Spectral functions with infinite projected entangled-pair states

• URL: http://arxiv.org/abs/2405.10628v2
• Date: Fri, 01 Nov 2024 21:19:08 GMT
• Title: Spectral functions with infinite projected entangled-pair states
• Authors: Juan Diego Arias Espinoza, Philippe Corboz,
• Abstract summary: We extend the iPEPS toolbox by a method to efficiently evaluate non-equal time two-point correlators. It is based on an iPEPS ansatz of the ground state in a large unit cell, with an operator applied in the center of the cell. At every time step, the two-point correlators within a cell are computed based on the corner transfer matrix renormalization group method.
• Score: 0.0
• License:
• Abstract: Infinite projected entangled-pair states (iPEPS) provide a powerful tool to study two-dimensional strongly correlated systems directly in the thermodynamic limit. In this work, we extend the iPEPS toolbox by a method to efficiently evaluate non-equal time two-point correlators, enabling the computation of spectral functions. It is based on an iPEPS ansatz of the ground state in a large unit cell, with an operator applied in the center of the cell, which is evolved in real-time using the fast-full update method. At every time step, the two-point correlators within a cell are computed based on the corner transfer matrix renormalization group method. Benchmark results for the 2D transverse field Ising model show that the main features of the dynamical structure factor can already be reproduced at relatively small bond dimensions and unit cell sizes. The results for the magnon dispersion are found to be in good agreement with previous data obtained with the iPEPS excitation ansatz.

Related papers

• Pseudospectral method for solving PDEs using Matrix Product States [0.0]
  This research focuses on solving time-dependent partial differential equations (PDEs) using matrix product states (MPS) We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives.
  arXiv  Detail & Related papers  (2024-09-04T17:53:38Z)
• DA-Flow: Dual Attention Normalizing Flow for Skeleton-based Video Anomaly Detection [52.74152717667157]
  We propose a lightweight module called Dual Attention Module (DAM) for capturing cross-dimension interaction relationships in-temporal skeletal data. It employs the frame attention mechanism to identify the most significant frames and the skeleton attention mechanism to capture broader relationships across fixed partitions with minimal parameters and flops.
  arXiv  Detail & Related papers  (2024-06-05T06:18:03Z)
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method [0.0]
  We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models. We demonstrate for the two dimensional spinless fermion model and for the Hubbard model on torus geometry that several orders of magnitude in computational time can be saved.
  arXiv  Detail & Related papers  (2023-11-23T17:07:47Z)
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States [0.0]
  The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. Our analysis reveals that PEPS-METTS achieves accurate long-range correlations with significantly lower bond dimensions.
  arXiv  Detail & Related papers  (2023-10-12T17:23:55Z)
• Random insights into the complexity of two-dimensional tensor network calculations [0.27708222692419743]
  Projected entangled pair states offer memory-efficient representations of some quantum many-body states. Projected entangled pair states offer memory-efficient representations of some quantum many-body states that obey an entanglement area law.
  arXiv  Detail & Related papers  (2023-07-20T17:34:06Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Achieving Efficient Distributed Machine Learning Using a Novel Non-Linear Class of Aggregation Functions [9.689867512720083]
  Distributed machine learning (DML) over time-varying networks can be an enabler for emerging decentralized ML applications. We propose a novel non-linear class of model aggregation functions to achieve efficient DML over time-varying networks.
  arXiv  Detail & Related papers  (2022-01-29T03:43:26Z)
• Sketching as a Tool for Understanding and Accelerating Self-attention for Long Sequences [52.6022911513076]
  Transformer-based models are not efficient in processing long sequences due to the quadratic space and time complexity of the self-attention modules. We propose Linformer and Informer to reduce the quadratic complexity to linear (modulo logarithmic factors) via low-dimensional projection and row selection. Based on the theoretical analysis, we propose Skeinformer to accelerate self-attention and further improve the accuracy of matrix approximation to self-attention.
  arXiv  Detail & Related papers  (2021-12-10T06:58:05Z)
• PnP-DETR: Towards Efficient Visual Analysis with Transformers [146.55679348493587]
  Recently, DETR pioneered the solution vision tasks with transformers, it directly translates the image feature map into the object result. Recent transformer-based image recognition model andTT show consistent efficiency gain.
  arXiv  Detail & Related papers  (2021-09-15T01:10:30Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)

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.