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arXiv:2009.11881 · Physical Review Research

Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

Hugo A. Camargo, Lucas Hackl, Michał P. Heller, Alexander Jahn, Tadashi Takayanagi, Bennet Windt

Published Mar 17, 2021• 38 citations
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Abstract

The authors study quantum information-theoretic quantities in Gaussian mixed states, identifying universal properties and providing a comparison with existing results from conformal field theory and holography.
DOI
10.1103/physrevresearch.3.013248

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Identifying spatial quantum correlations in mixed states is challenging because thermal mixed-state contributions obscure the entanglement encoded in subsystem entropy. Here, we introduce the entanglement projected entropy (EPE), a purification-independent Gaussian spatial filter for mixed fermionic states. By resolving subsystem entropy into Gaussian entropy channels and projecting their purification partners onto the physical complement, we obtain a closed-form expression in terms of the physical covariance matrix. In a one-dimensional free-fermion chain, it removes the volume-law mixed-state background and recovers the zero-temperature conformal scaling with the c/3c/3c/3 coefficient. In a two-dimensional half-filled πππ-flux model, it reveals a universal finite-temperature scaling collapse governed by a Dirac infrared length fixed by the low-energy velocity. These results establish EPE as an entropy-channel filter that exposes boundary-sensitive universal scaling hidden beneath mixed-state entropy.