We investigate analytically and numerically a one-dimensional periodically driven free-fermionic system subjected to monitoring of the local particle density. Based on the analytical approach that describes the long-wavelength physics of the time-dependent Hamiltonian in the field-theoretical language using the nonlinear sigma-model (NLSM), we reveal that driving does not alter the universality class of the problem. As a consequence, the system retains the area-law behavior in the thermodynamic limit, with an intermediate diffusive regime giving rise to logarithmic growth of entanglement entropy for a small monitoring rate. At the same time, driving leads to a renormalization of the bare coupling constant of the NLSM, which controls the space-time ``conductivity''in the diffusive regime. We derive the analytic form of this renormalization, which becomes particularly strong in the case of a ``maximally symmetric''drive and sufficiently short driving period. In addition, we employ the Wiener-Hopf method to investigate the ballistic-diffusive crossover. These analytical predictions are corroborated by numerical simulations of the von-Neumann entanglement entropy and the density correlation function. Our numerical results clearly demonstrate that, with an increase in the system size, there are successive crossovers from ballistic to diffusive behavior and ultimately to localization. Furthermore, in the diffusive regime, we observe weak-localization corrections that are in agreement with the analytical predictions of the NLSM. Overall, our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems, paving a way for broader investigations of driven quantum matter.
We develop a formalism for studying Floquet dynamics for systems with non-relativistic conformal invariance in d spatial dimensions. Our analysis indicates the existence of two dynamical phases, hyperbolic and elliptic, separated by a parabolic transition surface. We demonstrate this by studying the fidelity of the driven state and the expectation value of a conformal generator in the many body ground state during the drive. Stroboscopically, they behave exponentially in the hyperbolic phase, show oscillatory behavior in the elliptic phase, and exhibit power-law on the transition surface. Our analysis is completely universal and can be directly applied to several systems including trapped fermions near unitarity and resonant anyons. The former can provide experimental signatures of these dynamical phases. We also comment on a holographic perspective of such driven non-relativistic CFTs and demonstrate that the hyperbolic phase is associated with a timelike stationary-limit surface, such as an ergosphere, in the bulk, while the parabolic phase corresponds to an extremal Killing horizon.
D. Das, Sumit R. Das, Arnab Kundu et al.· 0 citations
Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
We investigate the dissipative dynamics of a one-dimensional sawtooth-shaped Bose–Hubbard model subjected to an external magnetic flux and staggered single-particle dissipation. By combining the Lindblad master equation with a mean-field decoupling and further reducing the dynamics to an effective three-site model, we derive the nonlinear evolution equations that govern the system. Our results reveal that the magnetic flux, acting through the next-nearest-neighbor hopping, determines the preferential direction of particle flow, while the imbalance in dissipation forces the steady-state population to accumulate at lattice sites with weaker loss. Furthermore, we find that two-particle dissipation accelerates the relaxation process when it becomes negative (i.e., gain), whereas positive two-particle loss suppresses localization. These findings demonstrate that directional localization and relaxation dynamics can be controlled by the sign of the next-nearest-neighbor hopping t′ and the magnetic phase, providing a tunable scheme for engineering dissipative quantum states in optical lattices.
Yi-Fan Gao, Yanhang Chen, Shuyu Dai et al.· Entropy· 0 citations
We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system--environment decomposition and derive the master equation to leading order in $G$. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance $l_0$, the dynamics reduces to a Caldeira--Leggett-type equation, with a decoherence rate dependent on the baseline length $l_0$.
O. Angeli, Anirudh Gundhi, Angelo Bassi· 0 citations
We study the formation, dynamics, and disorder robustness of bound states in attractively interacting SU(N) fermions on a one-dimensional ring lattice. Using exact diagonalization in fixed-momentum sectors and Bethe ansatz exact results as a guide, we resolve the many-body spectrum into bands related to the possible partitions of the particles into bound composites, and characterize their internal structure also through density-density and N-body correlations. A pinning quench protocol reveals a transition from dispersive spreading to dynamical localization as the attractive interaction increases relative to the single-particle hopping. We find that the bound state dynamics for one-particle per component occurs as a many-body quantum walk similar to that of a single particle with a re-normalized effective mass. Such a property, that is the quantum version of the shape-preserving motion of classical solitons, can provide the dynamical signature of the fermionic solitary waves. We probe the robustness of the fermionic bound-state dynamics under on-site disorder.
Aysha Alsubaihi, W. J. Chetcuti, Fr'ed'eric Chevy et al.· 0 citations
We study a general one-dimensional spinless fermionic system subject to a localized source, sink, and bulk dephasing. Within the Lindblad framework, we compute the time evolution of the density profile and spatial correlation functions. We find that the presence of bulk dephasing suppresses certain coherent quantum features, such as the Friedel oscillations, and it alters the transport dynamics to exhibit two distinct dynamical regimes instead of three as observed in the absence of dephasing. This effect can be understood as the destruction of ballistic motion caused by the dephasing noise. Under strong dephasing, the density profile becomes similar to the one expected for a classical diffusive regime. We also investigate the system in the presence of both a localized source and sink, placed at a distance of $\Delta$. Interestingly, quantum coherence generates secondary density peaks at integer multiples of the source-sink separation $\Delta$, which are systematically washed out as bulk dephasing drives the system toward the classical diffusive limit.
Elka Bhattacharya, Sushant Saryal, Soumya Ghosh et al.· 0 citations