Correlated valence-bond states

Abstract

We study generalizations of the singlet-sector amplitude-product (AP) states in the valence-bond basis of S=1/2 quantum spin systems. In the standard AP states, the weight of a tiling of the system into valence bonds (singlets of two spins) is a product of amplitudes depending on the length of the bonds. We here introduce correlated AP (CAP) states, in which the amplitude product is further multiplied by factors depending on two bonds connected to a pair of sites (here nearest neighbors). While the standard AP states can describe a phase transition between an antiferromagnetic (Neel) state and a valence-bond solid (VBS) in one dimension (which we also study here), in two dimensions it cannot describe VBS order. With the CAP states, Neel-VBS transitions are realized as a function of some parameter describing the bond correlations. We here study such phase transitions of CAP wave-functions on the square lattice. We find examples of direct first-order Neel-VBS transitions, as well as cases where there is an extended U(1) spin liquid phase intervening between the Neel and VBS states. In the latter case the transitions are continuous and we extract critical exponents and address the issue of a possible emergent U(1) symmetry in the near-critical VBS. We also consider variationally optimized CAP states for the standard Heisenberg model in one and two dimensions and the J-Q model in two dimensions, with the latter including four-spin interactions (Q) in addition to the Heisenberg exchange (J) and harboring VBS order for large Q/J. The optimized CAP states lead to significantly lower variational energies than the simple AP states for these models.

21 pages, 27 figures. v2: Expanded discussion of results

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• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Confinement and Deconfinement of Spinons in Two Dimensions
• Quantum Monte Carlo studies of spinons in one-dimensional spin systems
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Spontaneous symmetry breaking in correlated wave functions
• Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Typicality at quantum-critical points