Space-group symmetry operations are given a geometric description and a short-hand matrix notation in International Tables for Crystallography, Volume A, Space-Group Symmetry. We give here the space-group symmetry operations subtables with the corresponding Seitz (R∣t) notation for each included symmetry operation.
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http://dx.doi.org/10.1107/S010876731101378X | DOI Listing |
Phys Rev Lett
December 2024
RIKEN, Condensed Matter Theory Laboratory, CPR, Wako, Saitama 351-0198, Japan.
We show that the ground-state expectation value of twisting operator is a topological order parameter for U(1)- and Z_{N}-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems-it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (nonlocal) order parameter must take values in Nth roots of unity, and its value can be changed by a generalized lattice translation acting as an N-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis (LSM) ingappability for SU(N) spins if we further impose a general translation symmetry.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
Ens de Lyon, Université Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
We introduce a new paradigm for the preparation of deeply entangled states useful for quantum metrology. We show that, when the quantum state is an eigenstate of an operator A, observables G which are completely off diagonal with respect to A have purely quantum fluctuations, as quantified by the quantum Fisher information, namely, F_{Q}(G)=4⟨G^{2}⟩. This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation.
View Article and Find Full Text PDFPlast Reconstr Surg Glob Open
January 2025
From the Department of Plastic and Burn Surgery, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China.
Idiopathic upper eyelid retraction is a rare ocular symptom characterized by abnormal upward displacement of the upper eyelid, often without any identifiable systemic disease. This condition not only affects the patient's appearance but may also have a certain impact on their daily life and mental health. We report a case of adult idiopathic unilateral upper eyelid retraction, and based on the patient's specific condition, we used graded anterior plate blepharoplasty for treatment.
View Article and Find Full Text PDFWe report on the growth of a 2.86 at.% Ho:YGG crystal using the optical floating zone technique in an oxygen-rich environment, followed by the study of its structure, optical spectroscopy and first demonstration of continuous-wave laser operation at 2.
View Article and Find Full Text PDFSubwavelength light trapping in periodic structures with high quality (Q) factors is discovered to hold strong light-matter interactions for a variety of applications. Although dual-band or even multiple-band high-Q resonances are applicable to extend the operation range of a nanophotonic device, manipulating the high-Q modes individually is a necessity to implement plural intriguing applications in one system as well as optimize the capabilities across each spectrum. In this work, a novel approach is presented to independently control dual high-Q modes with distinct origins in an all-dielectric metasurface system.
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