Counterdiabatic Hamiltonians for multistate Landau-Zener problem

TL;DR

This paper extends the concept of counterdiabatic Hamiltonians to multistate Landau-Zener systems, providing a detailed analysis of their structure and practical calculation methods for transition probabilities.

Contribution

It introduces auxiliary Hamiltonians satisfying the zero curvature condition for multistate Landau-Zener problems, advancing the theoretical framework and computational techniques.

Findings

Counterdiabatic Hamiltonians satisfy the zero curvature condition.

The method effectively calculates transition probabilities in nonadiabatic regimes.

Application to spin models demonstrates practical utility.

Abstract

We study the Landau-Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are interpreted as the counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy the zero curvature condition. The general structures of the auxiliary Hamiltonians are studied in detail and the time-evolution operator is evaluated by using a deformation of the integration contour and asymptotic forms of the auxiliary Hamiltonians. For several spin models with transverse field, we calculate the transition probability between the initial and final ground states and find that the method is useful to study nonadiabatic regime.