326 research outputs found
Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
This is a short review on selected theory developments on Tensor Network (TN)
states for strongly correlated systems. Specifically, we briefly review the
effect of symmetries in TN states, fermionic TNs, the calculation of
entanglement Hamiltonians from Projected Entangled Pair States (PEPS), and the
relation between the Multi-scale Entanglement Renormalization Ansatz (MERA) and
the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement
in the emergence of several physical properties and objects through the TN
language. Some recent results along these lines are also discussed.Comment: Invited Colloquium for EPJB, 31 pages, 13 figures; revised version,
accepted for publicatio
Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit
In this paper the geometric entanglement (GE) of systems in one spatial
dimension (1D) and in the thermodynamic limit is analyzed focusing on two
aspects. First, we reexamine the calculation of the GE for
translation-invariant matrix product states (MPSs) in the limit of infinite
system size. We obtain a lower bound to the GE which collapses to an equality
under certain sufficient conditions that are fulfilled by many physical
systems, such as those having unbroken space (P) or space-time (PT) inversion
symmetry. Our analysis justifies the validity of several derivations carried
out in previous works. Second, we derive scaling laws for the GE per site of
infinite-size 1D systems with correlation length . In the case of
MPSs, we combine this with the theory of finite-entanglement scaling, allowing
to understand the scaling of the GE per site with the MPS bond dimension at
conformally invariant quantum critical points.Comment: 7 pages, 1 figure, revised version. Accepted for publication in QI
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