One-axis twisting with nearest neighbour interactions

Abstract

It is known that a maximally entangled state, GHZ state, is generated by the one-axis twisting Hamiltonian. Recently, it has been numerically shown that a Hamiltonian having neighboring interactions and a field only produces the same dynamics. It is intriguing because it was believed that all-with-all interactions are required for one-axis twisting. The purpose of this work is to reveal how such simple Hamiltonians can show the oneaxis twisting and mimic all-with-all interactions. In particular, we apply the many-body protected manifold technique to the Heisenberg XXX model with a staggered field in attempt to recover all-with-all interactions. We begin with a thorough review of one-axis twisting without and with decoherence. Then, we introduce the many-body protected manifold technique and apply it to the Heisenberg XXZ model, which acquires all-with-all interactions and can generate one-axis twisting. We apply this technique to the Heisenberg XXX model.