Gapped and gapless quantum spin liquids on the ruby lattice

Federico Becca

Saeed S. Jahromi, Mehdi Kargarian, Seyed Farhad Masoudi +1 more

The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact diagonalization and perturbative methods. The latter interactions combined with the structure of the lattice yield a model with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ gauge symmetry. We mapped out the phase diagram of the model and found gapped and gapless spin-liquid phases. While the low-energy sector of the gapped phase corresponds to the well-known topological color code model on a honeycomb lattice, the low-energy sector of the gapless phases is described by an effective spin model with three-body interactions on a triangular lattice. A gap is opened in the spectrum in small magnetic fields, where we showed that the ground state has a finite topological entanglement entropy. We argue that the gapped phases could be possibly described by exotic excitations, and their corresponding spectrum is richer than the Ising phase of the Kitaev model.

Subir Sachdev A

Atanu Maity, Rhine Samajdar, Yasir Iqbal

The ruby lattice has been the subject of much interest recently due its realization in Rydberg atom arrays, where its rich variety of frustrated interactions gives rise to topologically ordered quantum spin liquids. Similarly, numerical studies of ruby-lattice spin models, with both isotropic and anisotropic interactions, have provided evidence of gapped and gapless spin-liquid ground states with different low-energy gauge structures. Motivated by these findings, we perform a projective symmetry group (PSG) classification of U(1) and $\mathbb{Z}_{2}$ fermionic spinon mean-field theories$\unicode{x2014}$respecting space-group and time-reversal symmetries$\unicode{x2014}$for $S=1/2$ spins. We obtain a total of 50 U(1) and 64 $\mathbb{Z}_{2}$ PSGs, and upon restricting their realization via mean-field $\textit{Ansätze}$ with up to second-nearest-neighbor singlet amplitudes (relevant to the models studied here), only 8 U(1) and 18 $\mathbb{Z}_{2}$ distinct states are obtained. We present the singlet fields for all $\textit{Ansätze}$ up to third-nearest-neighboring bonds and discuss their spinon dispersions as well as their dynamical spin structure factors. Building on this information, we also obtain the phase diagram of the Heisenberg model in the presence of first ($J_{1}$), second ($J_{1}'$), and third ($J_{2}$) neighbor antiferromagnetic couplings within a self-consistent mean-field approximation.

Yuan-Ming Lu

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical ${\mathbb{Z}}_{2}$ gauge fields. Requiring $\text{U}(1)$ spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-$\frac{1}{2}$ systems on square, triangular, and kagome lattices, we show that all gapped symmetric ${\mathbb{Z}}_{2}$ spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped ${\mathbb{Z}}_{2}$ spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

Tarun Grover