Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields

Abstract

We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of a S=1 Haldane chain, placed in a strong external magnetic field $H$ exceeding the Haldane gap $\Delta$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\omega \gtrsim \Delta$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity $S^{\parallel }(q=\pi ,\omega )\propto (\omega -{\omega }_0{)}^{-{\alpha }^{\prime }}$. We study the behavior of the high-energy edge exponent ${\alpha }^{\prime }$ and the edge ${\omega }_0$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\Delta$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.

arXiv comment(v2) error in Eq.(11) corrected

References in corpus (20)

• The density-matrix renormalization group
• Luttinger Liquid Behavior in Carbon Nanotubes
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• Critical Properties of gapped spin-1/2 chains and ladders in a magnetic field
• Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
• The Fermi Edge Singularity and Boundary Condition Changing Operators
• Dynamics of a heavy particle in a Luttinger liquid
• Dynamical spin correlations in Heisenberg ladder under magnetic field and correlation functions in SO(5) ladder
• Haldane-Gapped Spin Chains as Luttinger Liquids: Correlation Functions at Finite Field
• Spectral properties of one dimensional insulators and superconductors
• Luttinger liquid behavior in spin chains with a magnetic field
• Spin orthogonality catastrophe in two-dimensional antiferromagnets and superconductors
• Specific Heat Study of an S=1/2 Alternating Heisenberg Chain System F_5PNN Under Magnetic Field
• Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S=1 Antiferromagnet Observed by the Specific Heat
• Zeeman levels with exotic field dependence in the high field phase of a S=1 Heisenberg antiferromagnetic chain
• Electron spin resonance in high-field critical phase of gapped spin chains
• Fermi-edge singularity in a spin-incoherent Luttinger liquid
• Low-energy excitations in the magnetized state of the bond-alternating quantum S=1 chain system NTENP
• Response functions of gapped spin systems in high magnetic field
• Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories

Cited by in corpus (8)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• From density-matrix renormalization group to matrix product states
• Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Spin-charge separation in two-component Bose-gases
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Vector chiral order in frustrated spin chains
• Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field