We present a formulation for investigating quench dynamics acrossquantum phase transitions in the presence of decoherence. We formulatedecoherent dynamics induced by continuous quantum non-demolitionmeasurements of the instantaneous Hamiltonian. We generalize thewell-studied universal Kibble-Zurek behavior for linear temporal driveacross the critical point. We identify a strong decoherence regimewherein the decoherence time is shorter than the standard correlationtime, which varies as the inverse gap above the groundstate. In thisregime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})} t - ∼ τ 2 ν z / ( 1 + 2 ν z ) for when the system falls out of equilibrium and the associatedfreeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})} ξ ‾ ∼ τ ν / ( 1 + 2 ν z ) show power-law scaling with respect to the quench rate 1/\tau 1 / τ ,where the exponents depend on the correlation length exponent \nu ν and the dynamical exponent z z associated with the transition. The universal exponents differ fromthose of standard Kibble-Zurek scaling. We explicitly demonstrate thisscaling behavior in the instance of a topological transition in a Cherninsulator system. We show that the freeze-out time scale can be probedfrom the relaxation of the Hall conductivity. Furthermore, onintroducing disorder to break translational invariance, we demonstratehow quenching results in regions of imbalanced excitation densitycharacterized by an emergent length scale which also shows universalscaling. We perform numerical simulations to confirm our analyticalpredictions and corroborate the scaling arguments that we postulate asuniversal to a host of systems.
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Kibble–Zurek Scaling from Linear Response Theory
While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in the quantum case. Concerning the crossing of thermodynamic critical points and describing its non-equilibrium dynamics, the Kibble–Zurek mechanism and linear response theory have been demonstrated to be among the very successful approaches. In the present work, we show that these two approaches are also consistent in the description of quantum phase transitions, and that linear response theory can even inform arguments of the Kibble–Zurek mechanism. In particular, we show that the relaxation time provided by linear response theory gives a rigorous argument for why to identify the “gap” as a relaxation rate, and we verify that the excess work computed from linear response theory exhibits Kibble–Zurek scaling.
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- Award ID(s):
- 2010127
- NSF-PAR ID:
- 10379606
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 24
- Issue:
- 5
- ISSN:
- 1099-4300
- Page Range / eLocation ID:
- 666
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/e24050666
