Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

Abstract

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k,\omega ).$ The description of the singularities of dynamic response functions near an edge $\epsilon (k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon (k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

arXiv commentfinal published version

References in corpus (32)

• Bosonization and Strongly Correlated Systems
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Quantum criticality and universal scaling of a quantum antiferromagnet
• Universal theory of nonlinear Luttinger liquids
• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Coulomb drag by small momentum transfer between quantum wires
• Dynamics of excitations in a one-dimensional Bose liquid
• Threshold singularities in the dynamic response of gapless integrable models
• ``X-Ray Edge'' Singularities in Nanotubes and Quantum Wires with Multiple Subbands
• Dynamic structure factor of the Calogero-Sutherland model
• Spectral functions of strongly interacting isospin-1/2 bosons in one dimension
• Finite-Energy Spectral-Weight Distributions of a 1D Correlated Metal
• Spectral properties of one dimensional insulators and superconductors
• Theory of hole propagation in one dimensional insulators and superconductors
• Luttinger liquids with curvature: Density correlations and Coulomb drag effect
• Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction
• Photo-Solitonic Effect
• Spin-charge separation in a strongly correlated spin-polarized chain
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Dynamical Functions of a 1D Correlated Quantum Liquid
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Exact dynamical structure factor of the degenerate Haldane-Shastry model
• Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields
• One-Particle Spectral Properties of 1D Mott-Hubbard Insulators
• Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics

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• Spin-charge separation effects in the low-temperature transport of 1D Fermi gases
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• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• Relaxation dynamics of local observables in integrable systems
• Dynamics of a one-dimensional spinor Bose liquid: a phenomenological approach
• Universal broadening of the light cone in low-temperature transport
• Threshold Singularities in the One Dimensional Hubbard Model
• The fate of 1D spin-charge separation away from Fermi points
• One-dimensional liquid ${}^4$He: dynamical properties beyond Luttinger liquid theory
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
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• Scattering of hole excitations in a one-dimensional spinless quantum liquid
• Charge dynamics in half-filled Hubbard chains with finite on-site interaction
• Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains
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• Dynamics of a Heisenberg spin chain in the quantum critical regime: NMR experiment versus effective field theory
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• Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid
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• Experimental Realization of One Dimensional Helium
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• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study
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