Scaling theory of entanglement entropy in confinements near quantum critical points

Abstract

We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics, and system sizes. In the theory, the recently introduced finite-entanglement scaling is generalized to the dynamics subjected to a linear driving along with a finite system size. Competition among the three scales as well as the correlation length of the system is analyzed in detail. Interesting regimes and their complicated crossovers together with their characteristics follow naturally. The theory is verified by time-evolving-block-decimation-based numerical simulations in the one-dimensional transverse-field Ising model under a linear driving.