Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''

Abstract

Here we give detailed derivations and provide additional examples to the main paper: arXiv:0706.0212. In particular, we discuss the scaling behavior of observables like correlation functions and density of excitations. We also analyze effects of nonintegrability of the Bose-Hubbard model on the long-time dynamics of the correlation functions. In addition we explicitly consider several interacting models, where we are able to analyze slow dynamics and classify it according to the regimes suggested in the main paper.

11 pages, 6 figures. The current version of the main paper arXiv:0706.0212 is not up to date according to the Nature Physics editorial policy

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Universal adiabatic dynamics across a quantum critical point
• 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
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Evolution of the macroscopically entangled states in optical lattices
• Many body generalization of the Landau Zener problem
• Robustness of adiabatic passage trough a quantum phase transition
• Production efficiency of Feshbach molecules in fermion systems
• Inconsistencies of the Adiabatic Theorem and the Berry Phase
• General conditions for a quantum adiabatic evolution

Cited by in corpus (97)

• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Quantum Simulation for High Energy Physics
• Defect production in non-linear quench across a quantum critical point
• Crystallization of strongly interacting photons in a nonlinear optical fiber
• Dynamics of a tunable superfluid junction
• Optimal non-linear passage through a quantum critical point
• Quantum Quench from a Thermal Initial State
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• One decade of quantum optimal control in the chopped random basis
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Quenching along a gapless line: A different exponent for defect density
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Coherent and dissipative dynamics at quantum phase transitions
• Virial theorems for trapped cold atoms
• Defect production due to quenching through a multicritical point
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• Theory of defect production in nonlinear quench across a quantum critical point
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
• Adiabatic nonlinear probes of one-dimensional Bose gases
• Quantum transitions driven by one-bond defects in quantum Ising rings
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Quench dynamics and parity blocking in Majorana wires
• Microscopic expression for the heat in the adiabatic basis
• Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points
• Sonic horizons and causality in the phase transition dynamics
• Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
• Dynamics of a many-particle Landau-Zener model: inverse sweep
• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
• Quantum time crystals with programmable disorder in higher dimensions
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Exponential precision by reaching a quantum critical point
• Kibble-Zurek Dynamics in a Trapped Ultracold Bose Gas
• Adiabaticity and localization in one-dimensional incommensurate lattices
• Exploring quantum criticality based on ultracold atoms in optical lattices
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Kibble-Zurek mechanism in the Ising Field Theory
• From sudden quench to adiabatic dynamics in the attractive Hubbard model
• Harnessing non-adiabatic excitations promoted by a quantum critical point
• Exact results on the quench dynamics of the entanglement entropy in the toric code
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid
• Dynamics after quenches in one-dimensional quantum Ising-like systems
• Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition
• Varying quench dynamics in the transverse Ising chain: the Kibble-Zurek, saturated, and pre-saturated regimes
• Adiabatic theorem for closed quantum systems initialized at finite temperature
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points
• Kink correlations, domain size distribution, and the emptiness formation probability after the Kibble-Zurek quench in the quantum Ising chain
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Probing quantum many-body correlations by universal ramping dynamics
• Interferometry based on quantum Kibble-Zurek mechanism
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Work statistics across a quantum critical surface
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• Quantum adiabatic cycles and their breakdown
• Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases
• Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate
• Adiabatic time evolution of highly excited states
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Thermodynamic entropy production in the dynamical Casimir effect
• Quantum critical engine at finite temperatures
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Driven Critical Dynamics in Tricitical Point
• Nano-welding of quantum spin-$1/2$ chains at minimal dissipation
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• Thermal-bath effects in quantum quenches within quantum critical regimes
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Observation of heat scaling across a first-order quantum phase transition in a spinor condensate
• Universality in nonlinear passage through the miscible-immiscible phase transition in two component Bose-Einstein condensates
• Echoes and defects in the Calogero model
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Non-adiabatic transitions in a massless scalar field
• Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints
• On the nonlinear response of a particle interacting with fermions in a 1D lattice
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Rate Function Modelling of Quantum Many-Body Adiabaticity
• Quantum dynamics of a spin model with an extensive degeneracy
• Quantum collapses and revivals of a matter wave in the dynamics of symmetry breaking
• Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics