arXiv subjects

Sergej Flach

Publications and source records attributed to Sergej Flach.

At least 55 records · Page 3Linked to original sources

arXiv2021

Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice

We study the characteristics of chaos evolution of initially localized energy excitations in the one-dimensional nonlinear disordered Klein-Gordon lattice of anharmonic oscillators, by computing the time variation of the fundamental frequencies of the motion of each oscillator. We focus our attention on the dynamics of the so-called `weak' and `strong chaos' spreading regimes [2010, EPL 91 30001], for which Anderson localization is destroyed. Based on the fact that large variations of the fundamental frequencies denote strong chaotic behavior, we show that in both regimes chaos is more intense at the central regions of the wave packet, where also the energy content is higher, while the oscillators at the wave packet's edges exhibit regular motion up until the time they gain enough energy to become part of the highly excited portion of the wave packet. Eventually, the percentage of chaotic oscillators remains practically constant, despite the fact that the number of excited sites grows as the wave packet spreads, but the portion of highly chaotic sites decreases in time. We show that the extent of the zones of regular motion at the edges of the wave packet in the strong chaos regime is much smaller than in the weak chaos case. Furthermore, we find that in the strong chaos regime the chaotic component of the wave packet is not only more extended than in the weak chaos one, but in addition the fraction of strongly chaotic oscillators is much higher. Another important difference between the weak and strong chaos regimes is that in the latter case a significantly larger number of frequencies is excited, even from the first stages of the evolution. Moreover, our computations confirmed the shifting of fundamental frequencies outside the normal mode frequency band of the linear system in the case of the so-called `selftrapping' regime where a large part of the wave packet remains localized.

nlin.CD↗

arXiv2021

Wannier-Stark flatbands in Bravais lattices

We systematically construct flatbands (FB) for tight-binding models on simple Bravais lattices in space dimension $d \geq 2$ in the presence of a static uniform DC field. Commensurate DC field directions yield irreducible Wannier-Stark (WS) bands in perpendicular dimension $d - 1$ with $d$-dimensional eigenfunctions. The irreducible bands turn into dispersionless flatbands in the absence of nearest neighbor hoppings between lattice sites in any direction perpendicular to the DC field. The number of commensurate directions which yield flatbands is of measure one. We arrive at a complete halt of transport, with the DC field prohibiting transport along the field direction, and the flatbands prohibiting transport in all perpendicular directions as well. The anisotropic flatband eigenstates are localizing at least factorially (faster than exponential).

cond-mat.quant-gas↗

arXiv2021

Metal-insulator transition in infinitesimally weakly disordered flatbands

We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d + 1) local unitary transformations parametrized by angles $θ_i$. Without loss of generality, we consider the case of two flat bands separated by a finite gap $Δ$. The perturbed states originating from the flat bands are described by an effective tight binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles $θ_i$. The original infinitesimal onsite disorder strength W is only affecting the overall scale of the effective Hamiltonian. Upon variation of the manifold angles for d = 1 and d = 2 we find that localization persists for any choice of local unitaries, and the localization length can be maximized for specific values of $θ_i$. Instead, in d = 3 we identify a non-perturbative metal-insulator transition upon varying the all bands flat manifold angles.

cond-mat.dis-nn↗

arXiv2021

Anderson localization of excitations in disordered Gross-Pitaevskii lattices

We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the weak and strong interaction regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov-de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For strong interactions, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective strong interaction field equations for the excitations and generalize to higher dimensions.

cond-mat.dis-nn↗

arXiv2021

Many-body localization transition from flatband fine-tuning

Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two--body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.

cond-mat.stat-mech↗

arXiv2021

Probing band topology using modulational instability

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically non-trivial wave fields.

physics.optics↗

arXiv2021

Flatband generator in two dimensions

Dispersionless bands -- \emph{flatbands} -- provide an excellent testbed for novel physical phases due to the fine-tuned character of flatband tight-binding Hamiltonians. The accompanying macroscopic degeneracy makes any perturbation relevant, no matter how small. For short-range hoppings flatbands support compact localized states, which allowed to develop systematic flatband generators in $d=1$ dimension in Phys. Rev. B {\bf 95} 115135 (2017) and Phys. Rev. B {\bf 99} 125129 (2019). Here we extend this generator approach to $d=2$ dimensions. The \emph{shape} of a compact localized state turns into an important additional flatband classifier. This allows us to obtain analytical solutions for classes of $d=2$ flatband networks and to re-classify and re-obtain known ones, such as the checkerboard, kagome, Lieb and Tasaki lattices. Our generator can be straightforwardly generalized to three lattice dimensions as well.

cond-mat.mes-hall↗

arXiv2020

Nonlinear caging in All-Bands-Flat Lattices

We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact localized eigenstates. We demonstrate that there always exist local unitary transformations that detangle such lattices into decoupled sites in dimension one. Starting from a detangled representation, inverting the detangling into entangling unitary transformations and extending to higher lattice dimensions, we arrive at an All-Bands-Flat generator for single particle states in any lattice dimension. The entangling unitary transformations are parametrized by sets of angles. For a given member of the set of all-bands-flat, additional short-range nonlinear interactions destroy caging in general, and induce transport. However, fine-tuned subsets of the unitary transformations allow to completely restore caging. We derive the necessary and sufficient fine-tuning conditions for nonlinear caging, and provide computational evidence of our conclusions for one-dimensional systems.

cond-mat.quant-gas↗

arXiv2020

Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices

We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves nonlinear caging, i.e. keeps compact excitations compact in the presence of Kerr-like local nonlinearities. Here we replace nonlinear terms by Bose-Hubbard interactions and study quantum caging. We prove the existence of degenerate energy renormalized compact states for two and three particles, and use an inductive conjecture to generalize to any finite number M of participating particles in one dimension. Our results explain and generalize previous observations for two particles on a diamond chain [Vidal et.al. Phys. Rev. Lett. 85, 3906 (2000)]. We further prove that quantum caging conditions guarantee the existence of extensive sets of conserved quantities in any lattice dimension, as first revealed in [Tovmasyan et al Phys. Rev. B 98, 134513 (2018)] for a set of specific networks. Consequently transport is realized through moving pairs of interacting particles which break the single particle caging.

cond-mat.quant-gas↗

arXiv2020

Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices

We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.

cond-mat.stat-mech↗

arXiv2020

Fragile Many Body Ergodicity

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales. Short range networks instead yield a dramatic slowing down of ergodization in action space, and lead to rare resonance diffusion. We use Josephson junction chains as a paradigmatic study case. We exploit finite time average distributions to characterize the thermalizing dynamics of actions. We identify a novel action resonance diffusion regime responsible for the slowing down. We extract the diffusion coefficient of that slow process and measure its dependence on the proximity to the integrable limit. Independent measures of correlation functions confirm our findings. The observed fragile diffusion is relying on weakly chaotic dynamics in spatially isolated action resonances. It can be suppressed, and ergodization delayed, by adding weak action noise, as a proof of concept.

nlin.CD↗

arXiv2020

Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices

We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control parameter space of the energy and norm densities. The expansion can slow down substantially if the expected final state is a non-ergodic non-Gibbs one, regardless of the disorder strength. Likewise stronger disorder delays expansion. We compare our results with recent studies for quantum many body quench experiments.

cond-mat.quant-gas↗

arXiv2020

Many-Body Flatband Localization

We generate translationally invariant systems exhibiting many-body localization from All-Bands- Flat single particle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon - dubbed Many-Body Flatband Localization (MBFBL) - is based on symmetries of both single particle and interaction terms in the Hamiltonian, and it holds for any interaction strength. We propose a generator of MBFBL Hamiltonians which covers both interacting bosons and fermions for arbitrary lattice dimensions, and we provide explicit examples of MBFBL models in one and two lattice dimensions. We also explicitly construct an extensive set of local integrals of motion for MBFBL models. Our results can be further generalized to long-range interactions as well as to systems lacking translational invariance.

cond-mat.stat-mech↗

arXiv2020

Deep Learning of Chaos Classification

We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional Lyapunov exponent computation is far from converging. We show the robustness of the neural network to varying control parameters, in particular we train with one set of control parameters, and successfully test in a complementary set. Furthermore, we use the neural network to successfully test the dynamics of discrete maps in different dimensions, e.g. the one-dimensional logistic map and a three-dimensional discrete version of the Lorenz system. Our results demonstrate that a convolutional neural network can be used as an excellent chaos indicator.

cs.LG↗

arXiv2020

Anomalous transport in a topological Wannier-Stark ladder

A dc (e.g. electric) field with commensurate lattice direction turns a single particle band structure in $d=3$ dimensions into an infinite set of equally spaced irreducible $(d-1)=2$-dimensional Wannier-Stark (WS) band structures that are spatially localized along the field direction. Particle transport is expected to be suppressed once the WS bands are gapped in energy. The topological character of the irreducible band structure leads to one-dimensional sets of boundary states which fill the energy gaps. As a result, eigenmodes are smoothly connected in energy and space and yield anomalous particle transport throughout the ladder. The number of chiral boundary modes can be tuned by the dc field strength and manifests through the distribution of dissipated energy and spatial motion, and the temperature dependence of angular momentum carried by particles.

cond-mat.quant-gas↗

arXiv2020

Non-Gibbs states on a Bose-Hubbard lattice

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature $β$ and the chemical potential $μ$. We prove the existence of non-Gibbs states, that is, pairs $(\varepsilon,n)$ which cannot be mapped onto $(β,μ)$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to infinite temperature $β=0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.

cond-mat.stat-mech↗

arXiv2020

Multifractality of correlated two-particle bound states in quasiperiodic chains

We consider the quasiperiodic Aubry-André chain in the insulating regime with localised single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyse the nature of these states including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyse their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalisation.

cond-mat.dis-nn↗

arXiv2019

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external direct current (dc) electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradient set perpendicularly to the ribbon preserves the flatband while removing the band-touching. The undriven CLS - which occupies two lattices sites over one unit cell - turns into a quincunx-shaped CLS spanned over two unit cells. Instead, an x-gradient acting parallel to the ribbon yields a Stark ladder of CLS whose spatial profile is unchanged with respect to the undriven case. We notably find that their superposition leads to Bloch-like oscillations in momentum space.

physics.optics↗