Monitored interacting Dirac fermions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915164186476544 |
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| author | Müller, Thomas Martin Buchhold, Michael Diehl, Sebastian |
| author_facet | Müller, Thomas Martin Buchhold, Michael Diehl, Sebastian |
| contents | We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $γ$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength $γ_c$. When $γ>γ_c$, the system enters a localized phase characterized by exponentially decaying density-density correlations beyond a finite correlation length; for $γ<γ_c$, the correlations decay algebraically. The transition is of BKT-type, reflected by a characteristic scaling of the correlation length. In the non-interacting limit, $γ_c\to0$ shifts to zero, reducing the algebraic phase to a single point in parameter space. This identifies weak measurements in the free case as an implicit double fine-tuning to the critical endpoint of the BKT phase transition. Along the non-interacting line, we compute the entanglement entropy from density-density correlation functions and find no entanglement transition at nonzero measurement strength in the thermodynamic limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_02645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monitored interacting Dirac fermions Müller, Thomas Martin Buchhold, Michael Diehl, Sebastian Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $γ$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength $γ_c$. When $γ>γ_c$, the system enters a localized phase characterized by exponentially decaying density-density correlations beyond a finite correlation length; for $γ<γ_c$, the correlations decay algebraically. The transition is of BKT-type, reflected by a characteristic scaling of the correlation length. In the non-interacting limit, $γ_c\to0$ shifts to zero, reducing the algebraic phase to a single point in parameter space. This identifies weak measurements in the free case as an implicit double fine-tuning to the critical endpoint of the BKT phase transition. Along the non-interacting line, we compute the entanglement entropy from density-density correlation functions and find no entanglement transition at nonzero measurement strength in the thermodynamic limit. |
| title | Monitored interacting Dirac fermions |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2502.02645 |