No-go rules for multitime Landau–Zener models

Abstract

Multitime Landau–Zener (MTLZ) model is a class of exactly solvable quantum many-body models which is multistate and multitime generalization of the two-state Landau–Zener model. Currently discovered MTLZ models include the “hypercubes”, the “fans” and their direct product models. In this work, we prove two no-go rules, named the “no \(K_{3,3}\)” rule and the “no 1221” rule, which forbid the existence of exact solutions for models with certain structures of interactions. We further apply these rules to show that for models with no more than 9 states, besides the models mentioned above there are no other MTLZ models. We also propose a scheme to systematically classify cases that could possibly host MTLZ models. Our work could serve as a guideline to search for new exactly solvable models within the MTLZ class.