Part 1: Two-local interactions
{"Image DocumentName": "Part 1: Two-local interactions", "Image ImageDescription": "N interacting quantum systems, each d-level. \u2026 N. Interactions may only be one- and two-body. Consider the whole state space. Which of these states are the ground state of some (nontrivial) two-local Hamiltonian? Lets look at the first assumption: that a many-body system has only one- and two-body interactions. When the interactions in a system are a sum of one- and two-body interactions, we say that the system is two-local. The question is, what effect does this assumption have on the possible ground states? In other words, first consider the whole set of states on the system. Which of these states represent the ground state of some two-local system? If you pick a particular state, is there some way of fiddling with the actual interactions, so that you get that state as the ground state? I should point out my use of the word nontrivial here. We\u2019re interested in the ground states of all possible two-local systems, with one exception: we\u2019re not interested in the system that has all interactions turned off. In that trivial case, every state belongs to a totally degenerate ground state. So the precise question is, what states can be the ground state of some nontrivial two-local Hamiltonian. I\u2019ll show, that there are holes in this set of possible states. That is, any state inside these regions are provably not the ground state of any nontrivial physically plausible system.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}