Angular-time evolution for the Affleck-Kennedy-Lieb-Tasaki chain and its edge-state dynamics

TL;DR

This paper investigates the angular-time evolution in the AKLT chain, analytically calculating spin correlation functions and exploring the physical interpretation of the entanglement Hamiltonian's dynamics.

Contribution

It provides an analytical approach to angular-time evolution and spin correlations in the AKLT chain using MPS representation, revealing new insights into edge-state dynamics.

Findings

Analytical expressions for angular-time spin correlations.

Representation of angular-time evolution operator in physical spin space.

Insights into edge-state dynamics and entanglement Hamiltonian interpretation.

Abstract

We study the angular-time evolution that is a parameter-time evolution defined by the entanglement Hamiltonian for the bipartitioned ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain with the open boundary. In particular, we analytically calculate angular-time spin correlation functions $\langle S_n^\alpha(\tau)S_n^\alpha(0)\rangle$ with $\alpha = x,y,z$, using the matrix-product-state (MPS) representation of the valence-bond-solid state with edges. We also investigate how the angular-time evolution operator can be represented in the physical spin space with the use of gauge transformation for the MPS. We then discuss the physical interpretation of the angular-time evolution in the AKLT chain.