Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings

TL;DR

This paper investigates how the entanglement entropy scales in finite quantum Ising chains with various coupling types, analyzing finite-size effects and critical point shifts using free-fermionic methods.

Contribution

It provides a systematic analysis of finite-size effects on entanglement entropy in different coupling regimes and evaluates the effective critical point shifts for open and periodic chains.

Findings

Scaling behavior aligns with universality near criticality

Finite-size corrections depend on boundary conditions

Effective critical point shifts follow distinct scaling laws

Abstract

Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random. We carry out a systematic study of finite-size effects at the quantum critical point, and evaluate subleading corrections both for open and for periodic boundary conditions. For a block corresponding to a half of a finite chain, the position of the maximum of the entropy as a function of the control parameter (e.g. the transverse field) can define the effective critical point in the finite sample. On the basis of homogeneous chains, we demonstrate that the scaling behavior of the entropy near the quantum phase transition is in agreement with the universality hypothesis, and calculate the shift of the effective critical point, which has different scaling behaviors for open and for periodic boundary conditions.