Topological Z2 resonating-valence-bond quantum spin liquid on the ruby lattice

Abstract

We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension D = 3. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, γ = −ln 2, consistent with that of a Z2 topological quantum spin liquid. We also calculate the ground-state energy of the spin-1 2 antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

Ergodic Archimedean dimers

“…We note that in the quantum Hamiltonian of Ref. [38], the hexagonal ring-exchange term was left out. The configuration shown in Fig.…”

Topological phase transitions and topological flat bands on the ruby lattice

“…This particular lattice was shown to support Z 2 topological insulators [28,29], fractional Chern insulators [30][31][32][33], and Mott insulators [34]. The 2D Ising model and the Kitaev spin model defined on the ruby lattice exhibit a very rich phase diagram [35][36][37][38][39][40]. Furthermore, the ruby lattice structure was found experimentally in some layered materials [41][42][43].…”

Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

“…Tensor-Network methods.-Tensor-Network (TN) methods [40][41][42][43][44][45] provide efficient representations for ground states of local Hamiltonians based on their entanglement structure [40]. In particular, the projected entangled-pair state (PEPS) method and its infinite version in the thermodynamic limit (iPEPS) [40,41,45,46], have played a major role in the characterization and discovery of many exotic phases, ranging from magnetically ordered states [47][48][49] to QSLs [19,21,50,51] and valence-bond crystals [52,53]. In particular, the modified version of the iPEPS algorithm, designed for the honeycomb structures [54], has been shown to be very successful for simulating and characterizing the Kitaev model and its variants, such as the Kitaev-Heisenberg model, in the thermodynamic limit [55][56][57].…”