Imaginary HTEE: Probing Criticality and Coherence

@misc{aliakbari2026imaginary,
  title = {{Imaginary HTEE: Probing Criticality and Coherence}},
  author = {M. Ali-Akbari and M. M. Daryaei Goki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18716},
  eprint = {2610.18716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18716},
  note = {CC0},
}

TY  - UNPB
TI  - Imaginary HTEE: Probing Criticality and Coherence
AU  - M. Ali-Akbari
AU  - M. M. Daryaei Goki
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18716
UR  - https://arxiv.org/abs/2610.18716
AB  - We study the imaginary part of the holographic timelike entanglement entropy (HTEE) in a charged asymptotically AdS_5 black-hole background whose dual field theory exhibits a critical point in the presence of a chemical potential μ and temperature T. Identifying the imaginary part of the HTEE with the imaginary part of the pseudoentropy, we derive an analytical expression for this quantity and investigate its behavior on the stable and unstable thermodynamic branches. We find that the imaginary HTEE vanishes in the uncharged limit and is induced entirely by a nonzero chemical potential, signaling the emergence of quantum coherence between the initial and final states. As the dimensionless ratio μ/T approaches its critical value, we obtain an inverse-square-root divergence in the derivative of the imaginary HTEE and extract the critical exponent θ_I = 1/2 analytically. We further show that the same exponent governs the temperature response at fixed chemical potential. Our results establish the imaginary part of the HTEE as a non-local quantum-information probe of criticality in strongly coupled systems, and they imply that the initial and final states become maximally coherent at the critical point.
ER  -