The wind carries pollen, and each grain moves as if on its own. But once the air swirls into a vortex, the pollen trajectories can no longer be separated: they are tangled. This is roughly how electrons behave in a strange metal: their motion is so strongly coupled to soft fluctuations of the medium that the usual particle carriers disappear.
Physicists built a model — a one-dimensional chain where electrons (two 'clouds' around special points) interact with a mediating field through random couplings. This is a simplified version of the so-called Yukawa-Sachdev-Ye-Kitaev model. When the mediating field becomes 'critical' (that is, ready for a sharp rearrangement), the system turns into a semblance of a strange metal. The main question was: how to measure quantum entanglement in such disorder?
The authors found a way to precisely compute this measure for any segment of the chain. And then a surprising picture emerged: entanglement between electrons and the mediating field within a single segment turned out to be no less important than entanglement between different segments. Both types of intertwining work together, and their combined contribution obeys a simple rule.
So the wind and pollen cease to be just a metaphor. In a strange metal, the medium does not merely hinder particles; it becomes their inseparable part. And the universal law of entanglement, found for a toy model, could be the very key that opens the door to understanding a whole class of mysterious materials — from high-temperature superconductors to the matter of neutron stars.
as written by the authors arXiv:2608.04098v1
The subsystem-size dependence of ground-state entanglement entropy and its crossover to thermal entropy as a function of temperature are well understood for one-dimensional (1D) gapless systems described by conformal field theory (CFT), and for free fermions with a Fermi surface in any dimension. However, little is known about the entanglement entropy for gapless fermionic systems without quasi-particles, such as a strange metal. Here we study the entanglement entropy of fermions in a solvable large-$$N$$ 1D lattice model akin to the Yukawa-Sachdev-Ye-Kitaev (Yukawa SYK) model. In this model, two Fermi points are coupled to scalar bosons via spatially random Yukawa interactions, providing a solvable model of a strange metal when the bosons become critical at a quantum critical point. We exactly compute the second R\'{e}nyi entropy of fermions in a spatial subregion in this model. Our results unravel crucial role of intra-subregion entanglement between fermionic and bosonic degrees of freedom along with the inter-subregion entanglement in understanding the ground states of such strongly coupled fermion-boson systems. We show that the crossover from thermal entropy to entanglement entropy, is captured by a single scaling ansatz, that collapses the second R\'{e}nyi entropy of fermions for different subregion sizes and temperatures into a single universal curve. We further show that the universal scaling curve for the critical strange metal is well described by the standard CFT formula, albeit with an effective central charge substantially larger than the non-interacting value.
Strange metals got their name not for their exotic composition, but for their unusual behavior: their electrical resistance grows strictly proportionally to temperature, rather than according to familiar laws. This occurs in high-temperature superconductors and still lacks a full explanation.