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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2210.03134 |
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| _version_ | 1866912088468750336 |
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| author | Liu, Bowei Chen, Hao Lian, Biao |
| author_facet | Liu, Bowei Chen, Hao Lian, Biao |
| contents | We define the entanglement entropy of free fermion quantum states in an arbitrary spacetime slice of a discrete set of points, and particularly investigate timelike (causal) slices. For 1D lattice free fermions with an energy bandwidth $E_0$, we calculate the time-direction entanglement entropy $S_A$ in a time-direction slice of a set of times $t_n=nτ$ ($1\le n\le K$) spanning a time length $t$ on the same site. For zero temperature ground states, we find that $S_A$ shows volume law when $τ\ggτ_0=2π/E_0$; in contrast, $S_A\sim \frac{1}{3}\ln t$ when $τ=τ_0$, and $S_A\sim\frac{1}{6}\ln t$ when $τ<τ_0$, resembling the Calabrese-Cardy formula for one flavor of nonchiral and chiral fermion, respectively. For finite temperature thermal states, the mutual information also saturates when $τ<τ_0$. For non-eigenstates, volume law in $t$ and signatures of the Lieb-Robinson bound velocity can be observed in $S_A$. For generic spacetime slices with one point per site, the zero temperature entanglement entropy shows a clear transition from area law to volume law when the slice varies from spacelike to timelike. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03134 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Entanglement Entropy of Free Fermions in Timelike Slices Liu, Bowei Chen, Hao Lian, Biao Statistical Mechanics High Energy Physics - Theory Quantum Physics We define the entanglement entropy of free fermion quantum states in an arbitrary spacetime slice of a discrete set of points, and particularly investigate timelike (causal) slices. For 1D lattice free fermions with an energy bandwidth $E_0$, we calculate the time-direction entanglement entropy $S_A$ in a time-direction slice of a set of times $t_n=nτ$ ($1\le n\le K$) spanning a time length $t$ on the same site. For zero temperature ground states, we find that $S_A$ shows volume law when $τ\ggτ_0=2π/E_0$; in contrast, $S_A\sim \frac{1}{3}\ln t$ when $τ=τ_0$, and $S_A\sim\frac{1}{6}\ln t$ when $τ<τ_0$, resembling the Calabrese-Cardy formula for one flavor of nonchiral and chiral fermion, respectively. For finite temperature thermal states, the mutual information also saturates when $τ<τ_0$. For non-eigenstates, volume law in $t$ and signatures of the Lieb-Robinson bound velocity can be observed in $S_A$. For generic spacetime slices with one point per site, the zero temperature entanglement entropy shows a clear transition from area law to volume law when the slice varies from spacelike to timelike. |
| title | Entanglement Entropy of Free Fermions in Timelike Slices |
| topic | Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2210.03134 |