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arXiv:1806.09722 · Physical review. B./Physical review. B

Quench dynamics of quantum spin models with flat bands of excitations

Raphaël Menu, Tommaso Roscilde

Published Nov 26, 2018• 18 citations
arXivHTMLPDF

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 kagom\'e lattice), or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice). Making use of linear spin-wave theory, we show that quantum quenches, equipped with single-spin imaging, can directly reveal the spatially localized nature of the dispersionless excitations, and their slow propagation or lack of propagation altogether. Moreover, we show that Fourier analysis applied to the postquench time evolution of wave-vector-dependent quantities allows for the spectroscopic reconstruction of the flat bands. Our results pave the way for future experiments with Rydberg quantum simulators, which can extend our linear spin-wave study to the fully nonlinear regime, characterized by the appearance of dense, strongly interacting gases of dispersionless excitations.

DOI
10.1103/physrevb.98.205145

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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 kagom'e lattice), or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice). Making use of linear spin-wave theory, we show that quantum quenches, equipped with single-spin imaging, can directly reveal the spatially localized nature of the dispersionless excitations, and their slow propagation or lack of propagation altogether. Moreover, we show that Fourier analysis applied to the postquench time evolution of wave-vector-dependent quantities allows for the spectroscopic reconstruction of the flat bands. Our results pave the way for future experiments with Rydberg quantum simulators, which can extend our linear spin-wave study to the fully nonlinear regime, characterized by the appearance of dense, strongly interacting gases of dispersionless excitations.
Quantum geometry underlies a wide range of correlated phenomena in electronic systems, yet accessing the geometry of individual bands remains experimentally challenging. Advances in quantum simulators, such as ultracold atoms in optical lattices, have enabled local state preparation and site-resolved measurements, offering direct access to quantum dynamics beyond conventional transport probes. These developments naturally raise the question of whether band-resolved quantum geometry can be extracted from local occupation readouts. Here, we propose an on-site quench protocol to probe the flat-band quantum geometry via local occupation measurements in an atomic lattice. Our scheme dynamically isolates the flat-band sector by coupling a one-dimensional flat-band lattice to a two-dimensional flat-band bath. The bath selectively removes dispersive excitations, while compact localized states remain trapped due to their overlap with the flat-band modes of the bath. We show that the late-time occupation pattern directly encodes the integrated overlaps between flat-band states separated by the wavevector of the initial density pattern, thereby enabling access to integrated quantum distances between the states separated by the commensurate momenta δk=2πs/rδk = 2 πs/rδk=2πs/r, s,r∈Zs,r \in \mathbb Zs,r∈Z and to the integrated flat-band quantum metric. Our results thereby establish a direct connection between quantum geometry and the long-time memory of an initial spatial pattern in flat-band systems.
The nature and spectrum of elementary excitations are defining features of a many-body system. In this study, we used a Rydberg quantum simulator to demonstrate a form of spectroscopy, called quench spectroscopy, that probes these low-energy excitations. We illustrated the method on a two-dimensional simulation of the spin-1/2 dipolar XY model. Through microscopic measurements of the spatial spin correlation dynamics following a quench, we extracted the dispersion relation of the elementary excitations for both ferro- and antiferromagnetic couplings. The ferromagnet exhibits elementary excitations behaving as linear spin waves, whereas in the antiferromagnet, spin waves appear to decay, suggesting the presence of strong nonlinearities. Our demonstration highlights the importance of power-law interactions on the excitation spectrum of a many-body system.
We present the spin-wave theory of the excitation spectrum and quench dynamics of the non-Hermitian transverse-field Ising model. The complex excitation spectrum is obtained for a generic hypercubic lattice using the linear approximation of the Holstein-Primakoff transformation together with the complex bosonic Bogolyubov transformation. In the one-dimensional case, our result compares very well with the exact quasiparticle dispersion relation obtained via a fermionic representation of the problem, at least in the regime of large dissipation and transverse field. When applied to the quench dynamics, however, we show that the linear spin-wave approximation breaks down and the bosonic theory is plagued by a divergence at finite times. We understand the origin of this instability using a single-mode approximation. While limited to short times, we show that this approach allows us to characterize the dynamics arising from the quench of the dissipative term and the light-cone structure of the propagation quantum correlations. Furthermore, for the one-dimensional case, the linear spin-wave dynamics shows good agreement with the exact fermionic solution, both for the local magnetization and the spin-spin correlations.
Understanding the nonequilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time postquench quantum dynamics. In classical many-body systems, the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first-order phase transition. Here, we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum nonequilibrium effects. We are able to gain an analytical understanding of the time evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a nonequilibrium phase transition and provides an approximate analytical solution deep in the quantum domain.
Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.
Flat bands in condensed matter systems can host emergent states of matter, from insulating states in twisted bilayer graphene to fractionalized excitations in frustrated magnets and quantum Hall materials. A key phenomenon in certain flat-band systems is Aharonov-Bohm caging, where particles become localized due to destructive interference caused by gauge fields. Here we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. By employing synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries and explore the control of Aharonov-Bohm caging during non-equilibrium dynamics through a tunable gauge field. Microscopic measurements of Rydberg pairs reveal the interaction-driven breakdown of Aharonov-Bohm caging in the limit of strong dipolar interactions, where lattice bands mix. In the limit of weak interactions, where caging persists, we observe effective magnetism arising from the interaction-driven mixing of degenerate flat-band states. These observations offer insights into emergent phenomena in synthetic quantum materials and expand our understanding of quantum many-body physics in engineered lattice systems.