Supersymmetry and multicriticality in a ladder of constrained fermions

TL;DR

This study explores a supersymmetric lattice model of constrained fermions, revealing complex phase behavior including density waves, floating phases, and multicritical points, with implications for understanding superfrustration and exotic ground states.

Contribution

It introduces a detailed numerical phase diagram of a superfrustrated fermionic model, identifying new phases and multicritical behavior near the supersymmetric point.

Findings

Identification of period-4 and period-5 density waves

Discovery of a floating incommensurate Luttinger liquid phase

Observation of a period-3 phase with competing instabilities

Abstract

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.