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.
Highlights
Supersymmetric lattice models It has long been known that supersymmetry in a quantum field theory (QFT) leads to special features in the physics described by such QFT, and to an enhanced mathematical control
We explore the vicinity of the supersymmetric point, which turns out to be a multicritical point connecting both gapped and floating phases
The model studied in the paper is a prototypical example of a model displaying superfrustration: an exponentially large degeneracy of supersymmetric ground states or, equivalently, a ground state entropy that is extensive in the system size [21,22,23]
Summary
The physics of a quantum many-body system is determined by a competition between various terms, in particular the kinetic and interaction terms, of its Hamiltonian. Supersymmetric lattice models It has long been known that (space-time) supersymmetry in a quantum field theory (QFT) leads to special features in the physics described by such QFT, and to an enhanced mathematical control An example of the latter is the Witten index [14] for theories with a complex (N = 2) supersymmetry, which guarantees the existence of zero-energy ground states, without the need of diagonalizing the Hamiltonian. Multicriticality The massive degeneracy of ground states (which typically come with a range of fermion densities) indicates that supersymmetric points are highly singular points in the ground state phase diagrams of these lattice models To study this phenomenon, we focus on a relatively simple case, which is the M1 model on a zig-zag ladder. We explore the vicinity of the supersymmetric point, which turns out to be a multicritical point connecting both gapped and floating phases
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