Year: 2024
Type: article
Abstract: Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not as successful because of the limited entanglement encoded in the wave-function ansatz. The fully augmented matrix product states (FAMPS), introduced recently in [Chin. Phys. Lett. 40, 057102 (2023)], extends MPS formalism to two dimensions and increases the entanglement in the wave-function ansatz, representing a significant advance in the simulation of two-dimensional quantum many-body physics. In the study of one-dimensional systems, the concept of a parent Hamiltonian for MPS has proven pivotal in the understanding of quantum entanglement. In this work, we extend this framework to two-dimensional systems. We illustrate the procedure to construct a two-dimensional Hamiltonian with given FAMPS as its exact ground state (the parent Hamiltonian for FAMPS). Additionally, through numerical simulations, we demonstrate the effectiveness of the algorithm outlined in [Chin. Phys. Lett. 40, 057102 (2023)] in precisely identifying the FAMPS for the constructed parent Hamiltonian. The introduction of FAMPS and its associated parent Hamiltonian provides a useful framework for the future investigations of two-dimensional quantum many-body systems.
Authors: Xiangjian Qian, Mingpu Qin
Institution: Shanghai Jiao Tong University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G7403570660, G8985750264
OpenAlex ID: W4402901630