Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity
Abstract
In this article, we address the possibility of topological quantum spin liquids with only short-range (spin) correlations in the whole phase diagram in a ladder system, through an exactly solvable model which represents a generalization of the two-dimensional Kitaev honeycomb spin model to a ribbon geometry. This system gives rise to ℤ2 gauge fields emerging in a static way in the ground state through Majorana fermions which then produce either $0$ or π flux. Through a quantum field theory perspective, mathematical and Density Matrix Renormalization Group results, we present our progress on the geometrical, topological and physical classification of this model through observables navigating on the whole phase diagram presenting three spin-liquid phases with a spin gap and a metallic phase in the sense of Majorana fermions. We propose a bulk-edge correspondence revealing the presence of protected zero-energy Majorana fermions at the edge in the phases with a gap and revealing also the presence of itinerant Majorana fermions in the bulk in the topological liquid phase. The proposed approach allows us to distinguish between properties of the brickwall ladder giving rise to a special line and those of the square ladder allowing for the gapless Majorana liquid phase. This model gives some hope on finding solutions for topological quantum spin models, e.g. with π flux, on a square lattice geometry. This approach also allows for a correspondence onto models of topological superconductivity.
Related
- A Clifford-index approach connecting boundary Dirac fermions to sigma-model topological terms in the periodic table of topological insulators and superconductors
- Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
- SC♯: superconductivity intertwined with topological order
- Relative entropy in quantum field theory: the case of squeezed fermions
- Fermions and the Tsirelson Problem in Real Quantum Theory
BibTeX
@misc{korolev2026topological,
title = {{Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity}},
author = {Magali Korolev and Fan Yang and Erik S. Sørensen and Karyn Le Hur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40297},
eprint = {2610.40297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40297},
}
RIS
TY - UNPB
TI - Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity
AU - Magali Korolev
AU - Fan Yang
AU - Erik S. Sørensen
AU - Karyn Le Hur
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40297
UR - https://arxiv.org/abs/2610.40297
AB - In this article, we address the possibility of topological quantum spin liquids with only short-range (spin) correlations in the whole phase diagram in a ladder system, through an exactly solvable model which represents a generalization of the two-dimensional Kitaev honeycomb spin model to a ribbon geometry. This system gives rise to ℤ_2 gauge fields emerging in a static way in the ground state through Majorana fermions which then produce either $0$ or π flux. Through a quantum field theory perspective, mathematical and Density Matrix Renormalization Group results, we present our progress on the geometrical, topological and physical classification of this model through observables navigating on the whole phase diagram presenting three spin-liquid phases with a spin gap and a metallic phase in the sense of Majorana fermions. We propose a bulk-edge correspondence revealing the presence of protected zero-energy Majorana fermions at the edge in the phases with a gap and revealing also the presence of itinerant Majorana fermions in the bulk in the topological liquid phase. The proposed approach allows us to distinguish between properties of the brickwall ladder giving rise to a special line and those of the square ladder allowing for the gapless Majorana liquid phase. This model gives some hope on finding solutions for topological quantum spin models, e.g. with π flux, on a square lattice geometry. This approach also allows for a correspondence onto models of topological superconductivity.
ER -