Critical points of the anyon-Hubbard model

Abstract

Anyons are particles with fractional statistics that exhibit a nontrivial change in the wavefunction under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density matrix renormalization group method and observed that gapped (Mott insulator) and gapless (superfluid) phases characterized the phase diagram, regardless of the value of the statistical angle. The phase diagram for higher densities was calculated and showed that the Mott lobes increase (decrease) as a function of the statistical angle (global density). The position of the critical point separating the gapped and gapless phases was found using quantum information tools, namely the block von Neumann entropy. We also studied the evolution of the critical point with the global density and the statistical angle and showed that the anyon-Hubbard model with a statistical angle $\theta =\pi /4$ is in the same universality class as the Bose-Hubbard model with two body interactions.

9 pages, 8 figures. Comments are welcome

References in corpus (36)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Entropy and Quantum Field Theory
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
• Phase separation in supersolids
• 1/2-Anyons in small atomic Bose-Einstein condensates
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• The Anyon Hubbard Model in One-Dimensional Optical Lattices
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Anyonic interferometry and protected memories in atomic spin lattices
• Dynamic properties of the one-dimensional Bose-Hubbard model
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Correlation functions of one-dimensional anyonic fluids
• Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Anyons in a weakly interacting system
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Magnetic and Superfluid Transitions in the d=1 Spin-1 Boson Hubbard Model
• Ground-state properties of anyons in a one-dimensional lattice
• Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors
• Re-entrance and entanglement in the one-dimensional Bose-Hubbard model
• Strongly interacting mesoscopic systems of anyons in one dimension
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
• Interacting spin-1 bosons in a two-dimensional optical lattice
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model

Cited by in corpus (26)

• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Ground State Properties of the One-Dimensional Unconstrained Pseudo-Anyon Hubbard Model
• Anyonic Haldane insulator in one dimension
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Probing the exchange statistics of one-dimensional anyon models
• Correlation functions of one-dimensional strongly interacting two-component gases
• Strongly repulsive anyons in one dimension
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• Three-body interaction effects on the ground state of one-dimensional anyons
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Inhomogeneous hard-core bosonic mixture with checkerboard supersolid phase: Quantum and thermal phase diagram
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension
• Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Statistics-tuned phases of pseudofermions in one dimension
• Quantum walk of two anyons across a statistical boundary
• Quantum phases of the biased two-chain-coupled Bose-Hubbard Ladder
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• One-dimensional anyons in relativistic field theory