Takaaki Hirano

Entanglement in an SU(n) valence-bond-solid state

We investigate entanglement properties in the ground state of the open/periodic SU(n) generalized valence-bond-solid state consisting of representations of SU(n). We obtain exact expressions for the reduced density matrix of a block of contiguous spins and explicitly evaluate the von Neumann and the Renyi entropies. We discover that the Renyi entropy is independent of the parameter α in the limit of large block sizes and its value 2log n coincides with that of von Neumann entropy. We also find the direct relation between the reduced density matrix of the subsystem and edge states for the corresponding open boundary system.

Exact analysis of entanglement in gapped quantum spin chains

We investigate the entanglement properties of the valence-bond-solid states with generic integer spin

Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter

S

Entanglement and Density Matrix of a Block of Spins in AKLT Model

. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy,

Degeneracy and consistency condition for Berry phases: Gap closing under a local gauge twist

2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}(S+1)

Block spin density matrix of the inhomogeneous AKLT model

, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose an application of the edge state as a qubit for quantum computation.

Topological identification of a spin- 1 2 two-leg ladder with four-spin ring exchange

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are

Quantized Berry phases of a Spin-1/2 frustrated two-leg ladder with four-spin exchange

S=1,2

A topological classification of gapped spin chains by quantized Berry phases: VBS picture and the fractionalization

dimerized Heisenberg chains and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.

Entanglement Entropy of 1D Gapped Spin Chains

AbstractWe study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension