Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field

Abstract

We investigate the properties of the Heisenberg S=1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase.

revised version, as published in PRB

References in corpus (43)

• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Implementation of Spin Hamiltonians in Optical Lattices
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Competing orders in one dimensional spin 3/2 fermionic systems
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• One-dimensional spin-liquid without magnon excitations
• Frustrated ferromagnetic spin-1/2 chain in a magnetic field: The phase diagram and thermodynamic properties
• Multi-magnon bound states in the frustrated ferromagnetic 1D chain
• Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
• Confinement and Superfluidity in one-dimensional Degenerate Fermionic Cold Atoms
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
• Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain
• Field-induced chiral phase in isotropic frustrated spin chains
• Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases
• Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap
• Pair Superfluidity of Three-Body Constrained Bosons in Two Dimensions
• Dynamical spin correlations in Heisenberg ladder under magnetic field and correlation functions in SO(5) ladder
• Middle-Field Cusp Singularities in the Magnetization Process of One-Dimensional Quantum Antiferromagnets
• Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire
• On the origin of biquadratic exchange in spin 1 chains
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• Vector chiral order in frustrated spin chains
• Haldane-Gapped Spin Chains as Luttinger Liquids: Correlation Functions at Finite Field
• Delta-Function Bose Gas Picture of S=1 Antiferromagnetic Quantum Spin Chains Near Critical Fields
• Single-particle versus pair condensation of hard-core bosons with correlated hopping
• Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain
• Ising Deconfinement Transition Between Feshbach-Resonant Superfluids
• Luttinger liquid behavior in spin chains with a magnetic field
• Exact Results of Dimerization Order Parameter in $SU(n)$ Antiferromagnetic Chains
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Commensurate and incommensurate correlations in Haldane gap antiferromagnets
• A note on density correlations in the half-filled Hubbard model
• Novel massless phase of Haldane-gap antiferromagnets in magnetic field
• Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields
• Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories

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