Distinguishing Quantum Phases through Cusps in Full Counting Statistics

• URL: http://arxiv.org/abs/2312.11191v1
• Date: Mon, 18 Dec 2023 13:38:59 GMT
• Title: Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Authors: Chang-Yan Wang, Tian-Gang Zhou, Yi-Neng Zhou, and Pengfei Zhang
• Abstract summary: We show that cusp singularities in the full counting statistics are a novel tool for distinguishing between ordered and disordered phases. Our discoveries can be readily tested using state-of-the-art ultracold atom and superconducting qubit platforms.
• Score: 4.009911029521761
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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(\alpha)=\langle \exp({i\alpha \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 $\partial_\alpha \log Z_A(\alpha)$ exhibits a discontinuity near $\alpha=\pi$ 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.

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