IQIM Postdoctoral and Graduate Student Seminar

Abstract: The characterization of ground states among all quantum states is an important problem in quantum many-body physics. In this talk, I will introduce a new class of simple states, including the well-known W state, that can only occur as a ground state of geometrically local Hamiltonians alongside an exactly degenerate partner, even in gapless or disordered models. I will show that these states are never an element of a stable gapped ground state manifold, which may provide a new method to discard a wide range of ‘unstable' entanglement area law states in the numerical search of gapped phases. On the other hand when these degenerate states are the ground states of gapless systems they possess an excitation spectrum with O(1/L^2) finite-size splitting. One familiar situation where this special kind of gaplessness occurs is at a Lifshitz transition due to a zero mode; a potential quantum state signature of such a critical point. I will demonstrate some pathological parent Hamiltonians (i.e. those that fall outside our definition of a local Hamiltonian) for which the W state is a unique ground state. Finally I will conclude by discussing generalizations to higher dimensions, other related states, and implications for understanding thermodynamic limits of many-body quantum systems.

[1] Lei Gioia, Ryan Thorngren, arXiv 2310.10716 (2023) [2] Lei Gioia, Chong Wang, Phys. Rev. X 12, 031007 (2022)

Lunch will be provided, following the talk, on the lawn north of the Bridge Building.