Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

Abstract

We construct energy-optimized resonating valence bond wavefunctions as a means to sketch out the zero-temperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest- (J1) and next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still controversial) but on exploring whether and how the Marshall sign structure breaks down in the vicinity of the phase boundaries. Numerical evaluation of two- and four-spin correlation functions is carried out stochastically using a worm algorithm that has been modified to operate in either of two modes: one in which the sublattice labelling is fixed beforehand and another in which the worm manipulates the current labelling so as to sample various sign conventions. Our results suggest that the disordered phase evolves continuously out of the (pi,pi) Neel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (pi,0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the results of a level crossing.

14 pages, 10 figures, 1 table. In Press

References in corpus (60)

• Quantum Monte Carlo with Directed Loops
• Spin-lattice coupling in frustrated antiferromagnets
• Lieb-Schultz-Mattis in Higher Dimensions
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Worm algorithms for classical statistical models
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• The Loop Algorithm
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• New quantum phase transitions in the two-dimensional J1-J2 model
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Ground state projection of quantum spin systems in the valence bond basis
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Phase Transitions in the Spin-Half J_1--J_2 Model
• Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
• Some formal results for the valence bond basis
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Quantum Phases of the Planar Antiferromagnetic J_1-J_2-J_3 Heisenberg-Model
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Spin liquid phase for the frustrated Quantum Heisenberg Antiferromagnet on a square lattice
• On The Violation Of Marshall-Peierls Sign Rule In The Frustrated $J_1-J_2$ Heisenberg Antiferromagnet
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
• Correlations and confinement in non-planar two-dimensional dimer models
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Low temperature broken symmetry phases of spiral antiferromagnets
• Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study
• Master equation approach to computing RVB bond amplitudes
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Spin liquid ground state in a two dimensional non-frustrated spin model
• Spin Hamiltonians with resonating-valence-bond ground states
• Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet
• Valence bond spin liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets
• Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet
• Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians
• Resonating valence bond wave function for the two dimensional fractional spin liquid
• Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions
• Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions
• Effects of ring exchange interaction on the Neel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
• On the nature of the transition from the spontaneously dimerized to the Neel phase in the two-dimensional J1-J2 model
• Superconductivity and Quantum Spin Disorder in Cuprates
• Valence bond solid phases in a cubic antiferromagnet
• Spin-wave interactions in quantum antiferromagnets
• Correlated valence-bond states
• Correlations in doped Antiferromagnets
• The Néel-VBS transition in three-dimensional SU($N$) antiferromagnets
• Comment on "Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets"

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• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Slow dynamics of the Fredkin spin chain
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice
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