Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

Abstract

We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to spin-1/2 wavefunctions. We first show that these models, besides the exact degeneracy of RK point, support gapless spinless excitations as well as a spin gap in the thermodynamic limit, signatures of an unusual spin liquid. We then extend the original construction to create a continuous family of SU(2) invariant spin models that reproduces the phase diagram of the quantum dimer model, and in particular show explicit evidences for existence of columnar and staggered phases. The original models thus appear as multicritical points in an extended phase diagram. Our results are based on the use of a combination of numerical exact simulations and analytical mapping to effective generalized quantum dimer models.

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

“…Also, it is likely that regions of (truly critical) RK phases exist also within our D = 5 and D = 7 PEPS manifolds. Although one cannot prove that such a RK dimer liquid is realized in the J 1 − J 2 spin-1/2 Heisenberg antiferromagnet, it is known that the critical RVB state is the ground state of a family of SU(2)-symmetric local spin-1/2 models with frustrating interactions [17,18]. In any case, the critical dimer correlations could survive in nearby phases of some RK point over a substantial intermediate range of distances.…”

“…In fact, generically the RK point appears to be a multi-critical point with all sorts of nearby phases in which the critical correlations present at the RK point could be correct over a substantial intermediate range of energy and length scales. SU(2)-invariant spin models have also been engineered [17,18] to mimic quantum dimer physics on the square lattice, with (critical) RVB ground state and Valence Bond Crystal (VBC) phases (spontaneously breaking translation symmetry), reflecting also the multi-critical nature of the RK point in SU(2)-symmetric systems.…”

Topological Z2 resonating-valence-bond spin liquid on the square lattice

“…The latter at λ = 0 would be a "deformation" of the parent Hamiltonian derived at λ = 0 (see Supplementary Materials and Ref. [41,42]), including e.g. (physically relevant) plaquette cyclic terms or other sorts of multi-spin interactions involving up to 6 sites.…”

Response to defects in multipartite and bipartite entanglement of isotropic quantum spin networks

“…In recent years, attempts have also been made to study the above dimer models using tensor network formalism [28], which unveils many important physics related to it. Moreover, proposal for engineering such isotropic models on spin lattices have also been reported [29][30][31].…”