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

TL;DR

This paper introduces a matrix-product-state (MPS) algorithm tailored for finite fractional quantum Hall systems, enabling efficient ground state searches and offering improvements over traditional DMRG methods.

Contribution

The authors develop a novel MPS-based code for finite FQH systems on a cylinder, differing from traditional DMRG, and demonstrate its efficiency and potential for generalization.

Findings

The MPS code efficiently finds ground states of FQH systems.

Performance comparison shows advantages over traditional DMRG.

Discussion on extending the method to infinite FQH systems.

Abstract

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.