Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

Abstract

Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the tensor network, $D$, that has to be truncated back in a way that minimizes a suitable error measure. This paper goes beyond simplified error measures -- like the one used in the full update (FU), the simple update (SU), and their intermediate neighborhood tensor update (NTU) -- and directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one. The optimization is performed in a tangent space of the iPEPS variational manifold. This gradient tensor update (GTU) is benchmarked by a simulation of a sudden quench of a transverse field in the 2D quantum Ising model and the quantum Kibble-Zurek mechanism in the same 2D system.

8 pages; version accepted to Phys. Rev. B after minor changes

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• Universal adiabatic dynamics across a quantum critical point
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Entropy scaling and simulability by Matrix Product States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

Cited by in corpus (14)

• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition
• Real-time operator evolution in two and three dimensions via sparse Pauli dynamics
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Generating function for projected entangled-pair states
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Spectral functions with infinite projected entangled-pair states
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Grassmann tensor networks