# Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

## TL;DR

This paper demonstrates that hybrid real-momentum space DMRG is more efficient than real-space DMRG for the 2D Hubbard model, enabling detailed analysis of charge and magnetic orderings in doped systems.

## Contribution

The study introduces a hybrid-space DMRG approach that reduces computational cost and applies it to analyze charge and magnetic orderings in doped 2D Hubbard models.

## Key findings

- Hybrid-space DMRG is more efficient than real-space DMRG.
- Ground state shows stripe charge-density at certain fillings.
- Charge ordering strength varies with U/t and boundary conditions.

## Abstract

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid real-momentum space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $U/t=8.0$. We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions.Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.