Amanda Young sitting on a window bench inside the LMU Physics builduing.

MCQST Distinguished PostDoc

Technical University of Munich

Forschungseinheit Dynamics, Zentrum Mathematik, M8

Boltzmannstraße 3

85748 Garching

+49 89 289 17086

young[at]ma.tum.de

Research Webpage

I love the diversity of mathematical techniques used to approach and understand questions in mathematical physics. There is always a creative solution.

Description

Main research focus: my research focuses on spectral and dynamical properties of quantum lattice systems.

A central question in the low-energy physics of quantum systems is whether the excitations above the ground states are gapped or gapless. My goal is to develop techniques for rigorously establishing spectral gaps through analyzing key quantum systems. Since joining MCQST, I have been investigating the spectral gap and low-lying excitations for fractional quantum Hall (FQH) systems. In a recent work, we proved a non-vanishing gap for an effective Hamiltonian of a 1/3-filled FQH system in the thin cylinder regime.


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

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