Coupled wire construction of a topological phase with chiral tricritical Ising edge modes

Abstract

Tricritical Ising (TCI) phase transition is known to occur in several interacting spin and Majorana fermion models and is described in terms of a supersymmetric conformal field theory (CFT) with central charge $c=7/10$. The field content of this CFT is highly nontrivial and includes among its primary fields the Fibonacci anyon, making it of potential interest to strategies seeking to implement fault-tolerant topological quantum computation with non-Abelian phases of matter. In this paper we explore the possibility that a TCI CFT can occur at the edge of a gapped two-dimensional topological state as a stable phase. We discuss a possible realization of this 2D phase based on a coupled-wire construction using the Grover-Sheng-Vishwanath chain model of Majorana zero modes coupled to Ising spins which is known to undergo the TCI phase transition. From the combined analysis using mean-field theory, conformal field theory and density matrix renormalization group (DMRG) on 2- and 4-leg ladders, we find that the left- and right-moving gapless TCI modes become spatially separated and reside on two opposite edges of the system, forming a precursor of the required 2D topological phase.

arXiv comment9 pages, 7 figures

References in corpus (30)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Entanglement Entropy and Quantum Field Theory
• Classification of topological quantum matter with symmetries
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• The Fractional Quantum Hall effect in an array of quantum wires
• From Luttinger liquid to non-Abelian quantum Hall states
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Roadmap to Majorana surface codes
• New quantum phases in a one-dimensional Josephson array
• Phase Diagram of the Interacting Majorana Chain Model
• Strongly interacting Majorana modes in an array of Josephson junctions
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• Quantum Spin Hall Effect in Strip of Stripes Model
• Pairing in Luttinger Liquids and Quantum Hall States
• Fractional Topological Superconductivity and Parafermion Corner States
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Electronic structure of topological superconductors in the presence of a vortex lattice
• Fibonacci Topological Superconductor
• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
• Pretopological fractional excitations in the two-leg flux ladder
• Fractional chiral superconductors
• Majorana-Hubbard model on the honeycomb lattice
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Phase diagrams of Majorana-Hubbard ladders
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice

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