Criticality in Translation-Invariant Parafermion Chains

Abstract

In this work we numerically study critical phases in translation-invariant ${\mathbb{Z}}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a ${\mathbb{Z}}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual ${\mathbb{Z}}_N$ clock models. For $3\le N\le 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.

arXiv commentpublished version

References in corpus (53)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Entanglement in quantum critical phenomena
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Interacting anyons in topological quantum liquids: The golden chain
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Condensate induced transitions between topologically ordered phases
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Genons, twist defects, and projective non-Abelian braiding statistics
• From Luttinger liquid to non-Abelian quantum Hall states
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Theory of defects in Abelian topological states
• Classification of Topological Defects in Abelian Topological States
• Wire deconstructionism of two-dimensional topological phases
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Criticality in self-dual sine-Gordon models
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Superconducting analogue of the parafermion fractional quantum Hall states
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Collective states of interacting Fibonacci anyons
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Synthetic Topological Degeneracy by Anyon Condensation
• Parafermionic conformal field theory on the lattice
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Topological phases in gapped edges of fractionalized systems
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Generalized Kitaev Models and Slave Genons
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Translation invariance, topology, and protection of criticality in chains of interacting anyons
• Commensurate and Incommensurate States of Topological Quantum Matter
• Construction of Modular Branching Functions from Bethe's Equations in the 3-State Potts Chain
• Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States
• Braiding of non-Abelian anyons using pairwise interactions
• Quantum spin ladders of non-Abelian anyons

Cited by in corpus (38)

• Topological phases with parafermions: theory and blueprints
• Anyon condensation and its applications
• Critical properties of the two-dimensional $q$-state clock model
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• The phase transitions between $Z_n\times Z_n$ bosonic topological phases in 1+1 D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases
• Energy as a detector of nonlocality of many-body spin systems
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Localization-protected order in spin chains with non-Abelian discrete symmetries
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Non-diagonal anisotropic quantum Hall states
• Parafermionization, bosonization, and critical parafermionic theories
• Free-fermion descriptions of parafermion chains and string-net models
• Matrix product states for topological phases with parafermions
• Changing anyonic ground degeneracy with engineered gauge fields
• Topological phase, supercritical point and emergent phenomena in extended ${\mathbb{Z}}_3$ parafermion chain
• Self-dual $S_3$-invariant quantum chains
• Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
• Quantum criticality in many-body parafermion chains
• A Brief History of Free Parafermions
• Extracting the Luttinger parameter from a single wave function
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Dynamical topological excitations in parafermion chains
• Topological and Geometric Universal Thermodynamics in Conformal Field Theory
• Anomalous domain wall condensation in a modified Ising chain
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Decoding quantum criticalities from fermionic/parafermionic topological states
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Twofold twist defect chains at criticality
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Noninteracting tight-binding models for Fock parafermions
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Phase diagram of an extended parafermion chain