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Register a new userEntanglement studies of resonating valence bonds on the frustrated square lattice
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We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte-Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et. al. [Physical Review B {bf 85}, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a t Hooft magnetic loop-type operator. From this identification, we calculate a value consistent with $ln(2)$ for the topological entanglement entropy directly for the RVB states via wave function Monte-Carlo. This corroborates the $mathbb{Z}_{2}$ nature of the RVB states. We furthermore define and elaborate on the concept of a pre-Kasteleyn orientation that may be useful for the study of lattices with non-planar topology in general.
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Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to singlet breaking on nearest-neighbor bonds describe the high-energy part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering (INS) study, we demonstrate that nearest-neighbor RVB excitations account for the bulk of the spectral weight above 0.5 meV. This renders YbMgGaO4 the first experimental system where putative RVB correlations restricted to nearest neighbors are observed, and poses a fundamental question of how complex interactions on the triangular lattice conspire to form this unique many-body state.
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.
We investigate the ground state nature of the transverse field Ising model on the $J_1-J_2$ square lattice at the highly frustrated point $J_2/J_1=0.5$. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem. However, the string-type anharmonic fluctuations of COA are able to lift the degeneracy toward a string-valence bond solid (VBS) state, which is obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent non-magnetic string-VBS phase is gapped and breaks lattice rotational symmetry with only two-fold degeneracy, which bears a continuous quantum phase transition at $Gamma/J_1 cong 0.50$ to the quantum paramagnet phase of high fields. The critical behavior is characterized by $ u cong 1.0$ and $gamma cong 0.33$ exponents.
The static and dynamic properties of V^{4+} spins (S = 1/2) in the frustrated square lattice compound Pb2(VO)(PO4)2 were investigated by means of magnetic susceptibility chi and 31P nuclear magnetic resonance (NMR) shift (K) and 31P nuclear spin-lattice relaxation rate 1/T1 measurements on a single crystal. This compound exhibits long-range antiferromagnetic order below TN simeq 3.65 K. NMR spectra above TN show two distinct lines corresponding to two inequivalent P sites present in the crystal structure. The observed asymmetry in hyperfine coupling constant for the in-plane (P1) P site directly points towards a distortion in the square lattice at the microscopic level, consistent with the monoclinic crystal structure. The nearest- and next-nearest-neighbor exchange couplings were estimated to be J1/kB = (-5.4 pm 0.5) K (ferromagnetic) and J2/kB = (9.3 pm 0.6) K (antiferromagnetic), respectively. 1/(T1 T chi) is almost T-independent at high temperatures due to random fluctuation of spin moments. Below 20 K, the compound shows an enhancement of 1/(T1 T chi) which arises from a growth of antiferromagnetic spin correlations above TN. Below TN and for the field applied along the c-axis, the NMR spectrum for the P1 site splits into two satellites and the spacing between them increases monotonically with decreasing T which is a direct evidence of a columnar antiferromagnetic ordering with spins lying in the ab-plane. This type of magnetic ordering is consistent with expectation from the J2/J1 simeq -1.72 ratio. The critical exponent beta = 0.25 pm 0.02 estimated from the temperature dependence of sublattice magnetization as measured by 31P NMR at 11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY model.
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.
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