Liu 
<i>et al.</i>
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Howie, Ross T.; Zhang, Huichao; Chen, Xiao‐Jia; Gregoryanz, Eugene

doi:10.1103/physrevlett.122.199602

Cited by 87 publications

(140 citation statements)

References 4 publications

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“…The definition of the wavefunction is the only user input needed, represented by the definition of the singles [eq. (27)] and doubles [eq. (28)] excitation classes and their respective contravariants,…”

Section: Implementation Details Equation Generationmentioning

confidence: 99%

“…[24] Another important contribution to the field of multireference correlation theory is the implementation of the ic-MRCC approach by Hanauer and K€ ohn, using the GeCCo tool. [25][26][27] Regardless of how the equations were obtained and factorized, the efficient implementation of algebraic expressions is a key task in obtaining a successful theoretical method. To fully utilize the power of modern computers, it is necessary to use matrix operations, available in optimized libraries for Basic Linear Algebra Subprograms (BLAS), [28] which are kept up to date with recent hardware development, [29] thereby making optimal use of the ever changing computational resources.…”

Section: Introductionmentioning

confidence: 99%

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A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

et al. 2017

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In this work, the automated generator environment for ORCA (ORCA-AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction-based quantum chemical methods. ORCA-AGE consists of three main modules: (1) generation of "raw" equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction-based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin-independent as well as spin-dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand-optimized code for some well-understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand-optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500-1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code. © 2017 Wiley Periodicals, Inc.

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Section: Implementation Details Equation Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

et al. 2017

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“…Concerning this matter, the findings will thus have the capability to push forward exciting applications for robust acoustic imaging way beyond the diffraction limit.The discovery of topological insulators (TIs) [1,2] and the strikingly robust transmission of reflectionless edge states have boosted intense research in classical systems such as photonics, [3][4][5][6][7][8][9] acoustics, [10][11][12][13][14][15][16][17][18][19][20][21][22] and mechanics. [23][24][25][26] Most recently, the concept of higher-order TIs (HOTIs), [27][28][29][30][31][32][33] which is a special class of TIs with unconventional bulk-boundary correspondence, was proposed to support the existence of the lower-dimensional boundary states. For example, in d-dimensional (dD) systems, a second-order TI (SOTI) has dD gapped bulk states, (d − 1)D gapped boundary states, and (d − 2)D gapless boundary states, which are 0D corner states…”

mentioning

confidence: 99%

“…We demonstrate that the band inversion signifies a topological phase transition, which can be characterized by a 2D Zak phase. [49,50] The Zak phase P can be calculated by the parities at high symmetric points through [33,43,50,51]…”

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confidence: 99%

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

et al. 2019

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in 2D system. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. [41][42][43][44][45][46] In order to make HOTIs more attractive for real-world applications as in sound wave control, several hurdles must be overcome. For example, most of the reported results focus solely on a single frequency band, whose limitations ought to be overcome in order to provide a broadband response for topologically robust acoustics. Also, the above reported acoustic implementations have, for the most part, been implemented inside waveguides or were designed in an acoustically rigid enclosure, which hinders their capabilities from external insonification. Lastly, in terms of compactness, it is desired to utilize building blocks of the HOTI on a subwavelength scale in order to confine sound in tight areas beyond the diffraction limit.In this work, we design topologically protected acoustic corner states at deep subwavelength scales by constructing a perforated crystal, also known as holey metamaterials. The advantage in using holey metamaterials resides in their high levels of integration and miniaturization at scales much smaller than the sound wavelength. Without being pierced by holes, those metamaterials would not be able to sustain surface-confined wave propagation. With perforations on the other hand, externally incident radiation is able to bind to the structure in the form of "spoof" surface acoustic waves (SAWs), thus enabling sound energy confinement way beyond the classical diffraction limit. [47,48] In addition to breaking the diffraction limit for spoof SAWs, we demonstrate that a topological phase transition, which is derived from an extended 2D Zak phase, can be tuned by simply shrinking or expanding the distance among a group of holes within the unit cell. Beyond measuring corner states within multiple nontrivial bandgaps, the first-order resonance in particular displays the strongest topological sound energy confinement down to a feature size of λ/50. Lastly, we experimentally verify their resilience against defects and design a HOTI device for topological subwavelength imaging, which may be relevant for sound energy focusing and detection. Figure 1a illustrates the schematic of deep-subwavelength acoustic SOTI under consideration, which is realized by a perforated rigid material whose holes are arranged in a square lattice. The perforation depth and the radii of holes are H = 12 cm and r = 0.5 cm, respectively. The lattice constant is a = 4.8 cm.The center-to-center distance between the adjacent holes in the unit cell is defined as R, which is chosen to be R/a = 0.5 for the Higher-order topological insulators (HOTIs) belong to a new class of materials with unusual topological phases. They have garnered considerable attention due to their capabilities in confining energy at the hinges and corners, which is entirely protected by the topology, and have thus become attractive structures for...

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“…The N = 32 gap determined in calcium (Z = 20) [3,4] has been found to persist in argon (Z = 18) [5], potassium (Z = 19) [6], scandium (Z = 21) [7], titanium (Z = 22) [8][9][10] and chromium (Z = 24) [11,12]. On the other hand, the N = 34 sub-shell closure has been suggested in 54 Ca [13][14][15] and in 52 Ar [16]. However, it has not been detected in the Sc [17], Ti [9,10,18] and the Cr [11,12] isotopes.…”

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confidence: 99%

On the robustness of sub-shell closures: A high angular momentum analysis of the titanium isotopes

Rodrı́guez

Egido

2020

Physics Letters B

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The potential sub-shell closures N = 32 and N = 34 are analyzed at high spins in the titanium isotopes within the generalized beyond mean field theory considering triaxial deformations and the angular frequency as generator coordinates together with the particle number and the angular momentum conservation. A good description of bulk properties, high angular momenta spectra and transition probabilities is obtained. The outcome at high spin in these nuclei is consistent with the magic number character of N = 32 but not of N = 34.

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Liu et al. Reply:

Cited by 87 publications

References 4 publications

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

On the robustness of sub-shell closures: A high angular momentum analysis of the titanium isotopes

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