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This research identifies specific temporal criticalities in open fermionic systems where entanglement or negativity gaps close, revealing that Gaussianity dictates these events more than symmetry constraints. The study demonstrates how different decoherence mechanisms, such as balanced loss/gain versus dephasing, alter the timing of these transitions relative to geometric decoherence times. These findings provide fundamental insights into the dynamics of quantum information preservation in dissipative environments like Kitaev chains.
Exact Temporal Criticalities of Entanglement and Negativity in Gaussian and Non-Gaussian Dissipative Kitaev Chains
arXiv:2610.03889v1 Announce Type: new Abstract: When the two largest eigenvalues of an entanglement or negativity spectrum meet, the gap of the corresponding entanglement or negativity Hamiltonian closes while entropies stay smooth, an event we call a temporal criticality. We ask when such criticalities occur in open fermionic systems, in which order, and whether they precede the geometric decoherence time, at which the negativity starts to fall. We compare loss and gain, which respect fermion parity only on average (weak symmetry) and keep the state Gaussian, with density dephasing, which respects it in every jump (strong symmetry) and makes the state non-Gaussian. We find that Gaussianity, rather than the symmetry, fixes the criterion for a criticality. In a Gaussian state the entanglement gap of a subsystem closes exactly when its two parity sectors carry equal weight, and the negativity gap closes exactly when this happens for the subsystem or its complement, so the negativity criticality never comes after the entanglement one. Uniform balanced loss and gain only shrink the two parities and leave both criticalities in place at every rate, for any quadratic Hamiltonian. In an open Kitaev chain, weak imbalanced loss and gain shift the criticalities by amounts set by the occupations at the cut, and at strong rates they allow a closing near the relaxation time only when an odd number of neighboring sites pass half filling. For dephasing we solve the non-Gaussian dynamics exactly at the point where the bond terms of the chain commute. Weak dephasing delays both criticalities and, away from the chain ends, moves them ahead of the parity balance, where the parity rules of Gaussian states would place them. As the dephasing rate approaches critical damping, both criticalities recede to infinite time, and at strong dephasing the negativity starts to fall long before either gap begins to shrink.
Abstract:When the two largest eigenvalues of an entanglement or negativity spectrum meet, the gap of the corresponding entanglement or negativity Hamiltonian closes while entropies stay smooth, an event we call a temporal criticality. We ask when such criticalities occur in open fermionic systems, in which order, and whether they precede the geometric decoherence time, at which the negativity starts to fall. We compare loss and gain, which respect fermion parity only on average (weak symmetry) and keep the state Gaussian, with density dephasing, which respects it in every jump (strong symmetry) and makes the state non-Gaussian. We find that Gaussianity, rather than the symmetry, fixes the criterion for a criticality. In a Gaussian state the entanglement gap of a subsystem closes exactly when its two parity sectors carry equal weight, and the negativity gap closes exactly when this happens for the subsystem or its complement, so the negativity criticality never comes after the entanglement one. Uniform balanced loss and gain only shrink the two parities and leave both criticalities in place at every rate, for any quadratic Hamiltonian. In an open Kitaev chain, weak imbalanced loss and gain shift the criticalities by amounts set by the occupations at the cut, and at strong rates they allow a closing near the relaxation time only when an odd number of neighboring sites pass half filling. For dephasing we solve the non-Gaussian dynamics exactly at the point where the bond terms of the chain commute. Weak dephasing delays both criticalities and, away from the chain ends, moves them ahead of the parity balance, where the parity rules of Gaussian states would place them. As the dephasing rate approaches critical damping, both criticalities recede to infinite time, and at strong dephasing the negativity starts to fall long before either gap begins to shrink.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2610.03889 [quant-ph]
(or arXiv:2610.03889v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.03889 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 400 words
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