Increasing of entanglement entropy from pure to random quantum critical chains

TL;DR

This paper investigates how entanglement entropy transitions from pure to random quantum critical chains, revealing model-dependent behaviors and confirming conjectures about effective central charge in disordered systems.

Contribution

It provides a detailed analysis of entanglement entropy in various models, including Potts and clock models, and clarifies the behavior of effective central charge in disordered chains.

Findings

Entanglement entropy diverges logarithmically with block size in both pure and disordered chains.

The ratio of entanglement entropy between pure and disordered systems varies depending on the model.

The study confirms conjectures about the universality of effective central charge in random quantum critical chains.

Abstract

It is known that the entropy of a block of spins of size $L$ embedded in an infinite pure critical spin chain diverges as the logarithm of $L$ with a prefactor fixed by the central charge of the corresponding conformal field theory. For a class of strongly random spin chains, it has been shown that the correspondent block entropy still remains universal and diverges logarithmically with an "effective" central charge. By computing the entanglement entropy for a family of models which includes the $N$-states random Potts chain and the $Z_N$ clock model, we give some definitive answer to some recent conjectures about the behaviour of the effective central charge. In particular, we show that the ratio between the entanglement entropy in the pure and in the disordered system is model dependent and we provide a series of critical models where the entanglement entropy grows from the pure to the random case.