Research: Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid

Random-singlets are quantum spin liquid-like phases in spin systems where two spins at arbitrary distances can be entangled at low energy. Phenomenological signatures of such phases were extensively studied about four decades ago in doped semiconductors and recently in various disordered magnetic materials. On the theoretical side such random-singlet states were well studied in disordered one-dimensional spin chains using an analytically tractable strong disorder renormalization group approach, but such an approach is elusive in higher dimensions. However several different numerical attempts in recent works suggest formation of emergent disorder-induced local moments at an intermediate energy; which ultimately freeze into a random singlet state at rather lower energies.

In this work we perform an asymptotically exact calculation to demonstrate  such emergent moments and random singlet phenomenology on an SU(2)- invariant version of Kitaev’s  integrable model of a honeycomb-lattice spin liquid. Using arbitrary precision numerics and analytical calculations to span the full range of low temperatures, we study the effects of vacancies (dilution by nonmagnetic impurities) and bond (exchange) disorder on the susceptibility. We show the magnetic susceptibility $\chi(T)$ of this system has the functional form $C/T + D T^{\alpha(T) -1}$(shown in the figure chit_withzero_10p.pdf), where $\alpha(T)$ tends to zero slowly as the temperature T goes to zero. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells(shown in the figure spintexture.png): it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder is the response of a random singlet phase.

We argue our results may hold in the presence some experimentally relevant perturbations to the model that we studied, thus this may lead to unexplored variants of cooperative physics of the low energy emergent degrees of freedom in a disordered quantum magnet. 

S. Sanyal, K. Damle, J. T. Chalker, R. Moessner,
Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid,
Phys. Rev. Lett. 127, 127201 (2021) (arXiv)