Quench dynamics and zero-energy modes: the case of the Creutz model

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In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model-describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field-the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points, we find that the revival period of the Loschmidt echo-measuring the overlap between initial and time-evolved states-is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench to an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench across an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.
© 2019 American Physical Society H.J H.J. acknowledges support from the Swedish Research Council through Grant No. 621-2014-5972. A.L. would like to thank Sharif University of Technology for financial support under Grant No. G960208. M.A.M.D. acknowledges financial support from the Spanish MINECO Grants No. FIS2012-33152, No. FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.D. has been supported in part by the US Army Research Office through Grant No. W911N F-14-1-0103.
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