Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

中文翻译：

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受限费米子阶梯中的超对称性和多重临界性

已知受约束费米子的超对称晶格模型具有奇异现象，例如超级受挫，具有广泛的基态简并性，但其性质通常是未知的。在这里，我们通过考虑从超对称点变形的超受挫模型来解决这个问题。通过数值研究其双参数相图，我们揭示了丰富的现象学。超对称点附近具有周期 4 和周期 5 的密度波，它们由具有平滑变化的密度的浮动相（不相称的 Luttinger 液体）连接。超对称点作为这三相之间的多临界点出现。在第 4 期相内，我们报告了持续到超对称点的价键固体型基态。我们关于从密度波阶段转变的数值数据与 Pokrovsky-Talapov 普遍性类一致。此外，我们的分析揭示了一个周期 3 相，其边界由单粒子和双粒子不稳定性之间的竞争决定，伴随着沿相图中一条线的密度分布的波矢加倍。