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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.
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 a
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 ma
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 fou
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 ren
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