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.

arXiv comment7 pages, 4 figures

References in corpus (32)

• Unpaired Majorana fermions in quantum wires
• 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
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Scaling of entanglement support for Matrix Product States
• Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Post-Matrix Product State Methods: To tangent space and beyond
• Robustness of a perturbed topological phase
• Superconducting Nanocircuits for Topologically Protected Qubits
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Fractional topological superconductors with fractionalized Majorana fermions
• Dualities and the phase diagram of the $p$-clock model
• Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions
• The Bond-Algebraic Approach to Dualities
• Strongly interacting Majorana modes in an array of Josephson junctions
• Matrix product states and variational methods applied to critical quantum field theory
• From Majorana Fermions to Topological Order
• Unified approach to Quantum and Classical Dualities
• Breakdown of a perturbed Z_N topological phase
• Fock Parafermions and Self-Dual Representations of the Braid Group
• Topological phases in gapped edges of fractionalized systems
• Fractionalization in Superconductor Josephson Junction Arrays Hinged by Quantum Spin Hall edges
• Holographic Symmetries and Generalized Order Parameters for Topological Matter
• Topological phases in two-dimensional arrays of parafermionic zero modes
• Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations

Cited by in corpus (25)

• Topological phases with parafermions: theory and blueprints
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Criticality in Translation-Invariant Parafermion Chains
• Parafermion chain with $2\pi /k$ Floquet edge modes
• Topological phases of parafermions: a model with exactly-solvable ground states
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Pretopological fractional excitations in the two-leg flux ladder
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Phase transitions in the ${\mathbb{Z}}_p$ and U(1) clock models
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Exact results for a $Z_3$ clock-type model and some close relatives
• Changing anyonic ground degeneracy with engineered gauge fields
• Topological phase, supercritical point and emergent phenomena in extended ${\mathbb{Z}}_3$ parafermion chain
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Dyonic zero-energy modes
• 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
• Overlap of parafermionic zero modes at a finite distance
• Interrelations among frustration-free models via Witten's conjugation
• Engineering a Josephson junction chain for the simulation of the clock model
• Noninteracting tight-binding models for Fock parafermions
• Phase diagram of an extended parafermion chain
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor