Time-direction Entanglement Entropy of Free Fermions
ORAL
Abstract
We follow the definition of time-direction entanglement entropy (TDEE) introduced in Liu et al. (2024) and calculate the TDEE for the gapless free fermion, band insulator, and Anderson insulator.
For the band insulator, with gapless fermions as a special limit, we use the Fisher–Hartwig conjecture to obtain an analytic expression for the TDEE and construct a phase diagram consistent with numerical results.
Counter-intuitively, the TDEE of a band insulator can exhibit volume-law, area-law, or logarithmic-law behavior depending on parameters, revealing distinct regimes of temporal entanglement. In the continuous-time limit, the TDEE becomes exactly one-half of the spatial entanglement entropy, establishing a direct correspondence between spatial and temporal entanglement.
For the Anderson insulator, we find a dynamical Page transition in the TDEE that arises from the localization of the wavefunction. The transition time scales with the localization length, linking the dynamics of temporal entanglement to the underlying spatial localization properties.
These results demonstrate that the TDEE unifies concepts from entanglement theory, localization, and nonequilibrium quantum dynamics, offering a new perspective on how quantum correlations develop and saturate along the time direction.
For the band insulator, with gapless fermions as a special limit, we use the Fisher–Hartwig conjecture to obtain an analytic expression for the TDEE and construct a phase diagram consistent with numerical results.
Counter-intuitively, the TDEE of a band insulator can exhibit volume-law, area-law, or logarithmic-law behavior depending on parameters, revealing distinct regimes of temporal entanglement. In the continuous-time limit, the TDEE becomes exactly one-half of the spatial entanglement entropy, establishing a direct correspondence between spatial and temporal entanglement.
For the Anderson insulator, we find a dynamical Page transition in the TDEE that arises from the localization of the wavefunction. The transition time scales with the localization length, linking the dynamics of temporal entanglement to the underlying spatial localization properties.
These results demonstrate that the TDEE unifies concepts from entanglement theory, localization, and nonequilibrium quantum dynamics, offering a new perspective on how quantum correlations develop and saturate along the time direction.
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Presenters
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Bowei Liu
- Princeton University