Simone Warzel

Mathematical Physics

Technical University of Munich

Mathematics Department

Boltzmannstr. 3

85748 Garching

tel. +49 89 289 17911

warzel[at]ma.tum.de

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Description

Research focus: mathematical physics, quantum many-body and statistical physics, disordered systems.

Most of the research in my group addresses fundamental issues concerning quantum dynamics in the presence of disorder, and topics related to critical phenomena.


Disordered and glassy systems

One focus are the (de)localization properties of many-particle wave functions in interacting disordered quantum systems. For finitely, but arbitrarily many interacting particles as well as for attractive hard-core particles at low energies we devised a mathematical proof for the persistence of Anderson localization.
We also studied toy scenarios under which wave functions are resonantly extended over parts of Fock space such as in the Rosenzweig-Porter model or the Anderson model on the Bethe lattice.

Another focus are the quantum effects induced by a transverse magnetic field on mean-field spin glasses such as the Sherrington-Kirkpatrick model. Here we proved the persistence of a low-temperature glass phase and derived Parisi-type formulas for the free energy of hierarchical glasses.


Fractional quantum Hall systems

Haldane models describe the physics of the fractional quantum Hall as well as of rotating Bose gases. Among the conjectured essential properties is a spectral gap above a highly degenerate ground-state.

We are devising techniques to prove this conjecture. Among the partial results is a proof of this conjecture for truncated versions of Haldane’s models and the associated classification of the ground state in terms of fractional matrix-product states.


Featured

Publications

Spectral Gaps and Incompressibility in a 𝜈 = 1/3 Fractional Quantum Hall System

B. Nachtergaele, S. Warzel, A. Young

Communications in Mathematical Physics 383, 1093–1149 (2021).

Show Abstract

We study an effective Hamiltonian for the standard ν=1/3 fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice. We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values. As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states. We also show that all the ground states labeled by a tiling have a finite correlation length, for which we give an upper bound. We demonstrate by example, however, that not all superpositions of tiling states have exponential decay of correlations.

DOI: 10.1007/s00220-021-03997-0

Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder

V. Beaud, J. Sieber and S. Warzel.

Journal of Physics A: Mathematical and Theoretical 52, 235202 (2019).

Show Abstract

We give a direct alternative proof of an area law for the entanglement entropy of the ground state of disordered oscillator systems—a result due to Nachtergaele et al (2013 J. Math. Phys. 54 042110). Instead of studying the logarithmic negativity, we invoke the explicit formula for the entanglement entropy of Gaussian states to derive the upper bound. We also contrast this area law in the disordered case with divergent lower bounds on the entanglement entropy of the ground state of one-dimensional ordered oscillator chains.

DOI:10.1088/1751-8121/ab1924

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