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Bipartite Fluctuations of Critical Fermi Surfaces (2404.04331v2)

Published 5 Apr 2024 in cond-mat.str-el, cond-mat.stat-mech, and hep-th

Abstract: Fluctuations of conserved quantities within a subsystem are non-local observables that provide unique insights into quantum many-body systems. In this paper, we explore the behaviors of 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 phase transition: $F \sim L\log(L)$ in Landau Fermi liquids and $F \sim L$ in charge insulators, where $L$ is the linear size of the subsystem under bipartition. In the case of composite Fermi liquids (under certain conditions), we also identify a universal constant term $-f(\theta)|\sigma_{xy}|/(2\pi)$ arising when the subsystem geometry incorporates a sharp corner. Here, $f(\theta)$ represents a function of the corner angle, and $\sigma_{xy}$ denotes the Hall conductivity. At the critical point of each example, provided the transition is continuous, we find that the leading-order scaling $F \sim L$ is accompanied by a subleading universal corner contribution $-\log(L)f(\theta)C_{\rho}/2$ with the same angle dependence $f(\theta)$. The universal coefficient $C_{\rho}$ is linked to the predicted universal longitudinal (and Hall) resistivity jump $\Delta\rho_{xx}$ (and $\Delta\rho_{xy}$) at the critical point.

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  1. Xiao-Chuan Wu
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