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Bipartite Fluctuations of Critical Fermi Surfaces

Xiao-Chuan Wu

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Phys. Rev. X 15, 031035 – Published 6 August, 2025

DOI: https://doi.org/10.1103/dflw-rksw

Abstract

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∼Llog(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)|σxy|/(2π) when the subsystem geometry contains a sharp corner, where f(θ) denotes a function of the corner angle and σxy 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)Cρ/2 with the same angle dependence f(θ), and the universal coefficient Cρ 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.

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Popular Summary

Quantum phase transitions that go beyond the traditional symmetry-breaking framework remain one of the most intriguing puzzles in condensed matter physics. These transitions are especially hard to understand in metals, where an abundance of low-energy electronic excitations near the Fermi surface—a surface in momentum space that determines many key properties of metals—complicates the picture. In this work, we propose a nonlocal diagnostic tool that uses the geometry of its associated spatial subregions to detect such unconventional metallic quantum phase transitions. We find that how charge fluctuations depend on the shape of a region—particularly when it has sharp corners—reveals universal features of the critical point.

Our theoretical study focuses on a class of continuous transitions from ordinary metals to exotic insulating phases where electrons fractionalize and form collective quantum states. We show that charge fluctuations follow distinct scaling behaviors across the transition. More importantly, at criticality, when the chosen spatial subregion contains sharp corners, a universal subleading term appears in the fluctuations. This “corner term” acts as a geometric fingerprint of the quantum critical point and links directly to transport properties at criticality, offering a unique view into the nature of the transition.

These predictions are grounded in field-theoretic arguments and yield formulas that can be tested in experiments and simulations. By focusing on the shape dependence of charge fluctuations, our approach provides a practical method for identifying elusive metallic quantum critical points in a wide range of strongly correlated materials.

Article Text

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Phys. Rev. X 15, 031035– Published 6 August, 2025
  • Received 5 September 2024
  • Revised 10 January 2025
  • Accepted 9 June 2025
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