# Entanglement in a valence-bond solid state.

@article{Fan2004EntanglementIA, title={Entanglement in a valence-bond solid state.}, author={Heng Fan and Vladimir E. Korepin and Vwani P. Roychowdhury}, journal={Physical review letters}, year={2004}, volume={93 22}, pages={ 227203 } }

We study entanglement in a valence-bond solid state, which describes the ground state of an Affleck-Kennedy-Lieb-Tasaki quantum spin chain, consisting of bulk spin-1's and two spin-1/2's at the ends. We characterize entanglement between various subsystems of the ground state by mostly calculating the entropy of one of the subsystems; when appropriate, we evaluate concurrences as well. We show that the reduced density matrix of a continuous block of bulk spins is independent of the size of the…

## 103 Citations

Entanglement in Valence-Bond-Solid States

- Physics
- 2009

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was…

Entanglement of disjoint blocks in the one-dimensional spin-1 VBS

- Physics
- 2012

Starting with the valence-bond solid (VBS) ground state of the 1D AKLT Hamiltonian, we make a partition of the system in two subsystems A and B, where A is a block of L consecutive spins and B is its…

Entanglement in valence-bond-solid states on symmetric graphs

- Mathematics
- 2010

We study quantum entanglement in the ground state of the Affleck–Kennedy–Lieb–Tasaki model defined on two-dimensional graphs with reflection and/or inversion symmetry. The ground state of this spin…

Entanglement of the valence-bond-solid state on an arbitrary graph

- Physics
- 2008

The Affleck–Kennedy–Lieb–Tasaki (AKLT) spin interacting model can be defined on an arbitrary graph. We explain the construction of the AKLT Hamiltonian. Given certain conditions, the ground state is…

Valence Bond Calculations for Quantum Spin Chains: From Impurity Entanglement and Incommensurate Behaviour to Quantum Monte Carlo

- Physics
- 2014

In this thesis I present three publications about the use of valence bonds to gain information about quantum spin systems. Valence bonds are an essential ingredient of low energy states present in…

Entanglement Entropy of One-dimensional Gapped Spin Chains(Condensed matter: structure and mechanical and thermal properties)

- Physics
- 2007

We investigate the entanglement entropy (EE) of gapped S =1 and S =1/2 spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to…

Exact results for the bipartite entanglement entropy of the AKLT spin-1 chain

- Physics
- 2010

We study the bipartite entanglement between a subsystem of size l and the rest of the system of total size L as it occurs in a spin-1 Affleck–Kennedy–Lieb–Tasaki (AKLT) chain subject to open boundary…

Entanglement and quantum phase transitions in quantum mixed spin chains

- Physics
- 2006

The ground entanglement and thermal entanglement in quantum mixed spin chains consisting of two integer spins 1 and two half integer spins 1/2 arrayed as ${1/2}-{1/2}-1-1$ in a unit cell with…

Quantum critical point and entanglement in a matrix-product ground state

- Physics
- 2007

In this paper, we study the entanglement properties of a spin-1 model, the exact ground state of which is given by a matrix product (MP) state. The model exhibits a critical point transition at a…

Entanglement of an alternating bipartition in spin chains: relation with classical integrable models

- Physics
- 2015

We study the entanglement properties of a class of ground states defined by matrix product states, which are generalizations of the valence bond solid (VBS) state in one dimension. It is shown that…