Exact S-matrices for higher dimensional representations of generalized Landau-Zener Hamiltonians

TL;DR

This paper develops a Lie algebraic framework to derive exact scattering matrices for higher-dimensional Landau-Zener Hamiltonians, including new multi-level models, by reformulating them as integrable Lax equations.

Contribution

It introduces a systematic algebraic approach to construct exactly solvable multi-level Landau-Zener models using Lie algebraic structures and zero-curvature conditions.

Findings

Derived exact scattering matrices for higher-spin Landau-Zener models

Extended the approach to generalized bow-tie Hamiltonians with gauge fields

Constructed new six- and eight-dimensional solvable models

Abstract

We explore integrable Landau-Zener-type Hamiltonians through the framework of Lie algebraic structures. By reformulating the classic two-level Landau-Zener model as a Lax equation, we show that higher-spin generalizations lead to exactly solvable scattering matrices, which can be computed efficiently for any higher-spin representation. We further extend this approach to generalized bow-tie Landau-Zener Hamiltonians, employing non-Abelian gauge fields that satisfy a zero-curvature condition to derive their scattering matrices algebraically. This method enables the systematic construction of new exactly solvable multi-level models; as a result, we present previously unknown six-dimensional and eight-dimensional Landau-Zener models.