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

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 $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ 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.

19 pages, 8 figures, v2 minor modifications, 1 ref added

References in corpus (15)

• "Deconfined" quantum critical points
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Resonating valence bond states in the PEPS formalism
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Gauging quantum states: from global to local symmetries in many-body systems
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Criticality of a classical dimer model on the triangular lattice

Cited by in corpus (10)

• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• Lattice symmetry and emergence of antiferromagnetic quantum Hall states
• Realising square and diamond lattice $S=1/2$ Heisenberg antiferromagnet models in the $\alpha$ and $\beta$ phases of the coordination framework, KTi(C${}_2$O${}_4$)${}_2\cdot$\textit{x}H${}_2$O
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction