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Universal Postquench Prethermalization at a Quantum Critical Point

Pia Gagel, Peter P. Orth, and Jörg Schmalian
Phys. Rev. Lett. 113, 220401 – Published 26 November 2014
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    Abstract

    We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.

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    • Received 7 July 2014

    DOI:https://doi.org/10.1103/PhysRevLett.113.220401

    © 2014 American Physical Society

    Authors & Affiliations

    Pia Gagel1, Peter P. Orth1, and Jörg Schmalian1,2

    • 1Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
    • 2Institute for Solid State Physics, Karlsruhe Institute of Technology (KIT), 76021 Karlsruhe, Germany

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    Issue

    Vol. 113, Iss. 22 — 28 November 2014

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    • Figure 1
      Figure 1

      (a) Schematic description of the setup and quench protocol. (b) Schematic phase diagram as a function of temperature T and mass δri=r0,i−r0,c. Red arrows describe the quench protocol. Dynamics exhibits three time regimes: t<tγ=γ−z/(2(z−1)) with nonuniversal dynamics, the universal prethermalized regime tγ<t<t*∝δri−νz/κ which we study, and a quasiadiabatic regime t>t* described by equilibrium critical exponents. Here, γ is the system-bath coupling and κ/ν the scaling dimension of δri. (c) Correlation length collapse and light-cone-like revival following a quench with initial length ξi. Inset: sketches of order parameter configurations with domains of typical size ξ(t).

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    • Figure 2
      Figure 2

      Schematic order parameter dynamics ⟨φ(t)⟩. In the prethermalized regime tγ<t<t* (blue) it is governed by a new universal critical exponent θ. At longer times, ⟨φ(t)⟩ decays to zero quasiadiabatically as described by equilibrium exponents.

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    • Figure 3
      Figure 3

      (a) Prethermalization exponent θ as a function of dynamic critical exponent z. Plot shows Cz=θ(N+8)/(N+2)(1/ε), where N is the number of components of φ and ε=4−d−z. Blue dot indicates the analytical result of Eq. (14). (b) Free Keldysh scaling function f0K(qzt)−feq,0 after the quantum quench for different dynamic critical exponents z=1.2 (red dotted), 1.4 (yellow dashed), 2 (blue dot-dashed), and 2.5 (green). Inset shows the exponential decay of the envelope towards the equilibrium distribution, which becomes algebraic in the presence of interactions.

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