Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions

TL;DR

This paper demonstrates that symmetry can protect quantum adiabatic evolution during spontaneous symmetry-breaking transitions, even when the energy gap closes, by deriving a symmetry-dependent adiabatic condition.

Contribution

It introduces a symmetry-dependent adiabatic condition that ensures quantum adiabatic evolution persists despite degeneracies in symmetry-breaking transitions.

Findings

Symmetry conservation forbids transitions between states of different symmetry.

Adiabatic evolution can occur even with a vanishing energy gap under symmetry protection.

The results have applications in quantum state engineering and quantum computing.

Abstract

Quantum adiabatic evolution, an important fundamental concept inphysics, describes the dynamical evolution arbitrarily close to the instantaneous eigenstate of a slowly driven Hamiltonian. In most systems undergoing spontaneous symmetry-breaking transitions, their two lowest eigenstates change from non-degenerate to degenerate. Therefore, due to the corresponding energy-gap vanishes, the conventional adiabatic condition becomes invalid. Here we explore the existence of quantum adiabatic evolutions in spontaneous symmetry-breaking transitions and derive a symmetry-dependent adiabatic condition. Because the driven Hamiltonian conserves the symmetry in the whole process, the transition between different instantaneous eigenstates with different symmetries is forbidden. Therefore, even if the minimum energy-gap vanishes, symmetry-protected quantum adiabatic evolutioncan still appear when the driven system varies according to the symmetry-dependent adiabatic condition. This study not only advances our understandings of quantum adiabatic evolution and spontaneous symmetry-breaking transitions, but also provides extensive applications ranging from quantum state engineering, topological Thouless pumping to quantum computing.