Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect
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We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H(sin theta cos phi, sin theta sin phi cos theta) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for alpha < 1. We report a divergence of the Berry curvature at alpha(c) = 1 for magnetic fields aligned along the equator theta = pi/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schrodinger approach we find that, for a fixed field sweep velocity theta(t) = vt, the bath induces a crossover from ( quasi) adiabatic to nonadiabatic dynamical behavior when the spin bath coupling a increases. We also investigate the particular regime H/omega(c) << v/H << 1 with large bath cutoff frequency.c, where the dynamical Chern number vanishes already at alpha = 1/2. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of alpha = 1/2. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium.
This article is published as Henriet, Loïc, Antonio Sclocchi, Peter P. Orth, and Karyn Le Hur. "Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect." Physical Review B 95, no. 5 (2017): 054307. DOI: 10.1103/PhysRevB.95.054307. Posted with permission.