Commensurate and Incommensurate States of Topological Quantum Matter

Abstract

We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in mesoscopic arrays. In two space dimensions, we obtain the simplest representative of a topological universality class that we call Lifshitz. It is characterized by a topological tricritical point where a non-locally ordered homogeneous phase meets a disordered phase and a third phase that displays modulations of a non-local order parameter.

7 pages, 4 figures

References in corpus (9)

• Charge insensitive qubit design derived from the Cooper pair box
• Interacting anyons in topological quantum liquids: The golden chain
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological Order and Conformal Quantum Critical Points
• Scaling of entanglement support for Matrix Product States
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Robustness of a perturbed topological phase
• Fractional topological superconductors with fractionalized Majorana fermions

Cited by in corpus (12)

• Criticality in Translation-Invariant Parafermion Chains
• Pretopological fractional excitations in the two-leg flux ladder
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Dynamics of parafermionic states in transport measurements
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• An exact local mapping from clock-spins to fermions
• Engineering a Josephson junction chain for the simulation of the clock model
• Overlap of parafermionic zero modes at a finite distance
• Interrelations among frustration-free models via Witten's conjugation
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Noninteracting tight-binding models for Fock parafermions
• Phase diagram of an extended parafermion chain