TY - JOUR

T1 - Correlated atomic wires on substrates

T2 - I. Mapping to quasi-one-dimensional models

AU - Abdelwahab, Anas

AU - Jeckelmann, Eric

AU - Hohenadler, Martin

N1 - Funding information: This work was supported by the German Research Foundation (DFG) through SFB 1170 ToCoTronics and the Research Unit Metallic Nanowires on the Atomic Scale: Electronic and Vibrational Coupling in Real World Systems (FOR 1700, Grant No. JE 261/1-1). The authors gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JURECA at the Julich Supercomputing Centre.

PY - 2017/7/31

Y1 - 2017/7/31

N2 - 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.

AB - 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.

KW - cond-mat.str-el

KW - cond-mat.mes-hall

UR - http://www.scopus.com/inward/record.url?scp=85027272395&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.96.035445

DO - 10.1103/PhysRevB.96.035445

M3 - Article

VL - 96

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 3

M1 - 035445

ER -