From Complexification to Self-Similarity: New Aspects of Quantum Criticality

TL;DR

This paper reviews recent advances in quantum criticality, emphasizing complexification of partition functions, self-similarity phenomena, and their implications for understanding quantum phase transitions and non-Hermitian physics.

Contribution

It introduces the concept of complexification in quantum criticality, highlighting self-similarity and Fisher zeros, and connects these ideas with dynamical and non-Hermitian quantum phase transitions.

Findings

Identification of self-similarity in complex partition functions

Connection between Fisher zeros and critical phenomena

Insights into non-Hermitian quantum physics

Abstract

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical implications. This mini review provides a concise overview of recent developments in complexification, primarily covering finite temperature and equilibrium quantum phase transitions, as well as their connection with dynamical quantum phase transitions and non-Hermitian physics, with a particular focus on the significance of Fisher zeros. Starting from the newly discovered self-similarity phenomenon associated with complex partition functions, we further discuss research on self-similar systems briefly. Finally, we offer a perspective on these aspects.