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Topic

Theoretical Perspective on Bundled MPS and Low-Lying Excitations in Quantum Many-Body Systems

Department of Physics and Astronomy

Date & location

• Monday, August 17, 2026
• 9:00 A.M.
• Clearihue Building, Room B017

Examining Committee

Supervisory Committee

• Dr. Thomas Baker, Department of Physics and Astronomy, University of Victoria (Supervisor)
• Dr. Kristan Jensen, Department of Physics and Astronomy, UVic (Member)
• Dr. Irina Paci, Department of Chemistry, UVic (Outside Member)

External Examiner

• Dr. Ryland Giebelhaus, Department of Chemistry, UVic

Chair of Oral Examination

• Dr. Dennis Hore, Department of Chemistry, UVic

Abstract

This thesis develops a framework for understanding when different excited states of local quantum Hamiltonians can be efficiently represented in a common basis, one containing fewer states than the full Hilbert space. In the analytical part, we introduce metrics that quantify the “closeness” of excitations by comparing their truncated density matrices in a fixed single-particle basis, and relate these metrics to their energy differences. We show that large energy separations necessarily imply large differences between density matrices, while small energy differences fall into two categories: one in which the density matrices differ only slightly, and another in which they remain very different, as can occur in the presence of symmetry. We also extend these ideas to bundled matrix product states, in which multiple excitations are encoded simultaneously, and study how the required bond dimension grows as excitations with different energies are included.