Quantum Information Journal Club: ‘Some Properties of Local One-Dimensional Hamiltonians’
Speaker: José Garre Rubio
Títle: ‘Some Properties of Local One-Dimensional Hamiltonians’
Venue&Time: Gray Room 1 / 11:30
Abstract: In this talk, I will discuss several properties of local Hamiltonians associated with the W state and matrix product states (MPS). I will begin by showing that the W state cannot be the unique ground state of any local Hamiltonian. I will then present a condition that guarantees that the parent Hamiltonian of an arbitrary MPS is well behaved, encompassing the W-state case as an example. Finally, I will characterize the action of local Hamiltonians on injective MPS, an important class that describes unique ground states. Throughout the talk, I will highlight several open problems and possible directions for future research. The results presented are based on [JGR, Quantum Information Processing 24, 366 (2025)], [JGR, A. Turzillo, A. Molnár, Annales Henri Poincaré 1–23 (2025)], and [JGR, A. Molnár, N. Schuch, F. Verstraete, arXiv:2603.28349].