Scaling theory of entanglement entropy in confinements near quantum critical points

TL;DR

This paper develops a unified scaling theory for entanglement entropy considering finite bond dimensions, system sizes, and dynamics, validated through the 1D transverse-field Ising model under linear driving.

Contribution

It generalizes finite-entanglement scaling to include dynamics and finite system sizes, analyzing their interplay and crossovers near quantum critical points.

Findings

The theory captures complex crossover behaviors.

Validation with the 1D transverse-field Ising model.

Provides insights into entanglement scaling under various constraints.

Abstract

We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently 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 analysed in details. Interesting regimes and their complicated crossovers together with their characteristics follow naturally. The theory is verified with the one-dimensional transverse-field Ising model under a linear driving.