Quasi-local Edge Mode in XXX Spin Chain/Circuit with Interaction Boundary Defect

TL;DR

This paper investigates boundary effects in a Heisenberg spin-1/2 chain and identifies a quasi-localized edge mode that influences boundary correlations and exhibits a phase transition at a critical interaction strength.

Contribution

It explicitly constructs a quasi-local edge mode in a boundary-defected Heisenberg chain using a matrix-product approach, revealing boundary phase transition phenomena.

Findings

Existence of a quasi-local edge mode for strong boundary interactions

Non-decaying boundary correlations linked to the edge mode

Divergence of correlation length at a critical boundary interaction

Abstract

We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.