Measurement-induced phase transition for free fermions above one dimension
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911799998152704 |
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| author | Poboiko, Igor Gornyi, Igor V. Mirlin, Alexander D. |
| author_facet | Poboiko, Igor Gornyi, Igor V. Mirlin, Alexander D. |
| contents | A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ ε$ with $ε\ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $ν\approx 1.4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Measurement-induced phase transition for free fermions above one dimension Poboiko, Igor Gornyi, Igor V. Mirlin, Alexander D. Quantum Physics Disordered Systems and Neural Networks A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ ε$ with $ε\ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $ν\approx 1.4$. |
| title | Measurement-induced phase transition for free fermions above one dimension |
| topic | Quantum Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2309.12405 |