Fermionic Isometric Tensor Network States in Two Dimensions

• URL: http://arxiv.org/abs/2211.00043v3
• Date: Fri, 22 Mar 2024 18:16:31 GMT
• Title: Fermionic Isometric Tensor Network States in Two Dimensions
• Authors: Zhehao Dai, Yantao Wu, Taige Wang, Michael P. Zaletel,
• Abstract summary: We benchmarked a time-evolution block-decimation algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge modes to good accuracy. The real-time TEBD captures the scattering of two fermions and the chiral edge dynamics on the boundary of a Chern insulator.
• Score: 1.0249620437941
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize isometric tensor network states to fermionic systems, paving the way for efficient adaptations of 1D tensor network algorithms to 2D fermionic systems. As the first application of this formalism, we developed and benchmarked a time-evolution block-decimation (TEBD) algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge modes to good accuracy. The real-time TEBD captures the scattering of two fermions and the chiral edge dynamics on the boundary of a Chern insulator.

Related papers

• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• Two Dimensional Isometric Tensor Networks on an Infinite Strip [1.2569180784533303]
  We introduce the class ofisoTNS (isoTNS) for efficient simulation of 2D systems on finite square lattices. We iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBDsuperscript2) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.
  arXiv  Detail & Related papers  (2022-11-25T19:00:06Z)
• 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)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Adiabatic quantum algorithm for artificial graphene [0.0]
  We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. A full simulation of the algorithm is performed and ground energies are obtained for lattices with up to four hexagons.
  arXiv  Detail & Related papers  (2022-04-06T18:00:25Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks [0.0]
  We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs) We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers. We compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models.
  arXiv  Detail & Related papers  (2021-12-15T19:00:05Z)
• 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)
• 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)
• A Kernel-Based Approach to Non-Stationary Reinforcement Learning in Metric Spaces [53.47210316424326]
  KeRNS is an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes. We prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time.
  arXiv  Detail & Related papers  (2020-07-09T21:37:13Z)

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.