Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles

Abstract

A typical quantum state obeying the area law for entanglement on an infinite 2D lattice can be represented by a tensor network ansatz -- known as an infinite projected entangled pair state (iPEPS) -- with a finite bond dimension $D$. Its real/imaginary time evolution can be split into small time steps. An application of a time step generates a new iPEPS with a bond dimension $k$ times the original one. The new iPEPS does not make optimal use of its enlarged bond dimension $kD$, hence in principle it can be represented accurately by a more compact ansatz, favourably with the original $D$. In this work we show how the more compact iPEPS can be optimized variationally to maximize its overlap with the new iPEPS. To compute the overlap we use the corner transfer matrix renormalization group (CTMRG). By simulating sudden quench of the transverse field in the 2D quantum Ising model with the proposed algorithm, we provide a proof of principle that real time evolution can be simulated with iPEPS. A similar proof is provided in the same model for imaginary time evolution of purification of its thermal states.

9 pages, 10 figures, replaced with the published version

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Cited by in corpus (13)

• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Direct sampling of projected entangled-pair states
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Scaling of neural-network quantum states for time evolution
• Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Numerical continuum tensor networks in two dimensions
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG