Topological Phases in Quantum Magnets

Topology provides a novel framework for characterizing phases of
matter, extending beyond Landau’s traditional approach, which relies on
symmetries and local order parameters. While topology is often associated
with quantum phases, it is equally capable of characterizing classical
phases of matter. In the context of the second quantum revolution, it is
crucial to differentiate between classical and quantum topological phases,
and to understand the unique quantum effects within these phases.  In this
seminar, I will present two of my key works that explore topology in
quantum magnets.
One well-studied category of topological phases is band topology,
particularly in bosonic systems. While the formalism used in these systems
may appear quantum in nature, they often have classical analogues. To
investigate true quantum band topology, however, one must look at quantum
magnets that lack classical counterparts. A prime example of such a system
is SrCu₂(BO₃)₄, which realizes a (modified) Shastry-Sutherland model. The
ground state of SrCu₂(BO₃)₄ is a product state of singlets, a
configuration with no classical analogue. We propose that Weyl triplons, a
novel type of quantum excitation, are expected to emerge in the low-energy
magnetic excitations of SrCu₂(BO₃)₄. Our results show that when a minimal,
realistic interlayer coupling is introduced into the established
microscopic model for the system, the Dirac points in the zero-field
triplon spectrum of the 2D model split into two pairs of Weyl points along
the