Research

Overview:

My research interests are in mathematical physics, with an emphasis on studying spectral and dynamical properties of quantum lattice systems. My work uses a wide range of mathematics, including functional analysis, complex analysis, measure theory, probability theory and representation theory.

Recently, my work has focused on techniques for estimating spectral gaps and determining spectral gap stability of low-lying excitations of quantum spin systems. I am generally interested in studying ground state phases of quantum matter, for which a spectral gap above the ground state energy is key. Applications of my work are found in condensed matter physics, quantum information theory, and quantum computation.

Papers: My collective work can be viewed on arXiv.

1. Quasi-locality bounds for quantum lattice systems, part I: Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms- 2018, arXiv:1810.02428 (with B. Nachtergaele and R. Sims) arXiv

2. Quasi-locality bounds for quantum lattice systems, part II: Stability of gapped ground state phases of quantum spin systems- In preparation (with B. Nachtergaele and R. Sims)

3. Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems - 2018, Contemp. Math. 717 (with B. Nachtergaele and R. Sims) arXiv Journal

4. Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces - 2015, J. Stat. Phys. 162 (with M. Bishop and B. Nachtergaele) arXiv Journal

5. Product Vacua and Boundary State Models in d Dimensions - 2015, J. Stats. Phys. 160 (with S. Bachmann, E. Hamza, and B. Nachtergaele) arXiv Journal

6. On Enriching the Levin-Wen Model with Symmetry - 2015, J. Phys. A: Math. Theor. 48 (with L. Chang, M. Cheng, S. Cui, Y. Hu, W. Jin, R. Movassagh, P. Naaijkens, and Z. Wang) arXiv Journal

Dissertation:

A. Young, Spectral Properties of Multi-Dimensional Quantum Spin Systems, Ph.D. Dissertation, University of California, Davis, 2016