Subsystem distance after a local operator quench

Abstract

We investigate the time evolution of the subsystem trace distance and Schatten distances after local operator quenches in two-dimensional conformal field theory (CFT) and in one-dimensional quantum spin chains. We focus on the case of a subsystem being an interval embedded in the infinite line. The initial state is prepared by inserting a local operator in the ground state of the theory. We only consider the cases in which the inserted local operator is a primary field or a sum of several primaries. While a nonchiral primary operator can excite both left-moving and right-moving quasiparticles, a holomorphic primary operator only excites a right-moving quasiparticle and an anti-holomorphic primary operator only excites a left-moving one. The reduced density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to the RDM of the interval without any quasiparticles. Moreover, the RDMs of two intervals hosting quasiparticles at different positions are also orthogonal to each other. We calculate numerically the entanglement entropy, Rényi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains. These results match the CFT predictions in the proper limit.

v1, 32 pages, 9 figures; v2, 33 pages, 9 figures, published version

References in corpus (14)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Evolution of entanglement after a local quench
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Entanglement negativity after a global quantum quench
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Spin-charge separation in two-component Bose-gases
• Relative Entropies in Conformal Field Theory
• Entanglement of Local Operators in large N CFTs
• Notes on Quantum Entanglement of Local Operators
• Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
• Subsystem Trace Distance in Quantum Field Theory
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain