Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

26th IUPAP Conference on Computational Physics

物理学;计算机科学

Liu, Zhao^1 ; Bhatt, R.N.^1

Department of Electrical Engineering, Princeton University, Princeton

NJ

08544, United States^1

关键词: Computational costs;    Density matrix;    Density matrix renormalization group;    Exact diagonalization;    Matrix product state;    Matrix products;    Physical systems;    Quantum Hall systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/640/1/012044/pdf
DOI  :  10.1088/1742-6596/640/1/012044

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.