scholarly journals Berry Curvature and Riemann Curvature in Kinematic Space with Spherical Entangling Surface

2020 ◽  
pp. 2000048
Author(s):  
Xing Huang ◽  
Chen‐Te Ma
Keyword(s):  
Riemann Curvature ◽  
Berry Curvature ◽  
Kinematic Space

scholarly journals Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Fei Wang ◽  
Xuepeng Wang ◽  
Yi-Fan Zhao ◽  
Di Xiao ◽  
Ling-Jie Zhou ◽  
...  
Keyword(s):  
Hall Effect ◽  
Electric Fields ◽  
First Principles ◽  
Berry Phase ◽  
Condensed Matter ◽  
Anomalous Hall Effect ◽  
First Principles Calculations ◽  
Sign Reversal ◽  
Berry Curvature ◽  
Topological Materials

AbstractThe Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

scholarly journals 2D‐Berry‐Curvature‐Driven Large Anomalous Hall Effect in Layered Topological Nodal‐Line MnAlGe

2021 ◽  
pp. 2006301
Author(s):  
Satya N. Guin ◽  
Qiunan Xu ◽  
Nitesh Kumar ◽  
Hsiang‐Hsi Kung ◽  
Sydney Dufresne ◽  
...  
Keyword(s):  
Hall Effect ◽  
Anomalous Hall Effect ◽  
Nodal Line ◽  
Berry Curvature ◽  
Curvature Driven

scholarly journals Does SUSY have friends? A new approach for LHC event analysis

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Anna Mullin ◽  
Stuart Nicholls ◽  
Holly Pacey ◽  
Michael Parker ◽  
Martin White ◽  
...  
Keyword(s):  
Hadron Collider ◽  
Local Network ◽  
Proton Collision ◽  
Event Analysis ◽  
Final State ◽  
Proton Proton ◽  
Kinematic Space ◽  
Boosted Decision Tree ◽  
The Individual ◽  
Particle Search

Abstract We present a novel technique for the analysis of proton-proton collision events from the ATLAS and CMS experiments at the Large Hadron Collider. For a given final state and choice of kinematic variables, we build a graph network in which the individual events appear as weighted nodes, with edges between events defined by their distance in kinematic space. We then show that it is possible to calculate local metrics of the network that serve as event-by-event variables for separating signal and background processes, and we evaluate these for a number of different networks that are derived from different distance metrics. Using a supersymmetric electroweakino and stop production as examples, we construct prototype analyses that take account of the fact that the number of simulated Monte Carlo events used in an LHC analysis may differ from the number of events expected in the LHC dataset, allowing an accurate background estimate for a particle search at the LHC to be derived. For the electroweakino example, we show that the use of network variables outperforms both cut-and-count analyses that use the original variables and a boosted decision tree trained on the original variables. The stop example, deliberately chosen to be difficult to exclude due its kinematic similarity with the top background, demonstrates that network variables are not automatically sensitive to BSM physics. Nevertheless, we identify local network metrics that show promise if their robustness under certain assumptions of node-weighted networks can be confirmed.

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

scholarly journals Spacetime as a quantum circuit

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. Ramesh Chandra ◽  
Jan de Boer ◽  
Mario Flory ◽  
Michal P. Heller ◽  
Sergio Hörtner ◽  
...  
Keyword(s):  
Path Integral ◽  
Constant Scalar Curvature ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Special Role ◽  
Gravitational Action ◽  
Volume Conjecture ◽  
Interesting Connection ◽  
Kinematic Space ◽  
Boundary States

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

Orbital angular momentum-driven anomalous Hall effect

2021 ◽  
Author(s):  
Oliver Dowinton ◽  
Mohammad Bahramy
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Transition Metal Oxides ◽  
Magnetic State ◽  
Magnetic Moments ◽  
Anomalous Hall Effect ◽  
Ferromagnetic State ◽  
Periodic Systems ◽  
Spin States ◽  
Berry Curvature

Abstract Orbital angular momentum (OAM) plays a central role in regulating the magnetic state of electrons in non-periodic systems such as atoms and molecules. In solids, on the other hand, OAM is usually quenched by the crystal field, and thus, has a negligible effect on magnetisation. Accordingly, it is generally neglected in discussions around band topology such as Berry curvature (BC) and intrinsic anomalous Hall conductivity (AHC). Here, we present a theoretical framework demonstrating that crystalline OAM can be directionally unquenched in transition metal oxides via energetic proximity of the conducting d electrons to the local magnetic moments. We show that this leads to `composite' Fermi-pockets with topologically non-trivial OAM textures. This enables a giant Berry curvature with an intrinsic non-monotonic AHC, even in collinearly-ordered spin states. We use this model to explain the origin of the giant AHC observed in the forced-ferromagnetic state of EuTiO3 and propose it as a prototype for OAM driven AHC.

scholarly journals Experimental Observation of Hidden Berry Curvature in Inversion-Symmetric Bulk 2H−WSe2

2018 ◽  
Vol 121 (18) ◽  
Author(s):  
Soohyun Cho ◽  
Jin-Hong Park ◽  
Jisook Hong ◽  
Jongkeun Jung ◽  
Beom Seo Kim ◽  
...  
Keyword(s):  
Experimental Observation ◽  
Berry Curvature

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

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