2018
DOI: 10.1103/physrevb.98.205145
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Quench dynamics of quantum spin models with flat bands of excitations

Abstract: We investigate the unitary evolution following a quantum quench in quantum spin models possessing a (nearly) flat band in the linear excitation spectrum. Inspired by the perspective offered by ensembles of individually trapped Rydberg atoms, we focus on the paradigmatic trasverse-field Ising model on two dimensional lattices featuring a flat band as a result of destructive interference effects (Lieb and Kagomé lattice); or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice… Show more

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Cited by 11 publications
(18 citation statements)
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“…We develop a general framework for unravelling excitation spectra and measure them experimentally. It generalizes previous results using power spectrum analysis of density ripples in one-dimensional quasicondensates [33] and spin correlations in two-dimensional models with flat bands [34]. We introduce the quench spectral function (QSF) and show that it yields the quasiparticle dispersion relation, irrespective of the system dimension, particle statistics, range of interactions, and the discrete or continuous nature of the model.…”
supporting
confidence: 71%
“…We develop a general framework for unravelling excitation spectra and measure them experimentally. It generalizes previous results using power spectrum analysis of density ripples in one-dimensional quasicondensates [33] and spin correlations in two-dimensional models with flat bands [34]. We introduce the quench spectral function (QSF) and show that it yields the quasiparticle dispersion relation, irrespective of the system dimension, particle statistics, range of interactions, and the discrete or continuous nature of the model.…”
supporting
confidence: 71%
“…Even more convincing results are obtained for the case of the two-dimensional TFIM, which is not exactly solvable; but whose dynamics can be quantitatively reconstructed via time-dependent variational calculations [28]. In both cases (1d and 2d) we show that the Gaussian Ansatz is able to capture fundamental features of the spatio-temporal structure of the quantum correlations developing after the quench, as observed in their Fourier transform (via a so-called quench spectroscopy scheme [14][15][16]), which allows one to reconstruct the dispersion relation of elementary excitations. The dispersion relation reconstructed via quench spectroscopy is in very good agreement with the best available benchmark results down to the critical field, and it captures in particular the softening of the excitation gap upon approaching the critical field, suggesting that the non-equilibrium dynamics is sensitive to ground-state quantum criticality.…”
Section: Introductionmentioning
confidence: 78%
“…The non-equilibrium unitary dynamics of quantum many-body systems represents a central topic of modern quantum physics: it lies at the core of the coherent manipulation of complex quantum states with quantum devices [1][2][3][4]; and it represents the mechanism by which equilibration and the emergence of statistical ensembles occurs [5][6][7][8][9][10]. In the case of systems with a time-independent Hamiltonian (which will be the focus of this work), central questions concern the propagation of correlations and entanglement, and the scrambling of quantum information [4,11]; how such phenomena manifest the nature of elementary excitations [12][13][14][15][16]; and how they lead to the onset of equilibration [7,8,10]. Answering to the above questions quantitatively for systems of increasing size is a significant challenge, due to the exponential increase of the Hilbert-space dimensions with system size, making an exact numerical treatment impractical for systems going beyond e.g.…”
Section: Introductionmentioning
confidence: 99%
“…The time-evolution of correlation functions displays a causal-cone-like structure in which the behavior close to the edges yields information about the characteristic propagation speeds of information in the system [17,19]. Spectral properties of collective excitations can also be extracted from the dynamics of correlation functions [24][25][26][27].…”
Section: Introductionmentioning
confidence: 99%