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arXiv:1112.6422 · Physical Review Letters

Nonequilibrium Dynamic Critical Scaling of the Quantum Ising Chain

Michael Kolodrubetz, Bryan K. Clark, David A. Huse

Published Jul 2, 2012• 142 citations
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Abstract

We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.

DOI
10.1103/physrevlett.109.015701

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We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.
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The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so that space and imaginary time are isotropic. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. The leading-order finite-size corrections are eliminated by comparing two systems with different sizes; this procedure is also performed automatically. Varying the decay exponent of the long-range interaction, σ, we investigate σ dependence of the dynamical exponent and the other critical exponents precisely in the mean-field, nonuniversal, and two-dimensional classical Ising universality regimes. We successfully obtained numerical evidence supporting σ=7/4 as the universality boundary between the latter two.
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