Lucas Hackl, Tommaso Guaita, Tao Shi, Jutho Haegeman, Eugene Demler, J. Ignacio Cirac
SciPost Phys. 9, 048 (2020) ·
published 8 October 2020
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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.
SciPost Phys. 5, 057 (2018) ·
published 5 December 2018
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Surprising properties of doped Mott insulators are at the heart of many
quantum materials, including transition metal oxides and organic materials. The
key to unraveling complex phenomena observed in these systems lies in
understanding the interplay of spin and charge degrees of freedom. One of the
most debated questions concerns the nature of charge carriers in a background
of fluctuating spins. To shed new light on this problem, we suggest a
simplified model with mixed dimensionality, where holes move through a Mott
insulator unidirectionally while spin exchange interactions are two
dimensional. By studying individual holes in this system, we find direct
evidence for the formation of mesonic bound states of holons and spinons,
connected by a string of displaced spins -- a precursor of the spin-charge
separation obtained in the 1D limit of the model. Our predictions can be tested
using ultracold atoms in a quantum gas microscope, allowing to directly image
spinons and holons, and reveal the short-range hidden string order which we
predict in this model.
