arXiv subjects

Sergej Flach

Publications and source records attributed to Sergej Flach.

At least 37 records · Page 2Linked to original sources

arXiv2024

Collective quantum phases in frustrated arrays of Josephson junctions

We study collective quantum phases and quantum phase transitions occurring in frustrated sawtooth arrays of small quantum Josephson junctions. Frustration is introduced through the periodic arrangement of $0$- and $π$- Josephson junctions with the Josephson coupling energies $αE_\mathrm{J}$ of different signs, $-1\leq α\leq 1$. The complexity of the potential landscape of the system is controlled by the frustration parameter $f=(1-α)/2$. The potential energy has a single global minimum in the non-frustrated regime ($f f_\mathrm{cr}=0.75$). We address the coherent quantum regime and identify several collective quantum phases: disordered (insulating) and ordered (superconducting) phases in the non-frustrated regime, as well as highly entangled patterns of vortices and anti-vortices in the frustrated regime. These collective quantum phases are controlled by several physical parameters: the frustration $f$, the Josephson coupling, and the charging energies of junctions and islands. We map the control parameter phase diagram by characterizing the quantum dynamics of frustrated Josephson junction arrays by spatially and temporally resolved quantum-mechanical correlation function of the local magnetization.

cond-mat.str-el↗

arXiv2024

Compact Localized States in Electric Circuit Flatband Lattices

We generate compact localized states in an electrical diamond lattice, comprised of only capacitors and inductors, via local driving near its flatband frequency. We compare experimental results to numerical simulations and find very good agreement. We also examine the stub lattice, which features a flatband of a different class where neighboring compact localized states share lattice sites. We find that local driving, while exciting the lattice at that flatband frequency, is unable to isolate a single compact localized state due to their non-orthogonality. Finally, we introduce lattice nonlinearity and showcase the realization of nonlinear compact localized states in the diamond lattice. Our findings pave the way of applying flatband physics to complex electric circuit dynamics.

cond-mat.mes-hall↗

arXiv2024

Flat band fine-tuning and its photonic applications

Flat bands - single-particle energy bands - in tight-binding networks have attracted attention due to the presence of macroscopic degeneracies and their extreme sensitivity to perturbations. This makes them natural candidates for emerging exotic phases and unconventional orders. The challenging part however is to construct flat band networks, whose existence relies on symmetries and fine-tuning. In this review we consider the recently proposed systematic ways to construct flat band networks based on symmetries or fine-tuning. We then discuss how the fine-tuning constructions can be further extended, adapted or exploited in presence of perturbations, both single-particle and many-body. This strategy has lead to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging and many-body nonergodic quantum models. We discuss what implications these results may have for the design of fine-tuned nanophotonic systems including photonic crystals, nanocavities, and metasurfaces.

physics.optics↗

arXiv2024

Trapping Hard-Core Bosons in Flatband Lattices

We investigate 1D and 2D cross-stitch lattices with hard-core bosons and analytically construct exact groundstates that feature macroscopic degeneracy. The construction relies on the presence of a flatband in the single particle spectrum and the orthogonality of the associated compact localized states (CLS). Up to filling fraction $ν=1/2$, the groundstate is constructed by occupying the CLS. Exactly at $ν=1/2$, the groundstate becomes a Wigner crystal. For higher filling fractions, the groundstate is constructed by filling the CLS sites completely one by one. Macroscopic degeneracy arises from the multiple choices available when occupying or filling the CLS sites. An occupied CLS acts as an impenetrable barrier for bosons both in 1D and 2D, leading to Hilbert space fragmentation. A similar phenomenology also holds for hard-core bosons on the diamond chain and its higher dimensional generalizations. We also discuss the mapping of these hard-core models onto spin models with quantum many-body scars.

cond-mat.str-el↗

arXiv2024

Dynamical chaos in the integrable Toda chain induced by time discretization

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step $τ$ and measure the Lyapunov time $T_Λ$ (inverse of the largest Lyapunov exponent $Λ$). A key observation is that $T_Λ$ is finite whenever $τ$ is finite but diverges when $τ\rightarrow 0$. We compare the Toda chain results with the nonitegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times $T_B \gg T_Λ$ due to certain positions and momenta becoming extremely large (``Not a Number''). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.

nlin.CD↗

arXiv2023

Thermalization slowing down in multidimensional Josephson junction networks

We characterize thermalization slowing-down of Josephson junction networks in 1, 2 and 3 spatial dimensions for systems with hundreds of sites by computing their entire Lyapunov spectra. The ratio of Josephson coupling $E_J$ to energy density $h$ controls two different universality classes of thermalization slowing-down, namely the weak coupling regime, $E_J/h \rightarrow 0$, and the strong coupling regime, $E_J/h \rightarrow \infty$. We analyze the Lyapunov spectrum by measuring the largest Lyapunov exponent and by fitting the rescaled spectrum with a general ansatz. We then extract two scales: the Lyapunov time (inverse of the largest exponent) and the exponent for the decay of the rescaled spectrum. The two universality classes, which exist irrespective of network dimension, are characterized by different ways the extracted scales diverge. The universality class corresponding to the weak-coupling regime allows for the coexistence of chaos with a large number of near-conserved quantities and is shown to be characterized by universal critical exponents, in contrast with the strong-coupling regime. We expect our findings, which we explain using perturbation theory arguments, to be a general feature of diverse Hamiltonian systems.

cond-mat.stat-mech↗

arXiv2023

Thermalization Universality-Class Transition Induced by Anderson Localization

We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We compute Lyapunov spectra, which display qualitatively distinct features depending on whether the proximity to the integrable limit is short or long ranged. For sufficiently small nonlinearity, translationally invariant systems fall into the long-range class. Adding disorder to such a system triggers a transition to the short-range class -- implying a breaking of this invariance -- and in the very limit of vanishing non-linearity Anderson localization emerges. The crossover from long- to short-range class is attained by tuning the localization length, $ξ$, from $ξ\approx N$ to $ξ\ll N$, where $N$ is the system size. As a consequence, the Lyapunov spectrum becomes exponentially suppressed, depending on how strongly its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.

nlin.CD↗

arXiv2023

Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder

We consider manifolds of tunable all-band flat (ABF) lattices in dimensions d = 1, 2, parametrized by a manifold angle parameter θ. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models where the disorder strength is scaled out. For weak magnetic flux disorder we observe sub-exponential localization at flatband energies in d = 1, which differs from the usual Anderson localization. We also find diverging localisation length at flatband energies for weak flux values in d = 2, however the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in d = 2 we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter θ.

cond-mat.mes-hall↗

arXiv2023

Superconductivity with Wannier-Stark Flat Bands

We investigate superconducting transport in the DC field induced Wannier-Stark flat bands in the presence of interactions. Flat bands offer the possibility of unconventional high temperature superconductivity, where the superfluid weight, $D_s$, is enhanced by the density overlap of the localized states. However, construction of flat bands typically requires very precise tuning of Hamiltonian parameters. To overcome this difficulty, we propose a feasible alternative to realize flat bands by applying a DC field in a commensurate lattice direction. We systematically characterize the superconducting behavior on these flat bands by studying the effect of the DC field and attractive Hubbard interaction strengths on the wavefunction, correlation length, pairing order parameter and the superfluid weight $D_s$. Our main result is that the superfluid weight is dramatically enhanced at an optimal value of the interaction strength and weak DC fields.

cond-mat.supr-con↗

arXiv2023

Uniform Anderson Localization in One-Dimensional Floquet Maps

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $θ$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field yields a uniform spectrum gaplessly occupying the entire unit circle. The resulting eigenstates are exponentially localized. Remarkably this Anderson localization is universal as all eigenstates have one and the same localization length $L_{loc}$. We present an exact theory for the calculation of the localization length as a function of the hopping, $1/L_\text{loc}=\left|\ln\left(|\sin(θ)|\right)\right|$, that is tunable between zero and infinity by variation of the hopping $θ$.

cond-mat.dis-nn↗

arXiv2023

Intermediate super-exponential localization with Aubry-André chains

We demonstrate the existence of an intermediate super-exponential localization regime for eigenstates of the Aubry-André chain. In this regime, the eigenstates localize factorially similarly to the eigenstates of the Wannier-Stark ladder. The super-exponential decay emerges on intermediate length scales for large values of the $\textit{winding length}$ -- the quasi-period of the Aubry-André potential. This intermediate localization is present both in the metallic and insulating phases of the system. In the insulating phase, the super-exponential localization is periodically interrupted by weaker decaying tails to form the conventional asymptotic exponential decay predicted for the Aubry-André model. In the metallic phase, the super-exponential localization happens for states with energies away from the center of the spectrum and is followed by a super-exponential growth into the next peak of the extended eigenstate. By adjusting the parameters it is possible to arbitrarily extend the validity of the super-exponential localization. A similar intermediate super-exponential localization regime is demonstrated in quasiperiodic discrete-time unitary maps.

cond-mat.quant-gas↗

arXiv2023

Critical States Generators from Perturbed Flatbands

One-dimensional all-bands-flat lattices are networks with all bands being flat and highly degenerate. They can always be diagonalized by a finite sequence of local unitary transformations parameterized by a set of angles $θ_{i}$. In our previous work, Ref.~\onlinecite{lee2023critical}, we demonstrated that quasiperiodic perturbations of the one-dimensional all-bands-flat lattice with $θ_{i} = π/4$ give rise to a critical-to-insulator transition and fractality edges separating critical from localized states. In this study we consider the full range of angles $θ_{i}$s available for the all-bands-flat model and study the effect of the quasiperiodic perturbation. For weak perturbation, we derive an effective Hamiltonian and we identify the sets of $θ_{i}$s for which the effective model maps to extended or off-diagonal Harper models and hosts critical states. For all the other values of the angles the spectrum is localized. Upon increasing the perturbation strength, the extended Harper model evolves into the system with energy dependent critical-to-insulator transitions, that we dub \emph{fractality edges}. The case where the effective model maps onto the off-diagonal Harper model features a critical-to-insulator transition at a finite disorder strength.

cond-mat.dis-nn↗

arXiv2022

Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands

We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice models. Such networks can be diagonalized by a finite sequence of local unitary transformations parameterized by angles $θ_i$. Without loss of generality, we focus on the case of two bands with bandgap $Δ$. Weak perturbations lead to an effective Hamiltonian with both on- and off-diagonal quasiperiodic terms that depend on $θ_i$. For some angle values, the effective model coincides with the extended Harper model. By varying the parameters of the quasiperiodic potentials, \iffalse and the manifold angles $θ_i$ \fi we observe localized insulating states and an entire parameter range hosting critical states with subdiffusive transport. For finite quasiperiodic potential strength, the critical-to-insulating transition becomes energy dependent with what we term fractality edges separating localized from critical states.

cond-mat.dis-nn↗

arXiv2022

Thermalization dynamics of macroscopic weakly nonintegrable maps

We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance $σ^2(T)$ of finite time average distributions for extended and local observables. We extract the ergodization time scale $T_E$ which marks the onset of thermalization, and determine the type of network through the subsequent decay of $σ^2(T)$. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time $T_Λ$ with $T_E$. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.

nlin.CD↗

arXiv2022

Correlated metallic two-particle bound states in Wannier--Stark flatbands

Tight-binding single-particle models on simple Bravais lattices in space dimension $d \geq 2$, when exposed to commensurate DC fields, result in the complete absence of transport due to the formation of Wannier--Stark flatbands [Phys. Rev. Res. $\textbf{3}$, 013174 (2021)]. The single-particle states localize in a factorial manner, i.e., faster than exponential. Here, we introduce interaction among two such particles that partially lifts the localization and results in metallic two-particle bound states that propagate in the directions perpendicular to the DC field. We demonstrate this effect using a square lattice with Hubbard interaction. We apply perturbation theory in the regime of interaction strength $(U)$ $\ll$ hopping strength $(t)$ $\ll$ field strength $(\mathcal{F})$, and obtain estimates for the group velocity of the bound states in the direction perpendicular to the field. The two-particle group velocity scales as $U {(t/\mathcal{F})}^ν$. We calculate the dependence of the exponent $ν$ on the DC field direction and on the dominant two-particle configurations related to the choices of unperturbed flatbands. Numerical simulations confirm our predictions from the perturbative analysis.

cond-mat.quant-gas↗

arXiv2022

Logarithmic expansion of many-body wave packets in random potentials

Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $ξ$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of the nonlinear terms. We observe the saturation of the cloud expansion of $N$ particles to a volume $\sim Nξ$. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean-field diffusion with the final saturation regime and is entirely controlled by particle number $N$. The temporal window of that regime grows exponentially with the localization length $ξ$.

cond-mat.dis-nn↗

arXiv2022

Anti-$\mathcal{PT}$ flatbands

We consider tight-binding single particle lattice Hamiltonians which are invariant under an antiunitary antisymmetry: the anti-$\mathcal{PT}$ symmetry. The Hermitian Hamiltonians are defined on $d$-dimensional non-Bravais lattices. For an odd number of sublattices, the anti-$\mathcal{PT}$ symmetry protects a flatband at energy $E = 0$. We derive the anti-$\mathcal{PT}$ constraints on the Hamiltonian and use them to generate examples of generalized kagome networks in two and three lattice dimensions. Furthermore, we show that the anti-$\mathcal{PT}$ symmetry persists in the presence of uniform DC fields and ensures the presence of flatbands in the corresponding irreducible Wannier-Stark band structure. We provide examples of the Wannier-Stark band structure of generalized kagome networks in the presence of DC fields, and their implementation using Floquet engineering.

cond-mat.mtrl-sci↗

arXiv2022

Lyapunov spectrum scaling for classical many-body dynamics close to integrability

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations. Long-range limits result in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging control parameter and the rescaled spectrum approaching an analytical function. Short-range limits result in a dramatic slowing down of thermalization which manifests through the rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one.

nlin.CD↗