Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models

A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of two-dimensional (2D) quantum lattice models is proposed. By transforming the 2D quantum model into a three-dimensional (3D) closed tensor network (TN) comprised of the tensor product density operator and a 3D brick-wall TN, the free energy of the system can be calculated with the imaginary time evolution, in which the network Tucker decomposition is suggested for the first time to obtain the optimal lower-dimensional approximation on the bond space by transforming the TN into a super-orthogonal form. The efficiency and accuracy of this algorithm are testified, which are fairly comparable with the quantum Monte Carlo calculations. Besides, the present ODTNS scheme can also be applicable to the 2D frustrated quantum spin models with nice efficiency

Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagom\'{e} lattice

The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as ferromagnetic, ferrimagnetic and paramagnetic phases, along with the second-order phase transitions, have been identified. The TRG results are quite accurate and reliable in comparison to the exact solutions. In a magnetic field, the magnetization ($m$), susceptibility and specific heat are studied by the TRG algorithm, where the $m=1/3$ plateaux are observed in the magnetization curves for some couplings. The experimental data of susceptibility for the complex Co(N$_3$)$_2$(bpg)$\cdot$ DMF$_{4/3}$ are fitted with the TRG results, giving the couplings of the complex $J=22K$ and $J'=33K$

Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice

We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$, the system scales exponentially, either with or without a magnetic field $h$: the order parameter, the five critical fields that separate the $J_e$-$h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on $J_e$. We calculate the temperature dependence of the specific heat, which can be directly compared with future experiments.Comment: 7 pages, 6 figure