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A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
  • R. Orús
  • Physics, Computer Science
  • 10 June 2013
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.
TLDR
An algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition is presented.
Infinite time-evolving block decimation algorithm beyond unitary evolution
The infinite time-evolving block decimation algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional (1D)
Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states
We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B
Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction
An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an
Robustness of a perturbed topological phase.
We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find
Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing
The infinite projected entangled pair states (iPEPS) algorithm [J. Jordan et al., Phys. Rev. Lett. 101, 250602 (2008)] has become a useful tool in the calculation of ground-state properties of
Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical
Entanglement entropy in the Lipkin-Meshkov-Glick model (4 pages)
We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical
Tensor networks for complex quantum systems
  • R. Orús
  • Physics, Computer Science
    Nature Reviews Physics
  • 10 December 2018
TLDR
This Review revisits the main tensor network structures, key ideas behind their numerical methods and their application in fields beyond condensed matter physics.
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