How universal is the one-particle Green's function of a Luttinger liquid?

Abstract

The one-particle Green's function of the Tomonaga-Luttinger model for one-dimensional interacting Fermions is discussed. Far away from the origin of the plane of space-time coordinates the function falls off like a power law. The exponent depends on the direction within the plane. For a certain form of the interaction potential or within an approximated cut-off procedure the different exponents only depend on the strength of the interaction at zero momentum and can be expressed in terms of the Luttinger liquid parameters $K_{\rho }$ and $K_{\sigma }$ of the model at hand. For a more general interaction and directions which are determined by the charge velocity $v_{\rho }$ and spin velocity $v_{\sigma }$ the exponents also depend on the smoothness of the interaction at zero momentum and the asymptotic behavior of the Green's function is not given by the Luttinger liquid parameters alone. This shows that the physics of large space-time distances in Luttinger liquids is less universal than is widely believed.

5 pages with 2 figures

References in corpus (3)

• One-Dimensional Fermi liquids
• Non-fermi-liquid single particle lineshape of the quasi-one-dimensional non-CDW metal Li_{0.9}Mo_{6}O_{17} : comparison to the Luttinger liquid
• Nonuniversal spectral properties of the Luttinger model

Cited by in corpus (30)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Charge transport through single molecules, quantum dots, and quantum wires
• Luttinger liquid universality in the time evolution after an interaction quench
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Luttinger liquid properties of the steady state after a quantum quench
• Luttinger liquid physics from infinite-system DMRG
• The spectral function of the Tomonaga-Luttinger model revisited: power laws and universality
• Spectral properties of one-dimensional Fermi systems after an interaction quench
• Relaxation dynamics of an exactly solvable electron-phonon model
• Dephasing by electron-electron interactions in a ballistic Mach-Zehnder interferometer
• Luttinger model approach to interacting one-dimensional fermions in a harmonic trap
• ESR theory for interacting 1D quantum wires
• Universal dephasing in a chiral 1D interacting fermion system
• Damping of zero sound in Luttinger liquids
• Dynamic scaling in the vicinity of the Luttinger liquid fixed point
• Physics in one dimension: theoretical concepts for quantum many-body systems
• Time evolution during and after finite-time quantum quenches in Luttinger liquids
• Spin-charge separation in transport through Luttinger liquid rings
• Spectral properties of one-dimensional spiral spin density wave states
• Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales
• Tunneling into quantum wires: regularization of the tunneling Hamiltonian and consistency between free and bosonized fermions
• The dynamic structure factor in impurity-doped spin chains
• Some sum rules for the non-Fermi liquids: new applications taking into account the mass renormalization factor
• Structural Evolution of 1D Spectral Function from Low- to High-Energy Limits
• How does a quadratic term in the energy dispersion modify the single-particle Green's function of the Tomonaga-Luttinger model?
• Breaking a "poor man" RG approach in the Luttinger liquid with one impurity
• Renormalization Group Study of a Fragile Fermi liquid in $1+\epsilon$ dimensions
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Investigating the roots of the nonlinear Luttinger liquid phenomenology