Logarithmic Entanglement and Emergent Dipole Symmetry from a Strongly Coupled Light-Matter Quantum Circuit
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866917423621341184 |
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| author | Santos, Luiz H. |
| author_facet | Santos, Luiz H. |
| contents | Hybrid systems where a quantum material strongly couples to a nonlocal cavity photon mode have emerged as a new frontier for controlling and probing quantum correlations, yet the structure and scaling of light-matter entanglement produced by the nonlocal coupling remains poorly understood. We address this problem through an exactly solvable framework based on reinterpreting the Power--Zienau--Woolley (PZW) transformation as a \textit{light-matter quantum circuit} that couples the photonic position quadrature $X \sim a + a^\dagger$ to the many-body dipole $\mathcal{P}$ of a one-dimensional quantum chain. We derive a closed-form expression for the reduced density matrix valid at all coupling strengths, in which off-diagonal elements between matter states of unequal dipole are suppressed by a Gaussian factor encoding the full weak-to-ultrastrong coupling crossover. At weak coupling, the reduced density matrix takes a Lindbladian form with $\mathcal{P}$ as the jump operator, and the entanglement entropy is controlled by the dipole variance. At ultrastrong coupling, the density matrix becomes exactly block-diagonal in dipole sectors, reflecting an \textit{emergent dipole symmetry} dynamically imposed by the photon field, with entanglement entropy given exactly by the Shannon entropy of the dipole-sector weight distribution. Applying this framework to a half-filled Su--Schrieffer--Heeger chain, we show that, at strong coupling, both the light-matter entanglement and the spatial entanglement of the photon-dressed matter state scale logarithmically with system size, $S_\infty \sim \fracα{2}\log L$, robust across the SSH phase diagram. The logarithm originates from the photon resolving a single collective coordinate $\mathcal{P}$ whose fluctuations grow as $L^{α/2}$, a distinct mechanism from the logarithmic entanglement of critical one-dimensional systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Logarithmic Entanglement and Emergent Dipole Symmetry from a Strongly Coupled Light-Matter Quantum Circuit Santos, Luiz H. Strongly Correlated Electrons Quantum Physics Hybrid systems where a quantum material strongly couples to a nonlocal cavity photon mode have emerged as a new frontier for controlling and probing quantum correlations, yet the structure and scaling of light-matter entanglement produced by the nonlocal coupling remains poorly understood. We address this problem through an exactly solvable framework based on reinterpreting the Power--Zienau--Woolley (PZW) transformation as a \textit{light-matter quantum circuit} that couples the photonic position quadrature $X \sim a + a^\dagger$ to the many-body dipole $\mathcal{P}$ of a one-dimensional quantum chain. We derive a closed-form expression for the reduced density matrix valid at all coupling strengths, in which off-diagonal elements between matter states of unequal dipole are suppressed by a Gaussian factor encoding the full weak-to-ultrastrong coupling crossover. At weak coupling, the reduced density matrix takes a Lindbladian form with $\mathcal{P}$ as the jump operator, and the entanglement entropy is controlled by the dipole variance. At ultrastrong coupling, the density matrix becomes exactly block-diagonal in dipole sectors, reflecting an \textit{emergent dipole symmetry} dynamically imposed by the photon field, with entanglement entropy given exactly by the Shannon entropy of the dipole-sector weight distribution. Applying this framework to a half-filled Su--Schrieffer--Heeger chain, we show that, at strong coupling, both the light-matter entanglement and the spatial entanglement of the photon-dressed matter state scale logarithmically with system size, $S_\infty \sim \fracα{2}\log L$, robust across the SSH phase diagram. The logarithm originates from the photon resolving a single collective coordinate $\mathcal{P}$ whose fluctuations grow as $L^{α/2}$, a distinct mechanism from the logarithmic entanglement of critical one-dimensional systems. |
| title | Logarithmic Entanglement and Emergent Dipole Symmetry from a Strongly Coupled Light-Matter Quantum Circuit |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2604.18670 |