Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUniversal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
119
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast (radiation) and slow (kink or domain wall) degrees of freedom. We find a universal long-time dynamics, largely independent of the microscopic details of the system, in which the kinks control the relaxation of relevant observables and correlations. The resulting late-time dynamics can be described by a set of phenomenological equations, which yield results in excellent agreement with the numerical tests.
rate research
Read More
We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.
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.
We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.
We study interaction-induced Mott insulators, and their topological properties in a 1D non-Hermitian strongly-correlated spinful fermionic superlattice system with either nonreciprocal hopping or complex-valued interaction. For the nonreciprocal hopping case, the low-energy neutral excitation spectrum is sensitive to boundary conditions, which is a manifestation of the non-Hermitian skin effect. However, unlike the single-particle case, particle density of strongly correlated system does not suffer from the non-Hermitian skin effect due to the Pauli exclusion principle and repulsive interactions. Moreover, the anomalous boundary effect occurs due to the interplay of nonreciprocal hopping, superlattice potential, and strong correlations, where some in-gap modes, for both the neutral and charge excitation spectra, show no edge excitations defined via only the right eigenvectors. We show that these edge excitations of the in-gap states can be correctly characterized by only biorthogonal eigenvectors. Furthermore, the topological Mott phase, with gapless particle excitations around boundaries, exists even for the purely imaginary-valued interaction, where the continuous quantum Zeno effect leads to the effective on-site repulsion between two-component fermions.
We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
