Scaling of entanglement entropy across Lifshitz transitions

TL;DR

This paper studies how entanglement entropy scales across Lifshitz quantum phase transitions, revealing critical exponents and singularities in different dimensions, with numerical and analytical insights including effects of weak interactions.

Contribution

It provides the first detailed analysis of entanglement entropy scaling at Lifshitz transitions, including critical exponents and interaction effects.

Findings

Entanglement entropy exhibits diverging length scales near Lifshitz critical points.

Distinct power-law singularities appear in 2D entanglement scaling at criticality.

Weak interactions modify entanglement scaling, analyzed via DMRG.

Abstract

We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results which show that Lifshitz transitions are characterized by a well-defined set of critical exponents for the entanglement entropy near the phase transition. In one dimension, we show that the entanglement entropy exhibits a length scale that diverges as the system approaches a Lifshitz critical point. In two dimensions, the leading and sub-leading coefficients of the scaling of entanglement entropy show distinct power-law singularities at critical points. The effect of weak interactions is investigated using the density matrix renormalization group algorithm.