Uhlmann quench and geometric dynamic quantum phase transition of mixed states

TL;DR

This paper introduces a formalism for incorporating geometric phases into the dynamics of mixed quantum states during quenches, revealing geometric quantum phase transitions with singularities and phase jumps.

Contribution

It develops the Uhlmann quench formalism, enabling the study of geometric phases and dynamic quantum phase transitions in mixed states during quantum quenches.

Findings

Geometric DQPTs exhibit singularities in the free energy analogue.

Jumps in the geometric phase occur at critical points.

Uhlmann phase reflects holonomy after cyclic processes.

Abstract

Dynamic quantum phase transitions (DQPT) following quantum quenches exhibit singular behavior of the overlap between the initial and evolved states. Here we present a formalism to incorporate a geometric phase into quench dynamics of mixed quantum states, a process named the Uhlmann quench, based on the Uhlmann parallel transport. To overcome the incompatibility between the Uhlmann parallel-transport condition and Hamiltonian dynamics, we formulate the evolution of purification of the density matrix in a form which not only respects the dynamics according to the density matrix but also follows the Uhlmann parallel-transport condition to generate a geometric phase after a quantum quench. For cyclic processes exemplified by a spin-1/2 system, geometric DQPTs (GDQPTs) can emerge with both singular behavior in the dynamic analogue of the free energy and jumps of the geometric phase. Moreover, the Uhlmann phase reflecting the holonomy is generated at the end of each cycle. The Uhlmann quench thus paves the way for investigating the interplay between quantum dynamics and geometric processes in mixed states.