Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid

Abstract

Quantum many-body edge and extended magnon excitations from the 1/3 -- plateau of the anisotropic Heisenberg model on an open AB${}_2$ chain in a magnetic field $h$ are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and $h$ in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge states degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\lambda$ approaches the critical point from the $\lambda >0$ side of the phase diagram.

arXiv comment10 pages, 10 figures

References in corpus (44)

• Topological Insulators
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological States and Adiabatic Pumping in Quasicrystals
• Topological Boundary Modes in Isostatic Lattices
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Complete classification of 1D gapped quantum phases in interacting spin systems
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Edge states and topological phases in one-dimensional optical superlattices
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Critical Properties of gapped spin-1/2 chains and ladders in a magnetic field
• Low-Lying Excited States and Low-Temperature Properties of an Alternating Spin-1 / Spin-1/2 Chain : A DMRG study
• Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
• Choreographed entangle dances: topological states of quantum matter
• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Topology and edge modes in quantum critical chains
• Multi-step approach to microscopic models for frustrated quantum magnets - the case of the natural mineral azurite
• Edge states in trimer lattices
• Nature of the spin dynamics and 1/3 magnetization plateau in azurite
• Matrix product states approach to the Heisenberg ferrimagnetic spin chains
• Elementary Excitations of Heisenberg Ferrimagnetic Spin Chains
• Thermodynamics of the (1,1/2) Ferrimagnet in Finite Magnetic Fields
• Chiral Magnonic Edge States in Ferromagnetic Skyrmion Crystals Controlled by Magnetic Fields
• Critical Behaviour of Mixed Heisenberg Chains
• Critical Behavior of Anisotropic Heisenberg Mixed-Spin Chains in a Field
• Delta-Function Bose Gas Picture of S=1 Antiferromagnetic Quantum Spin Chains Near Critical Fields
• Scattering particles in quantum spin chains
• Multi-critical Behavior in Topological Phase Transitions
• Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum
• The magnetic and crystal structure of azurite Cu${}_3$(CO${}_3$)${}_2$(OH)${}_2$ as determined by neutron diffraction
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• Spin Configuration in the 1/3 Magnetization Plateau of Azurite Determined by NMR
• Frustration-induced quantum phase transitions in a quasi-one-dimensional ferrimagnet: Hard-core boson map and the Ton ks-Girardeau limit
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Finite size spectrum, magnon interactions and magnetization of S=1 Heisenberg spin chains
• Tomonaga-Luttinger spin liquid in the spin-1/2 inequilateral diamond-chain compound K${}_3$Cu${}_3$AlO${}_2$(SO${}_4$)${}_4$
• Static and Dynamic Magnetic Properties of Spin-1/2 Inequilateral Diamond-Chain Compounds $A_3$Cu${}_3$AlO${}_2$(SO${}_4$)${}_4$ ($A$=K, Rb, and Cs)
• Quantum phase transitions in alternating spin-(1/2, 5/2) Heisenberg chains
• Quasi-One-Dimensional Quantum Ferrimagnets
• Breakdown of intermediate one-half magnetization plateau of spin-1/2 Ising-Heisenberg and Heisenberg branched chains at triple and Kosterlitz-Thouless critical points
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Magnetic properties of the quantum spin-1/2 XX diamond chain: The Jordan-Wigner approach
• Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds
• Magnetic field - temperature phase diagram of ferrimagnetic alternating chains: spin-wave theory from a fully polarized vacuum
• Luttinger liquid parameter for the spin-1 Heisenberg chain in a magnetic field

Cited by in corpus (10)

• Low temperature pseudo-phase transition in an extended Hubbard diamond chain
• Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain
• Ground-state phase diagram and thermodynamics of coupled trimer chains
• Quantum phase transitions and composite excitations of antiferromagnetic spin trimer chains in a magnetic field
• Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions
• The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field
• Quantum bicritical point and phase separation in a frustrated Heisenberg ladder
• Translational symmetry broken magnetization plateau of the S=1 antiferromagnetic Heisenberg chain with competing anisotropies
• Mixed-spin Heisenberg ladders in a magnetic field
• Translational-Symmetry-Broken Magnetization Plateaux of the $S=3/2$ Anisotropic Antiferromagnetic Chain