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1. Spin- and flux-gap renormalization in the random Kitaev spin ladder

   https://doi.org/10.1103/PhysRevB.106.L100402  

   Kao, Wen-Han; Perkins, Natalia B. (September 2022, Physical Review B)
2. Decoupling the electronic gap from the spin Chern number in spin-resolved topological insulators

   https://doi.org/10.1103/PhysRevB.110.214211  

   Tyner, Alexander C; Grindall, Cormac; Pixley, J H (December 2024, Physical Review B)

   In two-dimensional topological insulators, a disorder-induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in ${\mathbb{Z}}_2$trivial, spin-resolved topological insulators it is the spectral gap of the spin spectrum, in addition to the bulk mobility gap, which protects the nontrivial topology of the ground state. In this work, we show that these two gaps, the bulk electronic and spin gap, can evolve distinctly on the introduction of quenched short-ranged disorder and that an odd-quantized spin Chern number topologically protects states below the Fermi energy from localization. This decoupling leads to a unique situation in which an Anderson localization transition occurs below the Fermi energy at the topological transition. Furthermore, the presence of topologically protected extended bulk states nontrivial bulk topology typically implies the existence of protected boundary modes. We demonstrate the absence of protected boundary modes in the Hamiltonian and yet the edge modes in the eigenstates of the projected spin operator survive. Our work thus provides evidence that a nonzero spin-Chern number, in the absence of a nontrivial ${\mathbb{Z}}_2$index, does not demand the existence of protected boundary modes at finite or zero energy. Published by the American Physical Society2024 

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3. Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

   https://doi.org/10.1103/PhysRevB.105.085120  

   Christos, Maine; Haehl, Felix M.; Sachdev, Subir (February 2022, Physical Review B)
4. Effect of Structure on the Spin–Spin Interactions of Tethered Dicyanomethyl Diradicals

   https://doi.org/10.1021/jacs.8b08628  

   Zhang, Rui; Peterson, Joshua P.; Fischer, Logan J.; Ellern, Arkady; Winter, Arthur H. (October 2018, Journal of the American Chemical Society)
5. Integrability and quench dynamics in the spin-1 central spin XX model

   https://doi.org/10.21468/SciPostPhys.15.1.030  

   Tang, Long Hin; Long, David; Polkovnikov, Anatoli; Chandran, Anushya; Claeys, Pieter W (January 2023, SciPost Physics)

   Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-s central spin XX model is integrable for any s. 

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