发表机构
Simons Center for Geometry and Physics, Stony Brook University; Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology; INFN, Sezione di Torino; Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern; School of Physics and Astronomy, Tel Aviv University（石溪大学西蒙几何与物理中心; 麻省理工学院莱因韦伯理论物理中心; 都灵意大利国家核物理研究所; 伯尔尼大学理论物理研究所爱因斯坦基础物理中心; 特拉维夫大学物理与天文学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在近玻色子极限下求解任意子气体，发现其基态为晶体而非超流体，并确定了量子相变临界值$k_c\simeq2\text{--}5$，挑战了传统认知。
AI 中文摘要
我们重新审视了长期存在的任意子气体问题。我们研究了在固定$N/k$下大量任意子$N$的可解近玻色子极限，其中$1/k$表征统计相互作用。在该极限下，基态是一个具有$N/k$阶格点数的晶体。由长程规范场介导的统计相互作用在晶相内被完全屏蔽。所得状态是一种没有超流性的常规晶体。我们通过确定其单胞尺寸、基态能量、声学激发、角动量交叉及其他性质来表征该任意子晶体。我们的结果表明，在$k>k_c$时的晶体与$k<k_c$时的超流体之间存在量子相变，临界值$k_c\simeq2\text{--}5$。这些结果意味着仅具有统计相互作用的任意子气体不一定是超流体，这与普遍认知相反。我们还对任意子-任意子相互作用的重整化群演化进行了详细分析，识别出许多新的潜在不动点，并阐明了有限尺寸效应。
英文摘要
We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons $N$ at fixed $N/k$, where $1/k$ characterizes the statistical interaction. In this limit, the ground state is a crystal with order $N/k$ lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at $k>k_c$ and a superfluid at $k<k_c$, with a critical value $k_c\simeq2\text{--}5$. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon--anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.
Comments42 pages, 4 figures
