Gharibian: Ground state connectivity of local Hamiltonians
Sevag Gharibian, University of California, Berkeley
The study of ground spaces of local Hamiltonians is a fundamental task
in condensed matter physics. In terms of computational complexity
theory, a common focus in this area has been to estimate a given
Hamiltonian’s ground state energy. However, from a physics
perspective, it is often more relevant to understand the structure of
the ground space itself. In this paper, we pursue the latter direction
by introducing the notion of “ground state connectivity” of local
the adjacency matrix of a graph provides a useful window onto combinatorial properties of the graph itself, but this approach to graph theory has been a source of interesting and useful results for over 80 years.