2017/04/25 by Anas Abdelwahab, Eric Jeckelmann, Martin Hohenadler · 1 citation
Mathematics · Physics and Astronomy · #Bosonization #Condensed matter physics #Density matrix renormalization group #Electron #Fermion #Hubbard model #Lattice (music) #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Quantum wire #Statistical physics #Surface and Thin Film Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.035445
published as Phys. Rev. B 96, 035445 (2017)
arxiv created 2017/04/25 · openalex publication_date 2017/07/31 · arxiv updated 2017/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a theoretical study of correlated atomic wires deposited on substrates in two parts. In this first part, we propose lattice models for a one-dimensional quantum wire on a three-dimensional substrate and map them onto effective two-dimensional lattices using the Lanczos algorithm. We then discuss the approximation of these two-dimensional lattices by narrow ladder models that can be investigated with well-established methods for one-dimensional correlated quantum systems, such as the density-matrix renormalization group or bosonization. The validity of this approach is studied first for noninteracting electrons and then for a correlated wire with a Hubbard electron-electron repulsion using quantum Monte Carlo simulations. While narrow ladders cannot be used to represent wires on metallic substrates, they capture the physics of wires on insulating substrates if at least three legs are used. In the second part [Abdelwahab et al., following paper, Phys. Rev. B 96, 035446 (2017)], we use this approach for a detailed numerical investigation of a wire with a Hubbard interaction on an insulating substrate.