Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

Abstract

An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a $T=0$ renormalisation group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by RG relevant quantum fluctuations arising from backscattering processes.

Holographic entanglement renormalisation for fermionic quantum matter

“…It also appears interesting to identify the effects of electronic correlations on various aspects of the emergent space. The renormalisation group techniques applied in [160][161][162][163][164] could also be worth investigating towards answering these questions.…”

“…(see bottom panel of figure 15). It appears tempting to speculate on a possible universal origin underlying these similarities (see also [164] for a recent investigation of the entanglement properties of various quantum liquids).…”