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arXiv:2604.24887

Symmetry-Protected Topological Phases in the Triangular Majorana-Hubbard Ladder

Will Holdhusen, Alberto Nocera, Jian-Xin Zhu, Armin Rahmani

Published Apr 27, 2026• 0 citations
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Abstract

We uncover a family of symmetry-protected topological phases in a model of interacting Majorana fermions on triangular-lattice ladders. Included among these phases is one in which symmetry-protected topological order coexists with spontaneous symmetry breaking associated with an adiabatically evolving set of symmetries. Our results indicate a mechanism through which interactions among Majorana modes generate nontrivial symmetry-fractionalized orders. These phases may be realized in arrays of vortex-bound Majorana zero modes on the surface of topological superconductors.

DOI
10.48550/arxiv.2604.24887

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We uncover a family of symmetry-protected topological phases in a model of interacting Majorana fermions on triangular-lattice ladders. Included among these phases is one in which symmetry-protected topological order coexists with spontaneous symmetry breaking associated with an adiabatically evolving set of symmetries. Our results indicate a mechanism through which interactions among Majorana modes generate nontrivial symmetry-fractionalized orders. These phases may be realized in arrays of vortex-bound Majorana zero modes on the surface of topological superconductors.
Majorana modes can arise as zero energy bound states in a variety of solid state systems. A lattice of these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. This thesis is devoted to the study of interactions between the Majorana zero modes when such a lattice has a triangular geometry. We map the phase diagram of this model using a combination of mean field theory and numerical simulation of ladders through the density-matrix renormalization-group technique. Our analysis suggests that interactions drive a topologically non-trivial gapped phase into a gapless Luttinger liquid.
Majorana modes can arise as zero energy bound states in a variety of solid state systems. A lattice of these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. This thesis is devoted to the study of interactions between the Majorana zero modes when such a lattice has a triangular geometry. We map the phase diagram of this model using a combination of mean field theory and numerical simulation of ladders through the density-matrix renormalization-group technique. Our analysis suggests that interactions drive a topologically non-trivial gapped phase into a gapless Luttinger liquid.
Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional (1D) topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting 1D many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order. In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking. We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors. We further show that the interface between the interacting model and a 1D topological superconductor does not support Majorana modes. We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit. Our results demonstrate that robust Majorana-like zero modes may appear in a many-body system without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs.
Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing.Typical scenarios for one-dimensional (1D) topological superconductivity assume a broken gauge symmetry associated to a superconducting state.However, no interacting 1D many-body system is known to spontaneously break gauge symmetries.Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order.In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking.We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors.We further show that the interface between the interacting model and a 1D topological superconductor does not support Majorana modes.We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit.Our results demonstrate that robust Majorana-like zero modes may appear in a many-body system without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs.
In this work, we present a collection of three-dimensional higher-order symmetry-protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We use a coupled wire construction to generate three families of microscopic lattice models: insulators with helical hinge modes, superconductors with chiral Majorana hinge modes, and fractionalized insulators with helical hinge modes that carry fractional charge. In particular, these HOSPTs do not require spatial symmetry protection, but are instead protected by subsystem symmetries, and support ``fractonic'' quasiparticle excitations that move within only a low-dimensional submanifold of the system. We analyze the anomaly structure for the boundary theory and the entanglement Hamiltonian, and show that the side surfaces of these HOSPTs, despite being partially gapped, exhibit symmetry anomalies, and can only be realized as the boundary of three-dimensional HOSPT phases.
Classification of symmetry-protected topological phases such as the topological superconductor (TSC) is well known in the free fermion picture. Recently, it was observed that including many-body interactions that preserves symmetry gives rise to novel surface phases and breaks down the classification scheme. A complete understanding of the microscopic theory for such phases is missing. This paper is an attempt to understand the interaction that gives rise to these phases in the case of the three-dimensional TSC. The authors build a coupled wire model Hamiltonian for the gapless surface and show that the addition of a time-reversal symmetric two-body interaction, constructed in this paper, opens an energy gap in the spectrum. They also show this gapped surface phase is topologically nontrivial and is classified differently compared to the noninteracting case.