无约束紧致格点QED$_{2+1}$与声子耦合：高斯扇区、正交半金属和退禁闭临界性

中文摘要 AI 辅助

二维量子磁体的规范理论描述通过在物理希尔伯特空间中施加高斯定律来定义。在本工作中，我们研究了与键声子耦合的无约束紧致格点QED$_{2+1}$，其中局域高斯算符是守恒的，但其本征值并非先验固定。利用$N_f = 2$的精确辅助场量子蒙特卡罗模拟，我们研究了物理高斯扇区如何变得能量上有利，以及这一过程如何与禁闭和对称性破缺相关联。我们识别出一个正交半金属（OSM）相，其中费米子剥离了其规范电荷并形成狄拉克液体。该相混合了各种高斯扇区，并在明确施加高斯定律时变得不稳定。在施加高斯定律后，紧致性允许携带反铁磁（AFM）和价键固体（VBS）量子数的磁单极子激发。规范场涨落和自旋子-声子耦合调节了此类磁单极子之间的竞争，并生成了包含OSM、AFM和VBS序的相图。离开OSM相的转变与高斯定律的动态产生相吻合，而AFM和VBS带电磁单极子之间的竞争产生了与退禁闭量子临界性一致的转变。因此，我们的结果表明，在投影到物理希尔伯特空间后，紧致格点QED$_{2+1}$中的退禁闭总是对AFM或VBS序不稳定。

英文摘要

Gauge theoretic descriptions of 2D quantum magnets are defined on a restricted physical Hilbert space by imposing Gauss's law. In this work, we study an unconstrained compact lattice QED$_{2+1}$ coupled to bond phonons, in which local Gauss operators are conserved, but their eigenvalues are not a priori fixed. Using exact auxiliary-field quantum Monte Carlo simulations at $N_f = 2$, we investigate how the physical Gauss sector becomes energetically favourable, and how this process is connected to confinement and symmetry breaking. We identify an orthogonal semimetallic (OSM) phase, in which fermions striped off their gauge charge and form a Dirac liquid. This phase mixes various Gauss sectors, and becomes unstable when Gauss's law is explicitly enforced. Upon the imposition of Gauss's law, compactness allows for monopole excitations carrying antiferromagnetic (AFM) and valence-bond-solid (VBS) quantum numbers. Gauge field fluctuations and spinon-phonon coupling tune between the competition of such monopoles and generate a phase diagram with OSM, AFM and VBS orders. The transitions out of the OSM phase coincide with the dynamical generation of Gauss's law, while the competition between AFM and VBS charged monopoles produces a transition consistent with deconfined quantum criticality. Thus our results establish that upon the projection to the physical Hilbert space, deconfinement in compact lattice QED$_{2+1}$ is always unstable towards either AFM or VBS order.

发表机构

• Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论物理与天体物理研究所）
• Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）

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