Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

Abstract

We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and $Q^{†}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$. The system is strongly interacting for small $g$, and in the extreme limit $g=0$, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-$g$ limit, the system is non-interacting and SUSY is broken spontaneously. We study the model for modest values of $g$ and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.

13 pages, 5 figures, v3: published version

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• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Topological Quantum Computation on Supersymmetric Spin Chains
• Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry
• Off-Diagonal Long-Range Order Implies Vanishing Charge Gap
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain