Confinement, String Breaking and Entanglement Asymmetry in Quantum Ising Chain

Entanglement Asymmetry has been recently introduced as a subsystem probe of symmetry breaking in the theory of many-body quantum entanglement. In this work, we explore the interplay of confinement, string breaking and entanglement asymmetry on a quantum Ising chain. The model can be tuned to conserve the number of domain walls/kinks, and can exhibit both integrability and integrability breaking with confining field. We compare the kink-coserving dynamics simulated from matrix product states (MPS) with time-evolving block decimation (TEBD) with exact two-kinks evolution and discover how integrability sets an upper bound for the Renyi entropy, which can be broken upon introducing small confining field. We then briefly present a simple algorithm to calculate entanglement asymmetry in a generic MPS in generic interacting, non-integrable model. We then introduce kink entanglement asymmetry, a new type of entanglement asymmetry with non-local symmetry operator, which can be non-zero despite the fact that the Hamiltonian conserves kink number. As an alternative approach to deal with the non-locality of the kink variable, we perform a Kramers-Wannier transformation to map link variables (kink) to site variables (magnetization), and compute the entanglement dynamics associated with the transformed basis. Our work introduced a new type of novel entanglement asymmetry, and explored the time evolution of the entanglement asymmetry in the context of quantum quench in MPS.