# Dr. Martin Puschmann

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## Multifractal spectra of quantum Hall systems

The spin and integer quantum Hall transitions are prominent examples in the realm of Anderson localization. A distinguishing feature of these transitions is in the statistics of the amplitudes of the critical wavefunctions, conveniently described by their $q$th moments, i.e. the generalized inverse participation ratios (IPR). We analyze the system-size scaling of the IPRs, $P_q$, and extract the multifractal exponents $\tau_q$. The set of all $\tau_q$ yield the multifractal spectra, which allows for the comparsion with predictions steming from analytic quantum-field-theoretical approaches. For more information see e.g. arXiv:2104.12079

## Anderson localization

The integer quantum Hall (IQH) transition is a paradigmatic phase transition in the realm of Anderson localization, whose critical properties are not settled yet. The discrepancy between experiments and numerical studies is usually attributed to the electron-electron interactions being neglected in simulations. However, results of different recent numerical studies do not agree with each other. For more information see e.g. PRB (R) 99 (2019), 121301arXiv:2102.00271

In a related project, we investigate the effect of topological disorder on the critical behavior of Anderson transitions. The disorder is represent by random lattices whose construction formalism lead to short-ranged correlations within the randomness due to topological constraints. For more information see EPJ B 88 (2015), 314

## Collective modes at disordered quantum phase transitions

The research is devoted to the dynamics of the Goldstone and amplitude (Higgs) modes at a paradigmatic quantum phase transition, viz. the superfluid-Mott glass transition. Monte Carlo simulations show that the scalar susceptibility spectra of a disorder-free system yield a sharp Higgs mode that softens at criticality and obey scaling relations, whereas the spectra in case
of site dilution yield an almost constant and noncritical behavior, Collective mode eigen states
violating scaling relations. In order to understand the unexpected behavior of the collective Extended Goldstone (picture) vs. localized Higgs mode state of diluted modes, we develop an inhomogeneous quantum mean-field square lattice theory with Gaussian fluctuations for collective excitations in a disordered particle-hole symmetric Bose-Hubbard model. The resulting fluctuation Hamiltonian decouples into a Goldstone and Higgs collective mode part. We solve each part via a multimodal bosonic Bogoliubov transformation. For more information see PRL 125 (2020), 027002arXiv:2101.11065

## Teaching at University of Regensburg

 Winter 2021/22 Exercise for Classical Mechanics for Teachers Summer 2021 Exercise for Classical Mechanics Winter 2020/21 Exercise/Tutorium for Computational Condensed Matter Theory with Applications to Topological Systems

## Brief CV

 07/2020 - now Research associate, U Regensburg Research in the group of Ferdinand Evers 03/2018 - 06/2020 Postdoctoral Fellow, Missouri University of Science and Technology Research in the group of Thomas Vojta 10/2013 - 02/2018 Research associate, TU Chemnitz Ph.D. in 12/2017 in the group of Michael Schreiber 10/2008 - 10/2013 Study of Physics, TU Chemnitz M.S. in 10/2013; B.S. in 09/2011

## Publications

See personally curated list,  or

See the list on arXivGoogle Scholar , or ORCID

## Publications with affiliation to the University Regensburg

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## Dr. Martin Puschmann

Computational Condensed Matter Theory Group
Institut I - Theoretische Physik
Universität Regensburg,
D-93040 Regensburg

Contact:
martin.puschmann@ur.de
PHY 3.1.24
+49 (0) 941 943 2040