Distinguishing Quantum Phases through Cusps in Full Counting Statistics
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914948970446848 |
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| author | Wang, Chang-Yan Zhou, Tian-Gang Zhou, Yi-Neng Zhang, Pengfei |
| author_facet | Wang, Chang-Yan Zhou, Tian-Gang Zhou, Yi-Neng Zhang, Pengfei |
| contents | Measuring physical observables requires averaging experimental outcomes over numerous identical measurements. The complete distribution function of possible outcomes or its Fourier transform, known as the full counting statistics, provides a more detailed description. This method captures the fundamental quantum fluctuations in many-body systems and has gained significant attention in quantum transport research. In this letter, we propose that cusp singularities in the full counting statistics are a novel tool for distinguishing between ordered and disordered phases. As a specific example, we focus on the superfluid-to-Mott transition in the Bose-Hubbard model and introduce $Z_A(α)=\langle \exp({iα\sum_{i\in A}(\hat{n}_i}-\overline{n}))\rangle $ with $\overline{n}=\langle n_i \rangle$. Through both analytical analysis and numerical simulations, we demonstrate that $\partial_α\log Z_A(α)$ exhibits a discontinuity near $α=π$ in the superfluid phase when the subsystem size is sufficiently large, while it remains smooth in the Mott phase. This discontinuity can be interpreted as a first-order transition between different semi-classical configurations of vortices. We anticipate that our discoveries can be readily tested using state-of-the-art ultracold atom and superconducting qubit platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11191 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distinguishing Quantum Phases through Cusps in Full Counting Statistics Wang, Chang-Yan Zhou, Tian-Gang Zhou, Yi-Neng Zhang, Pengfei Quantum Gases Statistical Mechanics Strongly Correlated Electrons Quantum Physics Measuring physical observables requires averaging experimental outcomes over numerous identical measurements. The complete distribution function of possible outcomes or its Fourier transform, known as the full counting statistics, provides a more detailed description. This method captures the fundamental quantum fluctuations in many-body systems and has gained significant attention in quantum transport research. In this letter, we propose that cusp singularities in the full counting statistics are a novel tool for distinguishing between ordered and disordered phases. As a specific example, we focus on the superfluid-to-Mott transition in the Bose-Hubbard model and introduce $Z_A(α)=\langle \exp({iα\sum_{i\in A}(\hat{n}_i}-\overline{n}))\rangle $ with $\overline{n}=\langle n_i \rangle$. Through both analytical analysis and numerical simulations, we demonstrate that $\partial_α\log Z_A(α)$ exhibits a discontinuity near $α=π$ in the superfluid phase when the subsystem size is sufficiently large, while it remains smooth in the Mott phase. This discontinuity can be interpreted as a first-order transition between different semi-classical configurations of vortices. We anticipate that our discoveries can be readily tested using state-of-the-art ultracold atom and superconducting qubit platforms. |
| title | Distinguishing Quantum Phases through Cusps in Full Counting Statistics |
| topic | Quantum Gases Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2312.11191 |