The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S=1/2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the paircorrelation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1=2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union-Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.

Magnetic properties and magnetocaloric effects of Ho12Co7 compound are investigated by magnetization and heat capacity measurement. The Ho12Co7 compound undergoes antiferromagnetic (AFM)-AFM transition at T1 = 9 K, AFM-ferromagnetic (FM) transition at T2 = 17 K, and FM-paramagnetic transition at TC = 30 K, with temperature increasing. There are two peaks on the magnetic entropy change (ΔSM) versus temperature curves and the maximal value of –ΔSM is found to be 19.2 J/kg K with the refrigerant capacity value of 554.4 J/kg under a field change from 0 to 5 T. The shape of the ΔSM-T curves obtained from heat capacity measurement is in accordance with that from magnetization measurement. The excellent magnetocaloric performance indicates the applicability of Ho12Co7 as an appropriate candidate for magnetic refrigerant in low temperature ranges.

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