Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLocalized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
61
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Motivated by the recent discovery of ergodicity breaking in geometrically frustrated systems, we study the quench dynamics of interacting hardcore bosons on a sawtooth ladder. We identify a set of initial states for which this system exhibits characteristic signatures of localization like initial state memory retention and slow growth of entanglement entropy for a wide parameter regime. Remarkably, this localization persists even when the many-body spectrum is thermalizing. We argue that the localized dynamics originates from an interaction induced quantum interference. Our results show that the sawtooth ladder can be a fertile platform for realizing non-equilibrium quantum states of matter.
rate research
Read More
We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the Toric Code Model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under non-equilibrium situations is tested by studying the topological entropy and a novel dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors.
We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time $bar{t}simtau^{{2 u z}/({1+2 u z})}$ for when the system falls out of equilibrium and the associated freeze-out length $bar{xi}simtau^{ u/({1+2 u z})}$ show power-law scaling with respect to the quench rate $1/tau$, where the exponents depend on the correlation length exponent $ u$ and the dynamical exponent $z$ associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.
We study the non-equilibrium dynamics of a homogeneous quantum Ising ring after a quench, in which the transverse field $g$ suddenly changes from zero to a nonzero value. The long-timescale reduced dynamics of a single spin and of two nearest-neighbor spins, which involves the evaluation of expectation values of odd operators that break the fermion parity, is exactly obtained for finite-size but large rings through the use of a recently developed Pfaffian method [N. Wu, Phys. Rev. E 101, 042108 (2020)]. Time dependence of the transverse and longitudinal magnetizations, single-spin purity, expectation value of the string operator $X_j=prod^{j-1}_{l=1}sigma^z_lsigma^x_j$, several equal-time two-site correlators, and pairwise concurrence after quenches to different phases are numerically studied. Our main findings are that (i) The expectation value of a generic odd operator approaches zero in the long-time limit; (ii) $langle X_jrangle_t$ exhibits $j$-independent exponential decay for a quench to $g=1$ and the time at which $langle X_jrangle_t$ reaches its first maximum scales linearly with $j$; (iii) The single-spin purity dynamics is mainly controlled by $langlesigma^x_jrangle_t$ ($langlesigma^z_jrangle_t$) for a quench to $g<1$ ($ggeq 1$). For quenches to the disordered phase with $ggg1$, the single-spin tends to be in the maximally mixed state and the transverse and longitudinal correlators $langlesigma^z_jsigma^z_{j+1}rangle_t$ and $langlesigma^x_jsigma^x_{j+1}rangle_t$ respectively approaches $-0.25$ and $0.5$ in the thermodynamic limit; (iv) The nearest-neighbor entanglement acquires a finite plateau value that increases with increasing $g$, and approaches a saturated value $sim0.125$ for $ggg1$.
We study a mechanical system that was considered by Boltzmann in 1868 in the context of the derivation of the canonical and microcanonical ensembles. This system was introduced as an example of ergodic dynamics, which was central to Boltzmanns derivation. It consists of a single particle in two dimensions, which is subjected to a gravitational attraction to a fixed center. In addition, an infinite plane is fixed at some finite distance from the center, which acts as a hard wall on which the particle collides elastically. Finally, an extra centrifugal force is added. We will show that, in the absence of this extra centrifugal force, there are two independent integrals of motion. Therefore the extra centrifugal force is necessary for Boltzmanns claim of ergodicity to hold.
Generalised hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg $XXZ$ spin $1/2$ chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin-reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetisation and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to $2/3$, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
