Hai-Jun Liao

Gapless Spin-Liquid Ground State in the S=1/2 Kagome Antiferromagnet

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.

Phase Transition of the q -State Clock Model: Duality and Tensor Renormalization

We investigate the critical behavior and the duality property of the ferromagnetic q-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with q ≤ 5 and approximate self-dual points for q ≥ 6. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

Optimized contraction scheme for tensor-network states

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose an optimized contraction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted and improves dramatically the efficiency and accuracy of the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and it extends significantly the application scope of tensor-network methods.

Heisenberg antiferromagnet on the Husimi lattice

We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on projected entangled simplex states. The nature of the ground state varies strongly with the spin quantum number

Charge dynamics of the antiferromagnetically ordered Mott insulator

S

A generalized Lanczos method for systematic optimization of tensor network states

. For

Self-Consistent Spin-Wave Analysis of the 1/3 Magnetization Plateau in the Kagome Antiferromagnet

S=\frac{1}{2}

Analytic Continuation with Padé Decomposition

, it is an algebraic (gapless) quantum spin liquid. For

Finite-temperature charge dynamics and the melting of the Mott insulator

S=1

Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions

, it is a gapped, nonmagnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For