Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

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.