Abstract
We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J_1-J_2J1−J2 frustrated Heisenberg model. For J_2/J_1\sim 0.55J2/J1∼0.55 we show the emergence of critical (algebraic) dimer-dimer correlations – typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices – while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.
Highlights
Resonating Valence Bond (RVB) and the frustrated Heisenberg modelResonant valence bond (RVB) states were first proposed by Anderson [1] to describe a possible spin liquid ground state of the S = 1/2 antiferromagnetic Heisenberg model on the triangular lattice
The nearest neighbor (NN) RVB state, defined as an equal weight superposition of NN singlet bond coverings, was shown to be critical on the square lattice [9, 10] while several numerical work [11,12,13,14] have demonstrated that their analogs on the kagome and triangular lattices are 2 spin liquid states
Generically the Rokhsar Kivelson (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
Summary
Resonant valence bond (RVB) states were first proposed by Anderson [1] to describe a possible spin liquid ground state of the S = 1/2 antiferromagnetic Heisenberg model on the triangular lattice. Later on, it was introduced as the parent Mott state of high-Tc superconductors [2]. The NN RVB state, defined as an equal weight superposition of (non-orthogonal) NN singlet bond ( dubbed “dimer”) coverings, was shown to be critical on the square lattice [9, 10] while several numerical work [11,12,13,14] have demonstrated that their analogs on the kagome and triangular lattices are 2 spin liquid states. SU(2)-invariant spin models have 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 the multi-critical nature of the RK point in SU(2)-symmetric systems
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