Typical entanglement entropy in systems with particle-number conservation
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913628191457280 |
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| author | Yauk, Yale Patil, Rohit Zhang, Yicheng Rigol, Marcos Hackl, Lucas |
| author_facet | Yauk, Yale Patil, Rohit Zhang, Yicheng Rigol, Marcos Hackl, Lucas |
| contents | We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/V$, where $V_A$ is the volume of the subsystem. We expand our result as a power series $\langle S_A\rangle_N=a f V+b\sqrt{V}+c+o(1)$, and find that $c$ is universal (i.e., independent of the system type), while $a$ and $b$ can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19862 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Typical entanglement entropy in systems with particle-number conservation Yauk, Yale Patil, Rohit Zhang, Yicheng Rigol, Marcos Hackl, Lucas Quantum Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/V$, where $V_A$ is the volume of the subsystem. We expand our result as a power series $\langle S_A\rangle_N=a f V+b\sqrt{V}+c+o(1)$, and find that $c$ is universal (i.e., independent of the system type), while $a$ and $b$ can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts. |
| title | Typical entanglement entropy in systems with particle-number conservation |
| topic | Quantum Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.19862 |