Quantum adiabatic cycles and their breakdown

Abstract

An analytically solvable model for quasi-static transformations across quantum critical points featuring Bosonic quasi-particle excitations is presented. The model proves that adiabaticity breakdown is a general feature of universal slow dynamics in these systems. The existence of an "anti-adiabatic" dynamical phase with vanishing ground state fidelity in the slow drive limit is also proven. The relation of these findings with the Kibble-Zurek mechanism and their consequences on defect formation in many body systems ramped across a quantum phase transition are discussed.

arXiv comment9 pages, 2 figures

References in corpus (37)

• 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 a Quantum Phase Transition and Relaxation to a Steady State
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Field Theory in the Large N Limit: a review
• Universal adiabatic dynamics across a quantum critical point
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D
• 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''
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Adiabatic Theorem without a Gap Condition
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Finite-Size Scaling Exponents in the Dicke Model
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Real Space Renormalization in Statistical Mechanics
• Quantum versus classical statistical dynamics of an ultracold Bose gas
• On equilibration and coarsening in the quantum O(N) model at infinite $N$
• Dynamical critical scaling of long-range interacting quantum magnets
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• On the Time Dependence of Adiabatic Particle Number
• The Coherent State Representation of Quantum Fluctuations in the Early Universe
• Critical exponents of O(N) models in fractional dimensions
• Universal location of the Yang-Lee edge singularity in O(N) theories
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Finite-size scaling exponents and entanglement in the two-level BCS model
• The Unitary Gas and its Symmetry Properties
• Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
• Universal dynamical scaling of long-range topological superconductors
• On the Hamiltonian structure of Ermakov systems
• Dynamical crossing of an infinitely degenerate critical point
• A solvable model of the breakdown of the adiabatic approximation

Cited by in corpus (9)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Metastability and discrete spectrum of long-range systems
• Exponential precision by reaching a quantum critical point
• Harnessing non-adiabatic excitations promoted by a quantum critical point
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Universal defects statistics with strong long-range interactions
• Tracking Adiabaticity in Non-Equilibrium Many-Body Systems: The Hard Case of the X-ray Photoemission in Metals
• Echoes and defects in the Calogero model
• Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints