Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.Comment: 6+5 pages, 8 figure

Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field

Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling $\nu=5/2$, a result incompatible with both the Pfaffian and the Antipfaffian states, we have pushed the expansion of the effective Hamiltonian of the $5/2$ quantized Hall state to third-order in the parameter $\kappa=E_c/\hbar \omega_c \propto 1/\sqrt{B}$ controlling the Landau level mixing , where $E_c$ is the Coulomb energy and $\omega_c$ the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian and the AntiPfaffian induced at second-order is reduced by third-order corrections and disappears around $\kappa=0.4$, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of $\kappa$ the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured $5/2$ thermal conductance of the $5/2$ quantized Hall state.Comment: 10 pages + 5 p of appendix, all comments welcom

Many-body localization in a fragmented Hilbert space

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space, but still exponentially. Such a property allows us to study the MBL phase transition in systems including more than $50$ spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. But they also present distinct scalings with system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.Comment: 14 + 6 pages, all comments are welcom

G-Quadruplexes in RNA Biology: Recent Advances and Future Directions.

RNA G-quadruplexes (RG4s) are four-stranded structures known to control gene expression mechanisms, from transcription to protein synthesis, and DNA-related processes. Their potential impact on RNA biology allows these structures to shape cellular processes relevant to disease development, making their targeting for therapeutic purposes an attractive option. We review here the current knowledge on RG4s, focusing on the latest breakthroughs supporting the notion of transient structures that fluctuate dynamically in cellulo, their interplay with RNA modifications, their role in cell compartmentalization, and their deregulation impacting the host immune response. We emphasize RG4-binding proteins as determinants of their transient conformation and effectors of their biological functions

Time-evolution of local information: thermalization dynamics of local observables

Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such decoupling of local degrees of freedom for the mixed field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we can motivate algorithms based on the intuition that information for statistical reasons flow from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.Comment: 38 pages, 9 figure

Co-propagation of QKD & 6 Tb/s (60x100G) DWDM channels with ~17 dBm total WDM power in single and multi-span configurations

We report co-propagation experiments of the quantum channel (at 1310 nm) of a Quantum Key Distribution (QKD) system with Dense Wavelength Division Multiplexing (DWDM) data channels in the 1550 nm range. Two configurations are assessed. The first one is a single span configuration where various lengths of Standard Single Mode Fiber (SSMF) (from 20 to 70 km) are used and the total WDM channels power is varied. The Secure Key Rate (SKR) and the Quantum Bit Error Ratio (QBER) are recorded showing that up to ~17 dBm total power of 30 or 60 channels at 100 Gb/s can coexist with the quantum channel. A metric to evaluate the co-propagation efficiency is also proposed to better evaluate the ability of a QKD system to provide secure keys in a co-propagation regime. The second experiment is a three spans link with a cascade of three QKD systems and two trusted nodes in a 184 km total link length. We report the transmission of a coherent 400 Gb/s Dual Polarization DP-16QAM (Quadrature Amplitude Modulation) channel that transports a QKD secured 100 GbE data stream, with other fifty-four 100 Gb/s WDM channels. Encryption is demonstrated at the same time as co-propagation.Comment: arXiv admin note: text overlap with arXiv:2305.1374

Driven dissipative dynamics and topology of quantum impurity systems

In this review, we provide an introduction and overview to some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin-boson and related models, which describes a single spin-1/2 coupled to an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin-bath coupling. In these situations, the non-perturbative stochastic Schroedinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_z(t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling to a common bath. In the second part of this review, we discuss quantum engineering of spin-boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose-Einstein condensate, a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott-Superfluid transition.Comment: 39 pages, invited review, Comptes Rendus Acad\'emie des Sciences, Special Issue on Quantum Simulators, Version as publishe