Geometry of variational methods: dynamics of closed quantum systems
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Geometry of variational methods : dynamics of closed quantum systems. / Hackl, Lucas; Guaita, Tommaso; Shi, Tao; Haegeman, Jutho; Demler, Eugene; Cirac, J. Ignacio.
I: SciPost Physics, Bind 9, 048, 2020.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Geometry of variational methods
T2 - dynamics of closed quantum systems
AU - Hackl, Lucas
AU - Guaita, Tommaso
AU - Shi, Tao
AU - Haegeman, Jutho
AU - Demler, Eugene
AU - Cirac, J. Ignacio
N1 - 47+8 pages, 8 figures
PY - 2020
Y1 - 2020
N2 - 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: K\"ahler and non-K\"ahler. Traditional variational methods typically require the variational family to be a K\"ahler 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-K\"ahler 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.
AB - 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: K\"ahler and non-K\"ahler. Traditional variational methods typically require the variational family to be a K\"ahler 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-K\"ahler 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.
KW - quant-ph
KW - cond-mat.quant-gas
KW - cond-mat.str-el
KW - cond-mat.supr-con
U2 - 10.21468/SciPostPhys.9.4.048
DO - 10.21468/SciPostPhys.9.4.048
M3 - Journal article
VL - 9
JO - SciPost Physics
JF - SciPost Physics
SN - 2542-4653
M1 - 048
ER -
ID: 239257455