Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
arXiv:0806.4455 · doi:10.1103/PhysRevB.78.104426
Abstract
The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.
8 pages, 7 figures. (v2) minor revisions, published version
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 quantum phase transition: exact solution in quantum Ising model
- 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
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick 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''
- Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
- Defect production in non-linear quench across a quantum critical point
- Entanglement entropy in the Lipkin-Meshkov-Glick model
- Exact results for quench dynamics and defect production in a two-dimensional model
- Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
- Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
- Transition times in the Landau-Zener model
- Entropy and Correlation Functions of a Driven Quantum Spin Chain
- Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
- Quantum quenches in a spinor condensate
- Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
- Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
- Optimal non-linear passage through a quantum critical point
- Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
- Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
- Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate
- Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
- Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
- Dynamics of a quantum phase transition in the random Ising model
- Generation of many-particle entanglement in an ion trap by adiabatic ground-state transitions
- Entanglement Entropy beyond the Free Case
- Entanglement entropy in collective models
- Adiabatic quenches through an extended quantum critical region
- Robustness of adiabatic passage trough a quantum phase transition
- On the Thermodynamic Limit of the Lipkin Model
- Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
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- Quantum Simulation and Phase Diagram of the Transverse Field Ising Model with Three Atomic Spins
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- Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
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- On quantum mean-field models and their quantum annealing
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
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- Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
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- Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
- Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model
- Coherent Quantum Dynamics: What Fluctuations Can Tell
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- Slow interaction ramps in trapped many-particle systems: universal deviations from adiabaticity
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- Ultrafast critical ground state preparation via bang-bang protocols
- Thermalization processes induced by quantum monitoring in multi-level systems
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- Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
- Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy
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- Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model
- Apparent delay of the Kibble-Zurek mechanism in quenched open systems
- Thermalization of the Lipkin-Meshkov-Glick model in blackbody radiation
- Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model
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