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.
Highlights
Quench, the initial state is globally different from the energy eigenstates, as e.g. in [16, 17]; in a local quench, the initial state is locally different from an energy eigenstate, as for examples in the joining and splitting quenches [18,19,20] or in the local operator quench [12,13,14]
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 calculate numerically the entanglement entropy, Renyi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains
Summary
We review the 2D CFT approach to the quench by the insertion of local operator [12,13,14], and generalize it to the case in which the local operator is a sum of several primary fields. We calculate Renyi entropies as well as the trace and Schatten distances of the RDMs at different times after the local operator quench
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