Quantum

Time Direction Entanglement Entropy of Free Fermion Ground States

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Briefings

A new study by researchers analyzing free fermion quantum states defines time direction entanglement entropy (TDEE) using a sub-Hilbert space that minimally supports time-evolved operators. The research applies the Fisher-Hartwig conjecture to derive analytical frameworks for discrete time steps, revealing that TDEE scaling varies by system type: area law for gapless systems, logarithmic law for Anderson insulators, and volume law for specific gap regimes. The study also identifies a sub-Hilbert space that stabilizes in the continuum time limit, interpreted as a subspace of the Lieb-Robinson causal diamond.

Key points

• Researchers developed an analytical framework for time direction entanglement entropy (TDEE) using the Fisher-Hartwig conjecture for Toeplitz matrices.
• For disorderless 1D systems, TDEE exhibits area law, logarithmic law, or volume law depending on gap, bandwidth, and time step size.

Context

Entanglement entropy in time directions has been underexplored compared to spatial subregions. This work investigates TDEE for free fermion states, providing a new analytical approach and numerical results for Anderson insulators.

Limitations

Results are limited to free fermion systems; specific time step regimes and gap values are not fully characterized. The continuum time limit analysis is approximate, and the sub-Hilbert space stabilization remains a theoretical interpretation.

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