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Register a new userExact non-magnetic ground state and residual entropy of S = 1/2 Heisenberg diamond spin lattices
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Exactly solvable frustrated quantum spin models consisting of a diamond unit structure are presented. The ground states are characterized by tetramer-dimer states with a macroscopic degeneracy in a certain range of isotropic exchange interaction. The lower bound of the excitation gap is exactly calculated to be finite and the bulk entropy in the limit of zero temperature remains finite depending on the shape of the boundary of system. Residual entropy is in a range of 0~6.1% of the entropy at high temperature for hexagonal diamond lattice and 0~8.4% for square diamond lattice. These diamond lattices are generalized to any dimensions and it is likely to be synthesized experimentally.
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The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no Neel order, dimer order and plaquette order in the region of 0.42 $lesssim J_2/J_1lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.
We present a model compound with a spin-1/2 frustrated square lattice, in which three ferromagnetic (F) interactions and one antiferromagnetic (AF) compet. Considering the effective spin-1 formed by the dominant F dimer, this square lattice can be mapped to a spin-1 spatially anisotropic triangular lattice. The magnetization curve exhibits gapped behavior indicative of a dominant one-dimensional (1D) AF correlation. In the field-induced gapless phase, the specific heat and magnetic susceptibility show a phase transition to an ordered state with 2D characteristics. These results indicate that the spin-1 Haldane state is extended to the 2D system. We demonstrate that the gapped ground state observed in the present spin-1/2 frustrated square lattice originates from the one-dimensionalization caused by frustration.
Liu et al. [Phys.Rev.B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a Projected Entangled Pair State (PEPS) type wave function for the $S=1/2$ frustrated $J_1$-$J_2$ Heisenberg model on the square lattice and found a non-magnetic state argued to be a gapless spin liquid when the coupling ratio $g=J_2/J_1$ is in the range $g in [0.42,0.6]$. Here we show that their definition of the order parameter for another candidate ground state within this coupling window---a spontaneously dimerized state---is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of $g$ cannot be excluded (and is likely based on several other recent works).
The magnetic and thermodynamic properties of spin-1/2 Heisenberg diamond chains are investigated in three different cases: (a) J1, J2, J3>0 (frustrated); (b) J1, J3<0, J2>0 (frustrated); and (c) J1, J2>0, J3<0 (non-frustrated). The density matrix renormalization group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer matrix renormalization group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor S(q) shows peaks at wavevectors $q=api /3$ (a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however in the magnetic fields where the magnetization plateau with m=1/6 pertains, exhibits the peaks only at q=0, $2pi /3$ and $4pi /3$, which are found to be couplings-independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the double-peak structures of the susceptibility and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the XXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat and magnetization for the compound Cu$_{3}$(CO$_{3}$)$_{2}$(OH)$_{2}$ are fairly compared with our TMRG results.
The gem-stone dioptase Cu6Si6O18.6H2O has a chiral crystal structure of equilateral triangular helices consisting of Cu-3d spins. It shows an antiferromagnetic order with an easy axis along c at TN = 15.5 K under zero field, and a magnetization jump at HC = 13.5 T when the field is applied along c-axis. By 29Si-NMR measurements, we have revealed that the high-field state is essentially the two sub-lattice structure, and that the component within ab-plane is collinear. The result indicates no apparent match with the geometrical pattern of helical spin chain.
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