The iTEBD algorithm beyond unitary evolution

Abstract

The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit. Here we extend the algorithm to tackle a much broader class of problems, namely the simulation of arbitrary one-dimensional evolution operators that can be expressed as a (translationally invariant) tensor network. Relatedly, we also address the problem of finding the dominant eigenvalue and eigenvector of a one-dimensional transfer matrix that can be expressed in the same way. New applications include the simulation, in the thermodynamic limit, of open (i.e. master equation) dynamics and thermal states in 1D quantum systems, as well as calculations with partition functions in 2D classical systems, on which we elaborate. The present extension of the algorithm also plays a prominent role in the infinite projected entangled-pair states (iPEPS) approach to infinite 2D quantum lattice systems.

11 pages, 16 figures, 1 appendix with algorithms for specific types of evolution. A typo in the appendix figures has been corrected. Accepted in PRB

References in corpus (5)

• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Tensor renormalization group approach to 2D classical lattice models
• Criticality, the area law, and the computational power of PEPS

Cited by in corpus (4)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Magnetization Plateau of Classical Ising Model on Shastry-Sutherland Lattice
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States