Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases

Abstract

Using a matrix product state algorithm with infinite boundary conditions, we compute high-resolution dynamic spin and quadrupolar structure factors in the thermodynamic limit to explore the low-energy excitations of isotropic bilinear-biquadratic spin-1 chains. Haldane mapped the spin-1 Heisenberg antiferromagnet to a continuum field theory, the non-linear sigma model (NL$\sigma$M). We find that the NL$\sigma$M fails to capture the influence of the biquadratic term and provides only an unsatisfactory description of the Haldane phase physics. But several features in the Haldane phase can be explained by non-interacting multi-magnon states. The physics at the Uimin-Lai-Sutherland point is characterized by multi-soliton continua. Moving into the extended critical phase, we find that these excitation continua contract, which we explain using a field-theoretic description. New excitations emerge at higher energies and, in the vicinity of the purely biquadratic point, they show simple cosine dispersions. Using block fidelities, we identify them as elementary one-particle excitations and relate them to the integrable Temperley-Lieb chain.

arXiv comment9 pages, 5 figures; improved text, published version

References in corpus (35)

• The density-matrix renormalization group
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Bragg spectroscopy of a Bose-Einstein condensate
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Exact Excited States of Non-Integrable Models
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Implementation of Spin Hamiltonians in Optical Lattices
• Momentum-Resolved Bragg Spectroscopy in Optical Lattices
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Dimer state of spin-1 Bosons in an optical lattice
• Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition
• Infinite boundary conditions for matrix product state calculations
• Biquadratic interactions and spin-Peierls transition in the spin 1 chain LiVGe2O6
• Exact two-spinon dynamical correlation function of the Heisenberg model
• Bragg Spectroscopy of ultracold atoms loaded in an optical lattice
• Continuum in the spin excitation spectrum of a Haldane chain, observed by neutron scattering in CsNiCl3
• Exact two-spin dynamic structure factor of the one-dimensional s=1/2 Heisenberg-Ising antiferromagnet
• Thermodynamics of the bilinear-biquadratic spin one Heisenberg chain
• Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
• The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
• On the 3-particle scattering continuum in quasi one dimensional integer spin Heisenberg magnets
• Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models
• The Three-Magnon Contribution to the Spin Correlation Function in Integer-Spin Antiferromagnetic Chains
• Exact solution of the deformed biquadratic spin 1 hamiltonian
• Infinite boundary conditions for response functions and limit cycles in iDMRG, demonstrated for bilinear-biquadratic spin-1 chains
• Pulsed Neutron Spectroscopy of Low Dimensional Magnets: Past, Present, and Future
• Path Integral for Spin-1 Chain in the Fluctuating Matrix Product State Basis

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• Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain
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