Dynamic structure factor of the Calogero-Sutherland model

Abstract

We evaluate the dynamic structure factor $S(q,\omega )$ of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small $q$, the structure factor differs from zero in a finite interval of frequencies of the width $\delta \omega \propto q^2/m$. At the borders of this interval $S(q,\omega )$ exhibits power-law singularities with exponents depending only on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the X-ray absorption spectra of metals.

References in corpus (8)

• Bosonization and Strongly Correlated Systems
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Dynamic response of one-dimensional interacting fermions
• Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
• Coulomb drag by small momentum transfer between quantum wires
• ``X-Ray Edge'' Singularities in Nanotubes and Quantum Wires with Multiple Subbands
• Single-particle Green's functions of the Calogero-Sutherland model at couplings λ= 1/2, 1, and 2
• Exact Dynamical Correlations of the 1/r^2 Model

Cited by in corpus (32)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Dynamics of excitations in a one-dimensional Bose liquid
• Threshold singularities in the dynamic response of gapless integrable models
• Super-Tonks-Girardeau regime in trapped one-dimensional dipolar gases
• Asymptotic analysis and quantum integrable models
• Edge exponent in the dynamic spin structure factor of the Yang-Gaudin model
• Luttinger liquids with curvature: Density correlations and Coulomb drag effect
• Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near Mott-insulator to ferromagnetic liquid transition
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
• Damping of zero sound in Luttinger liquids
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics
• Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent
• Modulation theory of quantum tunneling into a Calogero-Sutherland fluid
• Thermal radiation as a probe of one-dimensional electron liquids
• Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics
• Non-equilibrium charge noise and dephasing from a spin-incoherent Luttinger liquid
• Excitation spectrum of a 2D long-range Bose-liquid with a supersymmetry
• Particle Propagator of Spin Calogero-Sutherland Model
• Dynamic structure factor of Calogero-Sutherland fluids
• Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations
• Investigating the roots of the nonlinear Luttinger liquid phenomenology