Continuous order-to-order quantum phase transitions from fixed-point annihilation

TL;DR

This paper introduces a novel mechanism for continuous quantum phase transitions driven by fixed-point annihilation, independent of fractionalization, with potential applications in various complex quantum systems.

Contribution

It proposes a new fixed-point collision mechanism for continuous order-to-order quantum phase transitions, expanding understanding beyond fractionalization-based theories.

Findings

Fixed-point annihilation can induce continuous phase transitions.

Applicable to systems like Weyl semimetals and topological insulators.

Potential relevance to materials like rare-earth pyrochlore iridates.

Abstract

A central concept in the theory of phase transitions beyond the Landau-Ginzburg-Wilson paradigm is fractionalization: the formation of new quasiparticles that interact via emergent gauge fields. This concept has been extensively explored in the context of continuous quantum phase transitions between distinct orders that break different symmetries. We propose a mechanism for continuous order-to-order quantum phase transitions that operates independently of fractionalization. This mechanism is based on the collision and annihilation of two renormalization group fixed points: a quantum critical fixed point and an infrared stable fixed point. The annihilation of these fixed points rearranges the flow topology, eliminating the disordered phase associated with the infrared stable fixed point and promoting a second critical fixed point, unaffected by the collision, to a quantum critical point between distinct orders. We argue that this mechanism is relevant to a broad spectrum of physical systems. In particular, it can manifest in Luttinger fermion systems in three spatial dimensions, leading to a continuous quantum phase transition between an antiferromagnetic Weyl semimetal state, which breaks time-reversal symmetry, and a nematic topological insulator, characterized by broken lattice rotational symmetry. This continuous antiferromagnetic-Weyl-to-nematic-insulator transition might be observed in rare-earth pyrochlore iridates $R_2$Ir$_2$O$_7$. Other possible realizations include kagome quantum magnets, quantum impurity models, and quantum chromodynamics with supplemental four-fermion interactions.