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

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.

arXiv comment16 pages, 14 figures

References in corpus (29)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Area laws for the entanglement entropy - a review
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Electrical Resistivity Anisotropy from Self-Organized One-Dimensionality in High-Temperature Superconductors
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• New Trends in Density Matrix Renormalization
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Fermionic multi-scale entanglement renormalization ansatz
• Density-matrix renormalization-group method in momentum space
• Stripes on a 6-Leg Hubbard Ladder
• Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
• Enhanced d_{x^2-y^2} pairing correlations in the two-leg Hubbard ladder
• Real-Space Parallel Density Matrix Renormalization Group
• Fermionic orbital optimisation in tensor network states
• Stripe formation in doped Hubbard ladders
• Pair Correlations in Doped Hubbard Ladders
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems
• Application of the Density Matrix Renormalization Group in momentum space
• Entanglement structure of the Hubbard model in momentum space

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