A
bstract
We study the longitudinal magnetotransport in three-dimensional multi-Weyl semimetals, constituted by a pair of (anti)-monopole of arbitrary integer charge (
n
), with
n
= 1
,
2 and 3 in a ...crystalline environment. For any
n >
1, even though the distribution of the underlying Berry curvature is
anisotropic
, the corresponding intrinsic component of the longitudinal magnetoconductivity (LMC), bearing the signature of the chiral anomaly, is
insensitive
to the direction of the external magnetic field (
B
) and increases as
B
2
, at least when it is sufficiently weak (the semi-classical regime). In addition, the LMC scales as
n
3
with the monopole charge. We demonstrate these outcomes for two distinct scenarios, namely when inter-particle collisions in the Weyl medium are effectively described by (a) a single and (b) two (corresponding to inter- and intra-valley) scattering times. While in the former situation the contribution to LMC from chiral anomaly is inseparable from the non-anomalous ones, these two contributions are characterized by different time scales in the later construction. Specifically for sufficiently large inter-valley scattering time the LMC is dominated by the anomalous contribution, arising from the chiral anomaly. The predicted scaling of LMC and the signature of chiral anomaly can be observed in recently proposed candidate materials, accommodating multi-Weyl semimetals in various solid state compounds.
A
bstract
We consider an analogue of Witten’s SL(2
,
ℤ) action on three-dimensional QFTs with U(1) symmetry for 2
k
-dimensional QFTs with ℤ
2
(
k −
1)-form symmetry. We show that the SL(2
,
ℤ) ...action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2
,
ℤ) anomaly of the bulk (2
k
+ 1)-dimensional ℤ
2
gauge theory.
This open access book presents a comprehensive exploration of diffusion metamaterials that control energy and mass diffusion. Currently, if from the perspective of governing equations, diffusion ...metamaterials and wave metamaterials (pioneered by J. B. Pendry in the 1990s) are recognised as the two most prominent branches in the field of metamaterials. These two branches differ in their emphasis on the diffusion equation (as the governing equation) and time-dependent characteristic lengths in diffusion metamaterials, as opposed to the wave equation (as the governing equation) and time-independent characteristic lengths in wave metamaterials. Organized into three distinct parts – 'Thermal Diffusion Metamaterials', 'Particle Diffusion Metamaterials', and 'Plasma Diffusion Metamaterials' – this book offers a rigorous exploration spanning physics, engineering, and materials science, aimed at advancing our understanding of diffusion processes controlled by diffusion metamaterials. Incorporating foundational theory, computational simulations, and laboratory experiments, the book equips researchers and scholars across these disciplines with comprehensive methods, insights, and results pivotal to the advancement of diffusion control. Beyond facilitating interdisciplinary discourse, the book serves as a catalyst for innovative breakthroughs at the crossroads of physics, thermodynamics, and materials science. Essentially, readers will acquire profound insights that empower them to spearhead advancements in diffusion science (diffusionics) and the engineering of metamaterials.
A
bstract
We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and ...fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators.
A
bstract
In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories ...coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(
N
)
k
Chern-Simons theories coupled to
N
f
real scalars in the fundamental representation, and SO(
k
)
–
N
+
N f
/ 2
theories coupled to
N
f
real (Majorana) fermions in the fundamental. For
N
f
= 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For
k
= 1 we get an interesting low-energy duality between
N
f
free Majorana fermions and an SO(
N
)
1
Chern-Simons theory coupled to
N
f
scalar fields (with
N
f
≤
N
− 2).
A
bstract
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with ...an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.
A
bstract
It was well known that there are
e
-particles and
m
-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ
2
topological order. Recent ...mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ
2
topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.
A
bstract
We classify and characterize fully all invertible anomalies and all allowed topo- logical terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard ...Model (BSM) physics. By all anomalies, we mean the inclusion of (1) perturbative local anomalies captured by perturbative Feynman diagram loop calculations, classified by ℤ free classes, and (2) nonperturbative global anomalies, classified by finite group ℤ
N
torsion classes. Our work built from 31 fuses the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and Freed-Hopkins theorem. For example, we compute bordism groups
Ω
d
G
and their invertible topological field theory invariants, which characterize
d
d topological terms and (
d −
1)d anomalies, protected by the following symmetry group
G
:
Spin
×
SU
3
×
SU
2
×
U
1
ℤ
q
for SM with
q
= 1
,
2
,
3
,
6;
Spin
×
Spin
n
ℤ
2
F
or Spin × Spin(
n
) for SO(10) or SO(18) GUT as
n
= 10
,
18; Spin × SU(
n
) for Georgi-Glashow SU(5) GUT as
n
=
5
;
Spin
×
SU
4
×
SU
2
×
SU
2
ℤ
q
′
ℤ
2
F
for Pati-Salam GUT as
q
′ = 1
,
2; and others. For SM with an extra discrete symmetry, we obtain
new
anomaly matching conditions of ℤ
16
, ℤ
4
and ℤ
2
classes
beyond
the familiar Witten anomaly. Our approach offers an alternative view of all anomaly matching conditions built from the lower-energy (B)SM or GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s. Swampland program, as bottom-up/top-down complements. Symmetries and anomalies provide constraints of kinematics, we further suggest constraints of quantum gauge dynamics, and new predictions of possible extended defects/excitations plus hidden BSM non-perturbative topological sectors.
A
bstract
A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used ...as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.
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