On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches

Abstract

We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. We express the critical exponent $\beta$ governing the decay of the steady-state propagator as an explicit functional of the switching protocol. At long distances $\beta$ depends only on the initial state while at short distances it is also history dependent. Continuous protocols of arbitrary complexity can be realized with infinitely long sequences. For quenches of finite duration we prove that there exist no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid. Nevertheless memory effects are washed out at short-distances. The adiabatic theorem is then investigated with ramp-switchings of increasing duration, and several analytic results for both the propagator and the excitation energy are derived.

7 pages, 4 figures

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Repulsively bound atom pairs in an optical lattice
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• The Luttinger model following a sudden interaction switch-on
• Dephasing and the steady state in quantum many-particle systems
• Strongly correlated fermions after a quantum quench
• Quantum quench dynamics of the Luttinger model
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Bound states in ab initio approaches to quantum transport: A time-dependent formulation
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• Collective excitations of trapped one-dimensional dipolar quantum gases
• Time-dependent evolution of two coupled Luttinger liquids
• Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder
• The effect of time-dependent coupling on non-equilibrium steady states

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