Locality and Subsystems from the Spectrum

ABSTRACT

The minimal ingredients to describe a quantum system are a Hamiltonian, an initial state, and a preferred tensor product structure that encodes a decomposition into subsystems. We explore a top-down approach in which the decomposition into subsystems emerges from the spectrum of the whole system. This approach has been referred to as quantum mereology. In practice, it is interesting to understand whether a given Hamiltonian is compatible with some given tensor product structure. More specifically, we ask: is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e., it contains only pairwise interactions? I will show that a generic Hamiltonian (e.g., a large random matrix) can be approximately written as a linear combination of two-body interaction terms with high precision; that is, the Hamiltonian is 2-local in a carefully chosen basis. Moreover, we find that these Hamiltonians are not fine-tuned, meaning that the spectrum is robust against perturbations of the coupling constants. Finally, by analyzing the adjacency structure of the couplings, we suggest a possible mechanism for the emergence of geometric locality from quantum chaos.

BIOGRAPHY

I’m a postdoc at Niels Bohr Institute, Copenhagen, interested in complex quantum systems dynamics and the emergence of classicality and locality. I graduated from New York University, where my PhD focused on the emergence of preferred tensor product structure decompositions.