Spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks

TL;DR

This study uses tensor network methods to explore the ground states of a spin-1/2 Heisenberg antiferromagnet on the star lattice, revealing two competing valence-bond-solid phases and a continuous quantum phase transition.

Contribution

The paper identifies and characterizes two distinct VBS phases on the star lattice, including a resonating VBS with six-site order, using iPEPS in the thermodynamic limit.

Findings

Discovery of two competing VBS phases.

Confirmation of a continuous quantum phase transition.

Ground state at isotropic point is a VBS.

Abstract

Using the infinite Projected Entangled Pair States (iPEPS) algorithm, we study the ground-state properties of the spin-$1/2$ quantum Heisenberg antiferromagnet on the star lattice in the thermodynamic limit. By analyzing the ground-state energy of the two inequivalent bonds of the lattice in different unit-cell structures, we identify two competing Valence-Bond-Solid (VBS) phases for different antiferromagnetic Heisenberg exchange couplings. More precisely, we observe (i) a VBS state which respects the full symmetries of the Hamiltonian, and (ii) a resonating VBS state which, in contrast to previous predictions, has a six-site unit-cell order and breaks $C_3$ symmetry. We also studied the ground-state phase diagram by measuring the ground-state fidelity and energy derivatives, and further confirmed the continuous nature of the quantum phase transition in the system. Moreover, an analysis of the isotropic point shows that its ground state is also a VBS as in (i), which is as well in contrast with previous predictions.