Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics

TL;DR

This paper investigates how global inconsistency conditions in quantum mechanics models relate to energy spectrum features like level crossing, revealing their role in constraining low-energy behaviors and phase transitions.

Contribution

It clarifies the implications of the global inconsistency condition in quantum mechanics models with topological angles, connecting it to level crossing phenomena.

Findings

Global inconsistency can be saturated by level crossing.

Energy spectra show degeneracies at high symmetry points.

Global inconsistency constrains phase transitions.

Abstract

An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.