Title: Majorana stripe order on the surface of a three-dimensional topological insulator,
Abstract: The issue on the effect of interactions in topological states concerns not
only interacting topological phases but also novel symmetry-breaking phases and
phase transitions. Here we study the interaction effect on Majorana zero modes
(MZMs) bound to a square vortex lattice in two-dimensional (2D) topological
superconductors. Under the neutrality condition, where single-body
hybridization between MZMs is prohibited by an emergent symmetry, a minimal
square-lattice model for MZMs can be faithfully mapped to a quantum spin model,
which has no sign problem in the world-line quantum Monte Carlo simulation.
Guided by an insight from a further duality mapping, we demonstrate that the
interaction induces a Majorana stripe state, a gapped state spontaneously
breaking lattice translational and rotational symmetries, as opposed to the
previously conjectured topological quantum criticality. Away from neutrality, a
mean-field theory suggests a quantum critical point induced by hybridization.