Adaptive Pseudoboson Density-Matrix Renormalization Group for Dilute 2D Systems

TL;DR

The paper introduces A3P-DMRG, an adaptive method for efficiently simulating dilute strongly correlated 2D quantum systems by focusing on low-occupation states, outperforming traditional DMRG in certain regimes.

Contribution

It presents a novel adaptive pseudoboson DMRG approach that compresses Hilbert spaces using probabilistic bounds and self-consistent basis optimization for dilute 2D systems.

Findings

A3P-DMRG effectively handles large dilute systems where conventional DMRG fails.

The method is particularly advantageous in low-filling and weak-coupling regimes.

Demonstrates applicability to ultra-cold atoms, photonic lattices, and Moiré materials.

Abstract

Simulating strongly correlated systems in two dimensions is notoriously challenging due to rapid entanglement growth and frustration. Here, we introduce the adaptive projected-purified pseudoboson density-matrix renormalization group (A3P-DMRG) tailored to explore the ground states of dilute lattice models. The method compresses cluster Hilbert spaces by retaining only the most probable low-occupation Fock states, identified via probabilistic bounds and refined through a self-consistent mean-field basis optimization. We demonstrate that A3P-DMRG is advantageous in low-filling and weak-coupling regimes for large system sizes where conventional DMRG struggles. This establishes the method as a versatile tool for studying dilute quantum many-body systems relevant to ultra-cold atom quantum simulators, photonic lattices, Moir\'e materials and quantum chemistry.