1,721,561 research outputs found
Andr\'e-Quillen cohomology of algebras over an operad
Get PDFWe study the Andr\'e-Quillen cohomology with coefficients of an algebra over
an operad. Using resolutions of algebras coming from Koszul duality theory, we
make this cohomology theory explicit and we give a Lie theoretic
interpretation. For which operads is the associated Andr\'e-Quillen cohomology
equal to an Ext-functor ? We give several criterion, based on the cotangent
complex, to characterize this property. We apply it to homotopy algebras, which
gives a new homotopy stable property for algebras over cofibrant operads.Comment: This version contains a previously missing PBW condition for K\"ahler
differential forms. Theorems 5.6.1 and 5.6.4 and the related examples have
been modified accordingl
Intermediate super-exponential localization with Aubry-Andr\'e chains
Get PDFWe demonstrate the existence of an intermediate super-exponential
localization regime for eigenstates of the Aubry-Andr\'e chain. In this regime,
the eigenstates localize factorially similarly to the eigenstates of the
Wannier-Stark ladder. The super-exponential decay emerges on intermediate
length scales for large values of the -- the
quasi-period of the Aubry-Andr\'e potential. This intermediate localization is
present both in the metallic and insulating phases of the system. In the
insulating phase, the super-exponential localization is periodically
interrupted by weaker decaying tails to form the conventional asymptotic
exponential decay predicted for the Aubry-Andr\'e model. In the metallic phase,
the super-exponential localization happens for states with energies away from
the center of the spectrum and is followed by a super-exponential growth into
the next peak of the extended eigenstate. By adjusting the parameters it is
possible to arbitrarily extend the validity of the super-exponential
localization. A similar intermediate super-exponential localization regime is
demonstrated in quasiperiodic discrete-time unitary maps.Comment: 9 pages, 9 figures. Comments are welcom
Cohomology and Andr\'e motives of hyperk\"ahler orbifolds
Get PDFOne of the main tools for the study of compact hyperk\"ahler manifolds is the
natural action of the Looijenga-Lunts-Verbitsky Lie algebra on the cohomology
of such manifolds. This also applies to the mildly singular holomorphic
symplectic varieties - hyperk\"ahler orbifolds, allowing us to prove that
Andr\'e motives of such orbifolds tend to be abelian
Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-Andr\'e Model
Get PDFWe study the ground state phases of interacting bosons in the presence of a
2D Aubry-Andr\'e potential. By using a a mean-field percolation analysis, we
focus on several superlattice and quasicrystalline regimes of the 2D
Aubry-Andr\'e model, including generalisations that account for a tilting or
skewing of the potential. We show that barriers to the onset of macroscopic
phases naturally arise from weakly modulated domains in the 2D Aubry-Andr\'e
model. This leads to the formation of mixed phases, in which the macroscopic
properties are dominated by a minority of the system. The phase diagrams then
exhibit substantially different features when compared against crystalline
systems, including a lobe-like or wave-like appearance of the Bose glass, sharp
extrusions and extended domains with weak percolation. By studying the 2D
Aubry-Andr\'e model across multiple regimes, we have shown that the unique
properties of mixed phases are not distinct to a small set of parameters.Comment: 22 pages, 16 figures, comments welcom
Generalised Andr\'e-Pink-Zannier Conjecture for Shimura varieties of abelian type
Get PDFIn this paper, we prove the generalised Andr\'e-Pink-Zannier conjecture (an
important case of the Zilber-Pink conjecture) for all Shimura varieties of
abelian type. Questions of this type were first asked by Y. Andr\'e in 1989. We
actually prove a general statement for all Shimura varieties, subject to
certain assumptions that are satisfied for Shimura varieties of abelian type
and are expected to hold in general. We also prove another result, a p-adic
Kempf-Ness theorem, on the relation between good reduction of homogeneous
spaces over p-adic integers with Mumford stability property in p-adic geometric
invariant theory
A Model for the Andr\'{e}-Quillen Cohomology of an -Category
Get PDFWe describe a comonad on -track categories, for each yielding an
explicit cosimplicial abelian group model for the Andr\'{e}-Quillen cohomology
of an -category.Comment: updated introductio
Localization spectrum of a bath-coupled generalized Aubry-Andr\'e model in the presence of interactions
Get PDFA generalization of the Aubry-Andr\'e model, the non-interacting GPD model
introduced in S. Ganeshan et al.,[ Phys. Rev. Lett. 114, 146601 (2015)], is
known analytically to possess a mobility edge, allowing both extended and
localized eigenstates to coexist. This mobility edge has been hypothesized to
survive in closed many-body interacting systems, giving rise to a new
non-ergodic metallic phase. In this work, coupling the interacting GPD model to
a thermal bath, we provide direct numerical evidence for multiple qualitative
behaviors in the parameter space of disorder strength and energy level. In
particular, we look at the bath-induced saturation of entanglement entropy to
classify three behaviors: thermalized, non-ergodic extended, and localized. We
also extract the localization length in the localized phase using the long-time
dynamics of the entanglement entropy and the spin imbalance. Our work
demonstrates the rich localization landscape of generalized Aubry-Andr\'e
models containing mobility edges in contrast to the simple Aubry-Andr\'e model
with no mobility edge.Comment: 9 pages + 6 figure
Multiple intermediate phases in the interpolating Aubry-Andr\'{e}-Fibonacci model
Get PDFWe investigate a generalized interpolating Aubry-Andr\'{e}-Fibonacci (IAAF)
model with p-wave superconducting pairing. In the Aubry-Andr\'{e} limit, we
demonstrate that the system experiences transitions from a pure phase, either
extended or critical, to a variety of intermediate phases and ultimately enters
a localized phase with increasing potential strength. These intermediate phases
include those with coexisting extended and localized states, extended and
critical states, localized and critical states and a mix of extended, critical
and localized states. Each intermediate phase exhibits at least one type of
mobility edge separating different states. As the system approaches the
Fibonacci limit, both the extended and localized phases diminish, and the
system tends towards a critical phase.Comment: 11 pages, 12 figure
Exact mobility edges in Aubry-Andr\'{e}-Harper models with relative phases
Get PDFMobility edge (ME), a critical energy separating localized and extended
states in spectrum, is a central concept in understanding the localization
physics. However, there are few models with exact MEs. In the paper, we
generalize the Aubry-Andr\'{e}-Harper model proposed in [Phys. Rev. Lett. 114,
146601 (2015)] and recently realized in [Phys. Rev. Lett. 126, 040603 (2021)],
by introducing a relative phase in the quasiperiodic potential. Applying
Avila's global theory we analytically compute localization lengths of all
single-particle states and determine the exact expression of ME, which both
significantly depend on the relative phase. They are verified by numerical
simulations, and a physical perception of the exact expression is also
provided. We further demonstrate that the exact expression of ME works for an
even broad class of generalized Aubry-Andr\'{e}-Harper models. Moreover, we
show that the exact ME is related to the one in the dual model which has
long-range hoppings.Comment: 6 pages, 3 figure
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