Transitionless quantum driving for spin systems

TL;DR

This paper applies transitionless quantum driving to spin systems, explicitly constructing driving Hamiltonians for models like XY and Lipkin-Meshkov-Glick, and discusses overcoming challenges at quantum phase transitions.

Contribution

It extends transitionless quantum driving techniques to spin systems, providing explicit constructions and analyzing behavior near quantum critical points.

Findings

Explicit driving Hamiltonians for XY and Lipkin-Meshkov-Glick models

Discussion on time-independent and equivalent driving Hamiltonians

Strategies to circumvent defects at quantum phase transitions

Abstract

We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the Schroedinger equation. For several typical systems such as the XY spin chain and the Lipkin-Meshkov-Glick model, the driving Hamiltonian is constructed explicitly. We discuss possible interesting situations when the driving Hamiltonian becomes time independent and when the driving Hamiltonian is equivalent to the original one. For many-body systems, a crucial problem occurs at the quantum phase transition point where the energy gap between the ground and first excited states becomes zero. We discuss how the defect can be circumvented in the present method.