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

2025/05/09 by Malikis, S., Cheianov, V. · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.06048

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.

Cited by

• Exact many-body wavefunction of the Kondo model with time-dependent interaction strength

Related

• Integrability in the multistate Landau-Zener model with time-quadratic commuting operators
• No-go rules for multitime Landau-Zener models
• Hidden sl(2)-Symmetry of the Generalized Landau-Zener Vibronic Model
• Multiplicity A_m Models
• Matrix exponential solution of the Landau-Zener problem