Exotic phases of matter and their characterization: quantum spin liquids in highly-frustrated magnets

For most of the last century, condensed matter physics has been dominated by the Landau's symmetry breaking theory. In this respect, by lowering the temperature, almost all forms of matter reorganize in order to generate some kind of long-range order (well known examples are given by the liquid-solid transition or the paramagnetic-ferromagnetic one). However, in the recent past, there is a clear evidence for several cases that escape this standard description and keep a disordered nature down to very low temperatures. Exotic physical behaviors originate from quantum fluctuations that can be further enhanced by the competition among different kind of interactions. This competition goes under the name of ``frustration'' and may eventually impede long-range ordering of the system.

In this talk, I give a general introduction to the concepts and ideas that has been used to characterize the so-called ``quantum spin liquids'' [1]. These are unconventional phases of matter, which may support topological order and fractional excitations. In particular, fractionalization is the phenomenon wherein the quantum numbers of the low lying excitations of a many-body system are non-integer multiples of those of the constituents, e.g.,
electrons in a metallic system, or of the natural excitations, e.g., spin flips in an insulating magnet.

Finally, I discuss recent results for the dynamical spin structure factor that have been obtained by using variational wave functions and quantum Monte Carlo methods [2-3].

[1] For a recent review, see L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502 (2017)
[2] F. Ferrari, A. Parola, S. Sorella, and F. Becca, Phys. Rev. B 97, 235103 (2018).
[3] F. Ferrari and F. Becca, Phys. Rev. B 98, 100405 (2018).