Time Dependent Variational Principle with Ancillary Krylov Subspace

• URL: http://arxiv.org/abs/2005.06104v3
• Date: Tue, 29 Sep 2020 17:05:32 GMT
• Title: Time Dependent Variational Principle with Ancillary Krylov Subspace
• Authors: Mingru Yang and Steven R. White
• Abstract summary: We propose an improved scheme to do the time dependent variational principle (TDVP) in finite matrix product states. We present a method to represent the time-evolving state in a MPS with its basis enriched by state-averaging with global Krylov vectors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an improved scheme to do the time dependent variational principle (TDVP) in finite matrix product states (MPS) for two-dimensional systems or one-dimensional systems with long range interactions. We present a method to represent the time-evolving state in a MPS with its basis enriched by state-averaging with global Krylov vectors. We show that the projection error is significantly reduced so that precise time evolution can still be obtained even if a larger time step is used. Combined with the one-site TDVP, our approach provides a way to dynamically increase the bond dimension while still preserving unitarity for real time evolution. Our method can be more accurate and exhibit slower bond dimension growth than the conventional two-site TDVP.

Related papers

• Relaxation Process During Complex Time Evolution In Two-Dimensional Integrable and Chaotic CFTs [6.631221795940245]
  We investigate the complex time evolution of a vacuum state with the insertion of a local primary operator in conformal field theories (2d CFTs)<n>This complex time evolution can be considered as a composite process constructed from Lorentzian time evolution and a Euclidean evolution induced by a post-selected measurement.
  arXiv  Detail & Related papers  (2026-01-14T08:51:01Z)
• Learning Multi-Modal Mobility Dynamics for Generalized Next Location Recommendation [51.00494428978262]
  We leverage multi-modal spatial-temporal knowledge to characterize mobility dynamics for the location recommendation task.<n>First, we construct a unified spatial-temporal relational graph (STRG) for multi-modal representation.<n>Second, we design a gating mechanism to fuse spatial-temporal graph representations of different modalities.
  arXiv  Detail & Related papers  (2025-12-27T14:23:04Z)
• RainDiff: End-to-end Precipitation Nowcasting Via Token-wise Attention Diffusion [64.49056527678606]
  We propose a Token-wise Attention integrated into not only the U-Net diffusion model but also the radar-temporal encoder.<n>Unlike prior approaches, our method integrates attention into the architecture without incurring the high resource cost typical of pixel-space diffusion.<n>Our experiments and evaluations demonstrate that the proposed method significantly outperforms state-of-the-art approaches, robustness local fidelity, generalization, and superior in complex precipitation forecasting scenarios.
  arXiv  Detail & Related papers  (2025-10-16T17:59:13Z)
• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Our scheme computes the entire state trajectory over a finite time window by minimizing a loss function that enforces the Schr"odinger's equation. We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Measurement-induced phase transitions by matrix product states scaling [0.0]
  We study the time evolution of long quantum spin chains subjected to continuous monitoring via matrix product states (MPS) at fixed bond dimension. We show that the error rate displays a phase transition in the monitoring strength, which can be well detected by scaling analysis with relatively low values of bond dimensions.
  arXiv  Detail & Related papers  (2024-02-20T17:22:36Z)
• Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction [49.66486092259376]
  The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. We provide a framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and gradient approximation.
  arXiv  Detail & Related papers  (2023-06-12T16:28:11Z)
• Temporal Entanglement in Chaotic Quantum Circuits [62.997667081978825]
  The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. We show that temporal entanglement always follows a volume law in time. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.
  arXiv  Detail & Related papers  (2023-02-16T18:56:05Z)
• Time-dependent variational principle with controlled bond expansion for matrix product states [0.0]
  We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) Our method alleviates the numerical difficulties of the standard, fixed-rank one-site TDVP integrator by increasing bond dimensions on the fly to reduce the projection error.
  arXiv  Detail & Related papers  (2022-08-23T13:44:34Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• Transient superconductivity in three-dimensional Hubbard systems by combining matrix product states and self-consistent mean-field theory [0.06999740786886534]
  We use matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. Our results confirm previous findings for purely 1D systems that for such a scenario superconductivity forms in a transient state.
  arXiv  Detail & Related papers  (2022-07-20T11:58:34Z)
• Learning to Accelerate Partial Differential Equations via Latent Global Evolution [64.72624347511498]
  Latent Evolution of PDEs (LE-PDE) is a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy.
  arXiv  Detail & Related papers  (2022-06-15T17:31:24Z)
• Clean two-dimensional Floquet time-crystal [68.8204255655161]
  We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. We observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.
  arXiv  Detail & Related papers  (2022-05-10T13:04:43Z)
• Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization [58.720142291102135]
  We propose a method for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. We observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.
  arXiv  Detail & Related papers  (2021-04-21T10:36:57Z)
• 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)

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.