Breakdown of the adiabatic limit in low dimensional gapless systems

Abstract

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.

11 pages, 5 figures, to appear in Nature Physics (originally submitted version)

References in corpus (25)

• Many-Body Physics with Ultracold Gases
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas
• Universal adiabatic dynamics across a quantum critical point
• Dynamical quantum noise in Bose-Einstein condensates
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Defect production in non-linear quench across a quantum critical point
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Error correcting codes for adiabatic quantum computation
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Dynamics of a quantum phase transition in the random Ising model
• Evolution of the macroscopically entangled states in optical lattices
• Many body generalization of the Landau Zener problem
• Lectures on string theory and cosmology
• Robustness of adiabatic passage trough a quantum phase transition
• Production efficiency of Feshbach molecules in fermion systems
• Validity of adiabaticity in Cavity QED
• Perturbative Analysis of Possible Failures in the Traditional Adiabatic Conditions
• Inconsistencies of the Adiabatic Theorem and the Berry Phase
• General conditions for a quantum adiabatic evolution

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