# The Quest for Solvable Multistate Landau-Zener Models

## TL;DR

This paper demonstrates that integrability conditions facilitate the discovery of new solvable multistate Landau-Zener models, revealing their abundance and extending their applicability to complex many-body systems with multiple level crossings.

## Contribution

The authors refine integrability conditions and develop a computer-assisted method to find new solvable MLZ models, including those with multiple diabatic level crossings.

## Key findings

- Integrability conditions enable efficient search for new solvable MLZ models.
- Solvable models are numerous, spanning simple to complex many-body systems.
- Extended the class of solvable models to include multiple level crossing points.

## Abstract

Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.