Knowledge Management System of Institute of Theoretical Physics, CAS
Hackl, Lucas; Guaita, Tommaso; Shi, Tao3,4 ; Haegeman, Jutho5; Demler, Eugene6; Cirac, J. Ignacio
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| Geometry of variational methods: dynamics of closed quantum systems | |
| Source Publication | SCIPOST PHYSICS
 |
| Language | 英语 |
| Keyword | STATES OPTIMIZATION ALGORITHMS MECHANICS COHERENT VORTEX |
| Abstract | We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kahler and non-Kahler. Traditional variational methods typically require the variational family to be a Kahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states. |
| 2020 | |
| ISSN | 2542-4653 |
| Volume | 9Issue:4Pages:48 |
| Cooperation Status | 国际 |
| Subject Area | Physics |
| MOST Discipline Catalogue | Physics, Multidisciplinary |
| DOI | 10.21468/SciPostPhys.9.4.048 |
| Indexed By | SCIE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.itp.ac.cn/handle/311006/27332 |
| Collection | SCI期刊论文 |
| Affiliation | 1.Univ Copenhagen, Dept Math Sci, QMATH, Univ Pk 5, DK-2100 Copenhagen, Denmark 2.Max Planck Inst Quantum Opt, Hans Kopfermann Str 1, D-85748 Garching, Germany 3.Munich Ctr Quantum Sci & Technol, Schellingstr 4, D-80799 Munich, Germany 4.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, CAS Ctr Excellence Topol Quantum Computat, Beijing 100049, Peoples R China 6.Univ Ghent, Dept Phys & Astron, Krijgslaan 281, B-9000 Ghent, Belgium 7.Harvard Univ, Dept Phys, Lyman Lab, 17 Oxford St, Cambridge, MA 02138 USA |
| Recommended Citation GB/T 7714 | Hackl, Lucas,Guaita, Tommaso,Shi, Tao,et al. Geometry of variational methods: dynamics of closed quantum systems[J]. SCIPOST PHYSICS,2020,9(4):48. |
| APA | Hackl, Lucas,Guaita, Tommaso,Shi, Tao,Haegeman, Jutho,Demler, Eugene,&Cirac, J. Ignacio.(2020).Geometry of variational methods: dynamics of closed quantum systems.SCIPOST PHYSICS,9(4),48. |
| MLA | Hackl, Lucas,et al."Geometry of variational methods: dynamics of closed quantum systems".SCIPOST PHYSICS 9.4(2020):48. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| Geometry of variatio（855KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | Application Full Text | |
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