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Register a new userPersistent dark states in anisotropic central spin models
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Added by
Renzo Tamiro Villazon Scholer
Publication date
2020
fields
Physics
and research's language is
English
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Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogenous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.
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Central spin models describe a variety of quantum systems in which a spin-1/2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.
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It is virtually impossible to evaluate the magnetic properties of large anisotropic magnetic molecules numerically exactly due to the huge Hilbert space dimensions as well as due to the absence of symmetries. Here we propose to advance the Finite-Temperature Lanczos Method (FTLM) to the case of single-ion anisotropy. The main obstacle, namely the loss of the spin rotational symmetry about the field axis, can be overcome by choosing symmetry related random vectors for the approximate evaluation of the partition function. We demonstrate that now thermodynamic functions for anisotropic magnetic molecules of unprecedented size can be evaluated.
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