## Doctoral research projects

### Current projects

- Yasemin Ergün,
*Phase transitions in quantum wires on substrates* - Gökmen Polat,
*Numerical investigations of correlated ladder models for doped Mott and charge transfer insulators*

### Completed projects

- Dr. Jan Bischoff,
*DMRG method for the linear DC-conductance of one-dimensional correlated systems*, 2019. - Dr. Christoph Brockt,
*Numerical study of the nonequilibrium dynamics of 1-D electron-phonon systems using a local basis optimization*, 2018. - Dr. Anas Omer Abdelwahab,
*Models for a quantum atomic chain coupled to a substrate*, 2018. - Dr. Martin Paech,
*Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme*, 2015. - Dr. Malcolm Einhellinger,
*Transport simulations in nanosystems and low-dimensional systems*, 2012.

## DFG Research Unit 1807

## Advanced Computational Methods for Strongly Correlated Quantum Systems

### Project “Advanced wave-function based methods for electron-phonon coupled systems”

The main goal of this project is the development of efficient and versatile computational methods for studying correlated low-dimensional quantum systems with strongly fluctuating bosonic degrees of freedom. In addition, we plan to adapt and test our algorithms on a broad variety of timely problems from condensed matter physics, mostly related to electron-phonon systems. These applications include phase transitions and local entanglement entropy, nonequilibrium and dissipative transport through electron-phonon coupled nanostructures, time-resolved spectroscopy and photoinduced phase transitions in quasi-one-dimensional materials, as well as spin transport in spin-phonon coupled models.

This project is carried out in collaboration with Prof. Dr. Fabian Heidrich-Meisner from the University of Göttingen.

### Publications

J. Stolpp, T. Köhler, S. R. Manmana, E. Jeckelmann, F. Heidrich-Meisner and S. Paeckel, Computer Physics Communications*Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert space without U(1) symmetry*,**269**, 108106 (2021), e-print arXiv:2011.07412- Dissertation
*DMRG method for the linear DC-conductance of one-dimensional correlated systems,* *Density-matrix renormalization group study of the linear conductance in quantum wires coupled to interacting leads or phonon*, Jan-Moritz Bischoff and Eric Jeckelmann, Phys. Rev. B**100**, 075151 (2019), e-print arxiv:1907.01844- Dissertation
*Numerical study of the nonequilibrium dynamics of 1-D electron-phonon systems using a local basis optimization*, Christoph Brockt, 2018 *Scattering of an electronic wave packet by a one-dimensional electron-phonon-coupled structure*, Christoph Brockt and Eric Jeckelmann, Phys. Rev. B**95**, 064309 (2017) , e-print arXiv:1612.04665*Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium*, C. Brockt, F. Dorfner, L. Vidmar, F. Heidrich-Meisner, and E. Jeckelmann, Phys. Rev. B**92**, 241106(R) (2015), e-print arXiv:1508.00694- F. Dorfner, L. Vidmar, C. Brockt, E. Jeckelmann, F. Heidrich-Meisner,
*Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model*, Phys. Rev. B**91**, 104302 (2015), e-print arXiv:1411.5074

## DFG Research Unit 1700

## Metallic nanowires on the atomic scale

### Project “Embedded one-dimensional electron-phonon systems”

The aim of this project is to gain a better understanding of one-dimensional physics in atomic wires on surfaces. These systems can be regarded as two-dimensional arrays of weakly-coupled chains with interacting electron and phonon degrees of freedom which are embedded in a three-dimensional environment. Our investigations are based on effective models for the low-energy properties of atomic wires on substrates. We use well-established methods such as mean-field approximations, bosonization, and the density-matrix renormalization group.

We generalize the theory of the Peierls transition driven by the coupling between electrons and lattice distortions to the grand-canonical ensemble to take into account the underlying substrate. We also examine the influence of the substrate and the inter-wire coupling on the Luttinger liquid properties of metallic wires. Finally, we investigate the occurence of quasi-one-dimensional long-range order in the wire system due to the coupling to the substrate.

### Publications

*Ground-state and spectral properties of an asymmetric Hubbard ladder*, Anas Abdelwahab, Eric Jeckelmann, and Martin Hohenadler, Phys. Rev. B**91**, 155119 (2015), e-print arXiv:1409.7315*Grand canonical Peierls transition in In/Si(111*), Eric Jeckelmann, Simone Sanna, Wolf Gero Schmidt, Eugen Speiser, and Norbert Esser, Phys. Rev. B**93**, 241407(R) (2016), e-print arXiv:1509.08296*Correlated atomic wires on substrates. I. Mapping to quasi-one-dimensional model,*Anas Abdelwahab, Eric Jeckelmann, and Martin Hohenadler, Phys. Rev. B**96**, 035445 (2017), e-print arXiv:1704.07350*Correlated atomic wires on substrates. II. Application to Hubbard wires*, Anas Abdelwahab, Eric Jeckelmann, and Martin Hohenadler, Phys. Rev. B**96**, 035446 (2017), e-print arXiv:1704.07359- Dissertation
*Models for a quantum atomic chain coupled to a substrate*, Anas Omer Abdelwahab, 2018 *Correlations and confinement of excitations in an asymmetric Hubbard ladder*, Anas Abdelwahab and Eric Jeckelmann, Eur. Phys. J. B**91**, 207 (2018), e-print arxiv:1707.08780*Luttinger liquid and charge-density-wave phases in a spinless fermion wire on a semiconducting substrate*, Anas Abdelwahab and Eric Jeckelmann, Phys. Rev. B**98**, 235138 (2018), e-print: arXiv:1810.02190.*Anisotropic 2D metallicity: Plasmons in Ge(100)-Au,*T. Lichtenstein, Z. Mamiyev, E. Jeckelmann, C. Tegenkamp, and H. Pfnür, J. Phys.: Condens. Matter 31, 175001 (2019)*Grand-canonical Peierls theory for atomic wires on substrates*, Yasemin Ergün and Eric Jeckelmann, Phys. Rev. B**101**, 085403 (2020), e-print: arXiv:1908.010202.*Dimensionality of metallic atomic wires on surfaces,*Eric Jeckelmann, Phys. Rev. B**101**, 245153 (2020), e-print: arXiv:2004.05580*Effective narrow ladder model for two quantum wires on a semiconducting substrate,*Anas Abdelwahab and Eric Jeckelmann, Phys. Rev. B**103**, 245405 (2021), e-print arXiv:2102.13412

## School for Contacts in Nanosystems

### Project “Electronic correlations and quantum dynamics in ultrathin nanowires”

This project is a theoretical study of quantum effects and electronic correlations in the transport and spectral properties of ultrathin quantum wires in contact with an environment (metallic leads and heat bath). The wires and their environment are represented by electron-phonon lattice models which are investigated with various, mostly numerical methods such as the density-matrix renormalization group and the time-evolving block decimation.

### Publications

- Doctoral thesis
*DMRG method for the linear DC-conductance of one-dimensional correlated systems,* *Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula*, Jan-Moritz Bischoff and Eric Jeckelmann, Phys. Rev. B**96**, 195111 (2017) ; e-print arXiv:1709.02723- Doctoral thesis
*Transport simulations in nanosystems and low-dimensional systems*, Malcolm Einhellinger, 2012 *Numerical method for non-linear steady-state transport in one-dimensional correlated conductors,*M. Einhellinger, A. Cojuhovschi, and E. Jeckelmann, Phys. Rev. B**85**, 235141 (2012), e-print arXiv:1201.5323