Quantum phase transitions from topology in momentum space

TL;DR

This paper explores quantum phase transitions driven by topological changes in the momentum space of fermionic systems, highlighting their universality and applicability to both condensed matter and relativistic quantum fields.

Contribution

It provides a comprehensive analysis of topological quantum phase transitions involving various Fermi structures and extends the framework to relativistic quantum field vacua.

Findings

Classifies quantum phase transitions by topology in momentum space

Shows universality of low-energy behavior near topological nodes

Connects topological transitions to Standard Model particle spectrum

Abstract

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner 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). Close to the nodes the behavior of the system becomes universal; and the universality classes are determined by the toplogical invariants in momentum space. When one changes the parameters of the system, the transitions are expected to occur between the vacua with the same symmetry but which belong to different universality classes. Different types of quantum phase transitions governed by topology in momentum space are discussed in this Chapter. They involve Fermi surfaces, Fermi points, Fermi lines, and also the topological transitions between the fully gapped states. The consideration based on the momentum space topology of the Green's function is general and is applicable to the vacua of relativistic quantum fields. This is illustrated by the possible quantum phase transition governed by topology of nodes in the spectrum of elementary particles of Standard Model.