Momentum space topology and quantum phase transitions

TL;DR

This paper explores how topology in momentum space governs low-energy physics and quantum phase transitions in strongly correlated fermionic systems, emphasizing the universality and robustness of emergent phenomena regardless of microscopic details.

Contribution

It demonstrates the role of momentum space topology in quantum phase transitions and provides examples illustrating the universality of low-energy emergent physics in strongly correlated systems.

Findings

Quantum phase transitions can occur between vacua with the same symmetry but different momentum-space topology.

Transitions between fully gapped states are also governed by changes in momentum-space topology.

Emergent low-energy physics is largely independent of microscopic details due to topological protection.

Abstract

Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Here we illustrate this universality on some examples of quantum phase transitions, which can occur between the vacua with the same symmetry but with diferent topology in momentum space. The quantum phase transitions between the fully gapped states with different momentum-space topology are also discussed.