Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuasi-adiabatic dynamics and state preparation in Floquet many-body systems
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Periodic driving has emerged as a powerful experimental tool to engineer physical properties of isolated, synthetic quantum systems. However, due to the lack of energy conservation and heating effects, non-trivial (e.g., topological) many-body states in periodically driven (Floquet) systems are generally metastable. Therefore it is necessary to find strategies for preparing long-lived many-body states in Floquet systems. We develop a theoretical framework for describing the dynamical preparation of states in Floquet systems by a slow turn-on of the drive. We find that the dynamics of the system is well approximated by the initial state evolving under a slowly varying effective Hamiltonian $H_{rm eff}^{(s)}(t)$, provided the ramp speed $s gg t_*^{-1} sim e^{-{mathcal{C} frac{omega}{J}}}$, the inverse of the characteristic heating time-scale in the Floquet system. At such ramp speeds, the heating effects due to the drive are exponentially suppressed. We compute the slowly varying effective Hamiltonian $H_{rm eff}^{(s)}(t)$, and show that at the end of the ramp it is identical to the effective Hamiltonian of the unramped Floquet system, up to small corrections of the order $O(s)$. Therefore, the system effectively undergoes a slow quench from $H_0$ to $H_{rm eff}$. As an application, we consider the passage of the slow quench through a quantum critical point (QCP), and estimate the energy absorbed due to the non-adiabatic passage through the QCP via a Kibble-Zurek mechanism. By minimizing the energy absorbed due to both the drive and the ramp, we find an optimal ramp speed $s_* sim t_*^{-z/({d+2z})}$ for which both heating effects are exponentially suppressed. Our results bridge the gap between the numerous proposals to obtain interesting systems via Floquet engineering, and the actual preparation of such systems in their effective ground states.
rate research
Read More
We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the transitions appear in the context of many-body localization. Using the combination of the mapping onto $l$-bits and exact diagonalization results, we explicitly demonstrate the presence of these singularities for a candidate model that features many-body localization. Our work paves the way for understanding dynamical quantum phase transitions in the context of many-body localization, and elucidating whether different phases of the latter can be detected from analyzing the former. The results presented are experimentally accessible with state-of-the-art ultracold-atom and ion-trap setups.
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. Perhaps the most successful and ubiquitous of these approaches is density functional theory (DFT). Its Kohn-Sham formulation has been the basis for many fundamental physical insights, and it has been successfully applied to fields as diverse as quantum chemistry, condensed matter and dense plasmas. Despite the progress made by DFT and related schemes, however, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. Based on the Bohmian trajectories formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without employing the adiabatic Born-Oppenheimer approximation.
The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g. typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, the Thouless energy tends to a value independent of system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of the Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting, and yields new insights into the MBL transition in Floquet systems.
It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in the context of a one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the phenomenology of many-body localization. However, at longer times, all finite wavelength spin polarizations decay in a finite time, independent of system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this long pre-thermal dynamical behavior, intermediate between full localization and diffusion, quasi-many body localization.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
