Spin-S Kagome quantum antiferromagnets in a field with tensor networks

TL;DR

This paper uses tensor network methods to map out the phase diagrams of spin-$S$ Kagome antiferromagnets in a magnetic field, revealing various quantum and semi-classical phases, including magnetization plateaus and spin liquids.

Contribution

First direct zero-temperature phase diagrams for spin-$S$ Kagome antiferromagnets up to $S=2$ in the thermodynamic limit using iPEPS, identifying novel quantum and classical phases.

Findings

Identification of magnetization plateaus at specific fractions of saturation.

Discovery of spin gapped phases, including a topologically trivial spin liquid for $S=2$.

Observation of coexistence of charge and bond orders in certain quantum phases.

Abstract

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 thanks to infinite Projected Entangled Pair States (iPEPS), a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau vs field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semi-classical, as the plateaus at $\frac{1}{3}$th, $(1-\frac{2}{9S})$th and $(1-\frac{1}{9S})$th of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-$\frac{1}{2}$ $\frac{1}{9}$-plateau exhibiting 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 field, such as the $S=2$ (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.