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Register a new userFibonacci steady states in a driven integrable quantum system
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We study an integrable system that is reducible to free fermions by a Jordan-Wigner transformation which is subjected to a Fibonacci driving protocol based on two non-commuting Hamiltonians. In the high frequency limit $omega to infty$, we show that the system reaches a non-equilibrium steady state, up to some small fluctuations which can be quantified. For each momentum $k$, the trajectory of the stroboscopically observed state lies between two concentric circles on the Bloch sphere; the circles represent the boundaries of the small fluctuations. The residual energy is found to oscillate in a quasiperiodic way between two values which correspond to the two Hamiltonians that define the Fibonacci protocol. These results can be understood in terms of an effective Hamiltonian which simulates the dynamics of the system in the high frequency limit.
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Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we consider a prototypical integrable spin system, the spin-$1/2$ transverse field Ising model in one dimension, in a pulsed magnetic field. The time dependence of the field is taken to be quasiperiodic by choosing the pulses to be of two types that alternate according to a Fibonacci sequence. We show that a novel steady state emerges after an exponentially long time when local properties (or equivalently, reduced density matrices of subsystems with size much smaller than the full system) are considered. We use the temporal evolution of certain coarse-grained quantities in momentum space to understand this nonequilibrium steady state in more detail and show that unlike the previously known cases, this steady state is neither described by a periodic generalized Gibbs ensemble nor by an infinite temperature ensemble. Finally, we study a toy problem with a single two-level system driven by a Fibonacci sequence; this problem shows how sensitive the nature of the final steady state is to the different parameters.
We study periodically driven bosonic scalar field theories in the infinite N limit. It is well-known that the free theory can undergo parametric resonance under monochromatic modulation of the mass term and thereby absorb energy indefinitely. Interactions in the infinite N limit terminate this increase for any choice of the UV cutoff and driving frequency. The steady state has non-trivial correlations and is synchronized with the drive. The O(N) model at infinite N provides the first example of a clean interacting quantum system that does not heat to infinite temperature at any drive frequency.
Laser technology has developed and accelerated photo-induced nonequilibrium physics from both scientific and engineering viewpoints. The Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is a forefront of quantum physics of light-matter interaction, but limited to ideal dissipationless systems. For the Floquet engineering extended to a variety of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (NESS) in periodically driven dissipative systems by focusing on the systems under high-frequency drive and time-independent Lindblad-type dissipation with the detailed balance condition. Our formula correctly describes the time-average, fluctuation, and symmetry property of the NESS, and can be computed efficiently in numerical calculations. Our approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems such as atoms and molecules, mesoscopic systems, and condensed matter.
Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as geometric generalized Gibbs ensemble, that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.
We study the survival of the current induced initially by applying a twist at the boundary of a chain of hard-core bosons (HCBs), subject to a periodic double $delta$-function kicks in the staggered on-site potential. We study the current flow and the work-done on the system at the long-time limit as a function of the driving frequency. Like a recent observation in the HCB chain with single $delta$-function kick in the staggered on-site potential, here we also observe many dips in the current flow and concurrently many peaks in the work-done on the system at some specific values of the driving frequency. However, unlike the single kicked case, here we do not observe a complete disappearance of the current in the limit of a high driving frequency, which shows the absence of any dynamical localization in the double $delta$-functions kicked HCB chain. Our analytical estimations of the saturated current and the saturated work-done, defined at the limit of a large time together with a high driving frequency, match very well with the exact numerics. In the case of the very small initial current, induced by a very small twist $ u$, we observe that the saturated current is proportional to $ u$. Finally, we study the time-evolution of the half-filled HCB chain where the particles are localized in the central part of the chain. We observe that the particles spread linearly in a light-cone like region at the rate determined by the maximum value of the group velocity. Except for a very trivial case, the maximum group velocity never vanishes, and therefore we do not observe any dynamical localization in the system.
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