Spectral function of spinless fermions on a one-dimensional lattice

Abstract

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, the spectral weight of the Luttinger liquid result for the dynamical structure factor of the Heisenberg model at zero field is compared with the exact two-spinon contribution.

30 pages, 18 figures

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• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
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• Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains
• Charge dynamics in half-filled Hubbard chains with finite on-site interaction
• Spin-charge coupling in quantum wires at zero magnetic field
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• Equilibrium dynamics of the XX chain
• Luttinger liquid physics from infinite-system DMRG
• Equilibration of a spinless Luttinger liquid
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Spectral function of the 2D Hubbard model: a density matrix renormalization group plus cluster perturbation theory study
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• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• The spectral function of the Tomonaga-Luttinger model revisited: power laws and universality
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• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• Low temperature dynamics of nonlinear Luttinger liquids
• Relaxation of weakly interacting electrons in one dimension
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• A renormalization group analysis of the one-dimensional extended Hubbard model
• Long time correlations of nonlinear Luttinger liquids
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• Recursive Method for the Density of States in One Dimension
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Equilibration of a one-dimensional quantum liquid
• Spectral Properties of Interacting One-Dimensional Spinless Fermions
• The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions
• Spectral properties of one-dimensional spiral spin density wave states
• Numerical Computation of Dynamically Important Excited States of Many-Body Systems
• Electron-Plasmon scattering in chiral 1D systems with nonlinear dispersion
• Form factors of bound states in the XXZ chain
• Robust effective ground state in a nonintegrable Floquet quantum circuit
• Mobile impurity approach to the optical conductivity in the Hubbard chain
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Solitons in a one-dimensional Wigner crystal
• Emergence and spectral-weight transfer of electronic states in the Hubbard ladder
• Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange
• Excitations in the Yang-Gaudin Bose gas
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Mobile impurities in integrable models
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Interaction distance in the extended XXZ model
• Integrability breaking and bound states in Google's decorated XXZ circuits
• Structural Evolution of 1D Spectral Function from Low- to High-Energy Limits
• A quantum phase transition detected through one dimensional ballistic conductance
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator
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• Luttinger parameters of interacting fermions in 1D at high energies
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• Kinetic processes in Fermi-Luttinger liquids
• Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
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