Spin-S Kagome Quantum Antiferromagnets In A Field With Tensor Networks

Spin-S Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S = 2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the 1/3 th, (1 - 2/9S) th, and (1 - 1/9S) th of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-1/2 1/9 plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U(1) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S = 2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.