Entanglement Transfer Dynamics in a Two-Leg Spin Ladder Under a Selective Magnetic Field

TL;DR

This study demonstrates high-fidelity entanglement transfer in a two-leg spin ladder with selective magnetic fields, revealing key dynamical timescales and robustness under disorder, using exact diagonalisation up to five rungs.

Contribution

It introduces a detailed analysis of entanglement transfer dynamics in a spin ladder with selective fields, including effective coupling derivation and robustness, extending understanding beyond 1D chains.

Findings

Achieved near-perfect entanglement transfer fidelity (F_max = 0.9998) for N=3 rungs.

Identified two independent timescales governing the dynamics: fast oscillation and slow transfer envelope.

Demonstrated robustness of transfer fidelity (>0.998) under uncorrelated coupling disorder.

Abstract

We investigate the dynamical transfer of bipartite entanglement through a two-leg spin-1/2 ladder governed by the anisotropic Heisenberg (XXZ-type) model with a selective magnetic field applied exclusively to the mediating rungs. Starting from a maximally entangled initial rung pair, we demonstrate high-fidelity entanglement transfer to the terminal pair (F_max = 0.9998 for N = 3 rung pairs), with the intermediate rungs remaining effectively disentangled throughout. The dynamics is governed by two independent timescales: a fast carrier oscillation at frequency omega_fast = 2*sqrt(1 + 4d^2) J (set by local rung physics, field-independent) and a slow transfer envelope with period T_slow = 2.37 h/J^2 (set by virtual inter-rung coupling, field-dependent). The effective inter-rung coupling J_eff = alpha(d,g) J^2/h is derived via second-order perturbation theory through two parallel virtual paths. We systematically study the effects of magnetic field strength, Hamiltonian anisotropy, and initial state on transfer quality, establish a global parameter space map of the fidelity, and demonstrate robustness under uncorrelated coupling disorder (mean F_max > 0.998 for delta <= 10%). All results are obtained by exact diagonalisation for systems of up to N = 5 rung pairs; extension to larger systems requires tensor-network methods such as DMRG. Compared to one-dimensional chain proposals, the ladder geometry enables a spatially selective control mechanism that suppresses intermediate entanglement while preserving coherent transfer, providing a distinct route to engineered quantum channels.