Mutual entropy and thermal area law in C*-algebraic quantum lattice systems
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909829271912448 |
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| author | Moriya, Hajime |
| author_facet | Moriya, Hajime |
| contents | We present a general definition of quantum mutual entropy for infinitely extended quantum spin and fermion lattice systems. Using this, we establish a thermal area law in these infinitely extended quantum systems. The proof is based on the local thermodynamical stability (LTS), a variational principle in terms of the conditional free energy. Our thermal area law in quasi-local C*-systems applies to general interactions with well-defined surface energies. We also examine the quantum mutual entropy between the left- and right-sided infinite regions of one-dimensional lattice systems. For general translation-invariant finite-range interactions on such systems, the thermal equilibrium state at any temperature exhibits a finite mutual entropy between these infinite disjoint regions. This further implies that the infinitely large quantum entanglement characteristic of critical ground states in one-dimensional systems is drastically destroyed by even a small positive temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05823 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutual entropy and thermal area law in C*-algebraic quantum lattice systems Moriya, Hajime Mathematical Physics 82B10 We present a general definition of quantum mutual entropy for infinitely extended quantum spin and fermion lattice systems. Using this, we establish a thermal area law in these infinitely extended quantum systems. The proof is based on the local thermodynamical stability (LTS), a variational principle in terms of the conditional free energy. Our thermal area law in quasi-local C*-systems applies to general interactions with well-defined surface energies. We also examine the quantum mutual entropy between the left- and right-sided infinite regions of one-dimensional lattice systems. For general translation-invariant finite-range interactions on such systems, the thermal equilibrium state at any temperature exhibits a finite mutual entropy between these infinite disjoint regions. This further implies that the infinitely large quantum entanglement characteristic of critical ground states in one-dimensional systems is drastically destroyed by even a small positive temperature. |
| title | Mutual entropy and thermal area law in C*-algebraic quantum lattice systems |
| topic | Mathematical Physics 82B10 |
| url | https://arxiv.org/abs/2510.05823 |