Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

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 Z2 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.

Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy

“…[44,58] for YC8-2 cylinder geometry. 2 QSL * is an improved RVB ansatz [59]. The lowest possible energies for all couplings belong first to the DMRG results and next to our PESS (D = 13) simulations.…”

“…Our energies obtained with both full-update (FU) and simple-update (SU) of the iPEPS as well as PESS results with full calculation of the environment are reported in Table 1 and compared to the results of Ref. [42,59] for U(1), 2 QSL and VBC as well as the DMRG results of Ref. [44,58].…”

“…[42] and 2 QSL * of Ref. [59] as well as those of the nematic state obtained with DMRG in Ref. [44] are also provided in the table.…”

Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

“…In order to understand the behavior of the system also away from those limiting cases, we use tensor network techniques introduced in earlier work to study the nature of the trimer model [19,26,[29][30][31]. Specifically, we compute iMPS fixed points of the transfer matrix from left and right, and use their symmetry breaking pattern with respect to the Z 3 × Z 3 symmetry in ket+bra to identify the topological nature of the system; this method also allows us to extract correlation lengths ξ for the trivial and anyon-anyon correlators (where the latter correspond to the inverse anyon mass).…”

“…In the PEPS picture, vison pairs correspond to strings of Z 3 symmetry actions, while spinons correspond to objects which transform as a nontrivial irrep under the symmetry, placed on the links when contracting tensors[12,19,30,31].…”