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Entanglement entropies and fermion signs of critical metals

Kaplis, N; Kruger, F; Zaanen, J; (2017) Entanglement entropies and fermion signs of critical metals. Physical Review B , 95 (15) , Article 155102. 10.1103/PhysRevB.95.155102. Green open access

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Abstract

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently has it been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wave-function Ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wave functions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces, a representation of the fermion sign structure in many-particle configurations space, show fractal behavior up to a length scale ξ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on ξ , the number of fermions and the exponent of the backflow. For the same wave functions we numerically calculate the second Rényi entanglement entropy S2. Our results show a crossover from volume scaling, S2 ∼ θ (θ = 2 in d = 2 dimensions), to the characteristic Fermi-liquid behavior S2 ∼ ln on scales larger than ξ . We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure. D

Type: Article
Title: Entanglement entropies and fermion signs of critical metals
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevB.95.155102
Publisher version: http://dx.doi.org/10.1103/PhysRevB.95.155102
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
URI: http://discovery.ucl.ac.uk/id/eprint/1547542
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