Abstract
We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries $Z_2$ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.
Highlights
The resonating valence bond (RVB) state, defined as an equal weight superposition of nearest neighbor (NN) singlet coverings, was first proposed by Anderson [1] to describe a possible spin liquid ground state (GS) of the S = 1/2 antiferromagnetic Heisenberg (HAF) model on the triangular lattice
We have introduced a simple yet powerful ansatz for the kagome Heisenberg antiferromagnet (KHAFM) with breathing anisotropy, termed simplex RVB
Our ansatz is physically motivated from algorithmic cooling, and effectively consists of p/2 imaginary time evolution layers with optimized step sizes applied to the NN RVB, approaching the true ground state as p → ∞
Summary
The resonating valence bond (RVB) state, defined as an equal weight superposition of (nonorthogonal) nearest neighbor (NN) singlet (or dimer) coverings, was first proposed by Anderson [1] to describe a possible spin liquid ground state (GS) of the S = 1/2 antiferromagnetic Heisenberg (HAF) model on the triangular lattice. Later on, it was introduced as the parent Mott state of high-Tc superconductors [2]. While the HLSM theorem [8] excludes a unique GS separated from the first excitations by a finite gap (so-called “trivial” spin liquid), a gapless spin liquid [9,10,11,12] or a gapful topological spin liquid (of the RVB type) [13,14,15] are the two favored candidates
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