Finite-size geometric entanglement from tensor network algorithms

Quantum Entanglement and Tensor Network RG

For many decades, the Landau theory of symmetry breaking has dominated thinking about phase transitions. Recent interest in topological phases and quantum orders, which lie beyond the realm of symmetry breaking theory. Need a more robust framework. RG provides. I describe how numerical RG can be used to understand phases beyond sym. breaking. Implementation for quantum ordered phases requires i...

Tensor network implementation of bulk entanglement spectrum

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these b...

Multigrid algorithms for tensor network states.

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves th...

Tensor Network States: Algorithms and Applications

Dicke model: Entanglement as a finite size effect

We analyze the Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a BoseEinstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state...