Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intertwined vestigial order in quantum materials: nematicity and beyond   A hallmark of the phase diagrams of quantum materials is the existence of
multiple electronic ordered states, which, in many cases, are not independent
competing phases, but instead display a complex intertwinement. In this review,
we focus on a particular realization of intertwined orders: a primary phase
characterized by a multi-component order parameter and a fluctuation-driven
vestigial phase characterized by a composite order parameter. This concept has
been widely employed to elucidate nematicity in iron-based and cuprate
superconductors. Here we present a group-theoretical framework that extends
this notion to a variety of phases, providing a classification of vestigial
orders of unconventional superconductors and density-waves. Electronic states
with scalar and vector chiral order, spin-nematic order, Ising-nematic order,
time-reversal symmetry-breaking order, and algebraic vestigial order emerge
from one underlying principle. The formalism provides a framework to understand
the complexity of quantum materials based on symmetry, largely without
resorting to microscopic models.

33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int