Journal Article

Bipartite Fluctuations of Critical Fermi Surfaces

Wu, Xiao-Chuan

2025

Overview

Fluctuations of conserved quantities within a subsystem are nonlocal observables that provide unique insights into quantum many-body systems. In this paper, we study bipartite charge (and spin) fluctuations across interaction-driven “metal-insulator transitions” out of Landau Fermi liquids. The “charge insulators” include a class of non-Fermi-liquid states of fractionalized degrees of freedom, such as compressible composite Fermi liquids (for spinless electrons) and incompressible spin-liquid Mott insulators (for spin- 1 / 2 electrons). We find that charge fluctuations F exhibit distinct leading-order scalings across the transition: F ∼ L log ( L ) in Landau Fermi liquids and F ∼ L in charge insulators, where L is the linear size of the subsystem. In composite Fermi liquids, under certain conditions, we also identify a universal constant term − f ( θ ) | σ x y | / ( 2 π ) when the subsystem geometry contains a sharp corner, where f ( θ ) denotes a function of the corner angle and σ x y is the Hall conductivity. At the critical point, provided the transition is continuous, the leading scaling F ∼ L is accompanied by a subleading universal corner contribution − log ( L ) f ( θ ) C ρ / 2 with the same angle dependence f ( θ ) , and the universal coefficient C ρ is directly related to the predicted universal jumps in longitudinal and Hall resistivities. These results establish fluctuation-transport relations, paving the way for numerical and experimental studies of unconventional quantum criticalities in metals.

• Publisher: American Physical Society