Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains

Abstract

We introduce and study a lattice fermion model in one dimension with explicit N = 1 supersymmetry (SUSY). The Hamiltonian of the model is defined by the square of a supercharge built from Majorana fermion operators. The model describes interacting Majorana fermions and its properties depend only on a single parameter g. When g = 1, we find that SUSY is unbroken and the ground states are identical to those of the frustration-free Kitaev chains. We also find a parameter regime in which SUSY is restored in the infinite volume limit. For sufficiently large g, we prove that SUSY is spontaneously broken and the low-lying excitations are gapless, which can be thought of as Nambu-Goldstone fermions. We then show numerically that these gapless modes have cubic dispersion at long wavelength.

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

“…we take t > 0 for concreteness throughout. References [87,88] recently studied this model motivated in part by interesting connections to supersymmetry; see also Ref. [89].…”

Supersymmetry in an interacting Majorana model on the kagome lattice

“…The extra symmetries discussed above render the g = 0 limit simpler than the generic model, but still seems intractable. The bowtie interaction terms do not commute, and we find that all ground states are entangled in real space, in contrast to known 1D SUSY Majorana models [27,28]. It turns out that thin-torus geometries -systems of size L x × 2 with L x any integer -are simpler because the real-space entanglement is limited to only one color (or sublattice).…”

“…The question of whether SUSY is recovered in the thermodynamic limit -that is, if E 0 /N → 0 when N → ∞, as seen in Refs. [27,28], is difficult to answer unequivocally with numerical exact diagonalization. To resolve this question, we adopt two complementary approaches: i) infinite density-matrix renormalization group (iDMRG) calculations for cylinders of width L y = 2, and ii) a numerical Schrieffer-Wolff degenerate perturbation theory calculation [43].…”

“…Their identification is beyond the scope of the numerical methods employed here, but we note that the gap to the first excited state induced to fifth-order (the lowest nontrivial order splitting the ground state manifold) decreases rapidly with system size -providing a suggestive hint. Confirming the presence of Nambu-Goldstone fermions using more sophisticated numerical methods, and understanding their dispersion relation (which is cubic for the 1D SUSY Majorana case [28]) could be interesting directions for future work.…”

“…The main advantage of using Majorana operators to construct a supercharge is that they square to identity [26], often resulting in simpler Hamiltonians. This led to recent proposals for 1D Majorana chains which admit a supersymmetric phase with an exactly solvable point [27,28].…”