Anyonic Liquids in Nearly Saturated Spin Chains

Abstract

Most Heisenberg-like spin chains flow to a universal free-fermion fixed point near the magnetic-field induced saturation point. Here we show that an exotic fixed point, characterized by two species of low-energy excitations with mutual anyonic statistics, may also emerge in such spin chains if the dispersion relation has two minima. By using bosonization, two-magnon exact calculations, and numerical density-matrix-renormalization-group, we demonstrate the existence of this anyonic-liquid fixed point in an XXZ spin chain with up to second neighbor interactions. We also identify a range of microscopic parameters, which support this phase.

arXiv comment5 pages, 3 figures, 3 pages of supplemental material (to appear in PRL)

References in corpus (38)

• Bose-Einstein Condensation in Magnetic Insulators
• Realization of Bose-Einstein condensation of dilute magnons in TlCuCl${}_3$
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Coupled Ladders in a Magnetic Field
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• The Fractional Quantum Hall effect in an array of quantum wires
• From Luttinger liquid to non-Abelian quantum Hall states
• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• Generalized Jordan-Wigner Transformations
• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Fermionization and bosonization of expanding 1D anyonic fluids
• Correlation functions of one-dimensional anyonic fluids
• Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Magnetic vortex crystals in frustrated Mott insulator
• Ground-state properties of one-dimensional anyon gases
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Deformed triangular lattice antiferromagnets in a magnetic field: role of spatial anisotropy and Dzyaloshinskii-Moriya interactions
• Ground states of a frustrated spin-1/2 antifferomagnet: Cs_2CuCl_4 in a magnetic field
• Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime
• A new class of exactly solvable interacting fermion models in one dimension
• General method for calculating the universal conductance of strongly correlated junctions of multiple quantum wires
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Magnon condensation with finite degeneracy on the triangular lattice
• How to find conductance tensors of quantum multi-wire junctions through static calculations: application to an interacting Y-junction
• Condensate-induced transitions and critical spin chains
• From spin to anyon notation: The XXZ Heisenberg model as a $D_3$ (or $su(2{)}_4$) anyon chain
• The Canted Spiral: An Exact Ground State of XXZ Zigzag Ladders
• Condensation of Anyons in Frustrated Quantum Magnets
• A hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points
• Double zigzag spin chain in strong magnetic field close to saturation
• Exactly integrable family of generalized Hubbard models with twisted Yangian symmetry

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• Criticality-Enhanced Magnetocaloric Effect in Quantum Spin Chain Material Copper Nitrate