Universal adiabatic dynamics in the vicinity of a quantum critical point

By A. Polkovnikov. 2003

313 citations recorded by the source corpus.

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second-order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated near the critical point, the number of created excitations still goes to zero in the limit of infinitesimally slow variation of the tuning parameter. It scales with the adiabaticity parameter as a power related to the critical exponents $z$ and $\ensuremath{\nu}$ characterizing the phase transition. We support general arguments by direct calculations for the Boson Hubbard and the transverse field Ising models.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9324442ddf5fb9d40b740218a38900bdf9020590

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Breakdown of the adiabatic limit in low-dimensional gapless systems (2007, methodology): “Then the density of excitations nex can be expressed as follows [5]:”
Quantum optimization of maximum independent set using Rydberg atom arrays (2022, background): “The exponent μ and the prefactor of the growth law are a priori unknown and are governed by a combination of the quantum Kibble-Zurek mechanism [36, 71], early-time coarsening [72], and “standard” late-time coarsening [73].”
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, methodology): “(Polkovnikov, 2005; Zurek et al., 2005).”
Probe branes, time-dependent couplings and thermalization in AdS/CFT (2010, background): “In the other limit, the parameter changes slowly across a critical point [39–42].”