Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
arXiv:1203.0932 · doi:10.1088/1367-2630/14/7/075001
Abstract
We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical form are investigated all leading to universal Luttinger liquid physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the Luttinger liquid phenomenology. For generic regular potentials the large time decay of the momentum distribution function towards the steady-state value is characterized by a power law with a universal exponent which only depends on the potential at zero momentum transfer. A commonly employed ad hoc procedure fails to give this exponent. Besides quenches from zero to positive interactions we also consider abrupt changes of the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and the one obtained in equilibrium at equal two-particle interaction.
21 pages, 4 figures
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- Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
- Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system
- Dynamical Transition in Interaction Quenches of the One-Dimensional Hubbard Model
- Parametric instability in periodically driven Luttinger liquids
- Spectral properties of one-dimensional Fermi systems after an interaction quench
- Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
- Marginal quenches and drives in Tomonaga-Luttinger liquids
- Quantum Quench for inhomogeneous states in the non-local Luttinger model
- Optimal protocols for finite-duration quantum quenches in the Luttinger model
- Small quenches and thermalization