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Register a new userRenyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
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In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second Renyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second Renyi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.
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My previous work [arXiv:1902.00977] studied the dynamics of Renyi entanglement entropy $R_alpha$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_alpha$ with Renyi index $alpha>1$ grows no faster than diffusively (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $dge2$.
The dynamics of quantum phase transitions poses one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the one-dimensional Bose-Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We thereby perform a largely certified analogue quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behaviour of the coherence length, reminiscent of the Kibble-Zurek mechanism. However, we find exponents that strongly depend on the final interaction strength and thus lie outside the scope of this mechanism.
Rydberg atoms in optical tweezer arrays provide a playground for nonequilibrium quantum many-body physics. The PXP model describes the dynamics of such systems in the strongly interacting Rydberg blockade regime and notably exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we study the PXP model in a strong staggered external field, which has been proposed to manifest quasiparticle confinement in light of a mapping to a lattice gauge theory. We characterize this confining regime using both numerical exact diagonalization and perturbation theory around the strong-field limit. In addition to the expected emergent symmetry generated by the staggered field, we find a second emergent symmetry that is special to the PXP model. The interplay between these emergent symmetries and the Rydberg blockade constraint dramatically slows down the systems dynamics beyond naive expectations. We devise a nested Schrieffer-Wolff perturbation theory to properly account for the new emergent symmetry and show that this treatment is essential to understand the numerically observed relaxation time scales. We also discuss connections to Hilbert space fragmentation and trace the origin of the new emergent symmetry to a nearly-$SU(2)$ algebra discovered in the context of many-body scarring.
Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as $r^{-alpha}$. While diffusion is recovered for $alpha>1.5$, longer-ranged couplings with $0.5<alphaleq 1.5 $ give rise to effective classical Levy flights; a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<alphaleq1.5$ autocorrelations show hydrodynamic tails decaying in time as $t^{-1/(2alpha-1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.
Quantum many-body systems exhibit diverse phases characterized by various types of correlations. One aspect of quantum correlations is whether a quantum phase is gapless or gapped, and there are already well-developed tools to probe these correlations. Another aspect is whether a quantum phase possesses a well-defined quasi-particle description or not, and the experimental method sensitive to this is still less developed. Here we present a protocol probing many-body correlations by time-dependently ramping a parameter in Hamiltonians to the same target value with variable velocities. The first-order correction beyond the adiabatic limit due to the finite ramping velocity is universal and path-independent, and reveals many-body correlations of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response, and experimentally demonstrate it in studying the Bose-Hubbard model in ultracold-atom platforms. It is shown both theoretically and experimentally that this non-adiabatic linear response is significant in the quantum critical regime without well-defined quasi-particles, and is vanishingly small deeply in both superfluid and Mott insulators with well-defined quasi-particles.
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