Alexei Andreanov

Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry

We analyse the symmetries and the self-consistent perturbative approaches of dynamical field theories for glass-forming liquids. In particular, we focus on the time-reversal symmetry, which is crucial to obtain fluctuation–dissipation relations (FDRs). Previous field theoretical treatment violated this symmetry, whereas others pointed out that constructing symmetry-preserving perturbation theories is a crucial and open issue. In this work we solve this problem and then apply our results to the mode-coupling theory of the glass transition (MCT). We show that in the context of dynamical field theories for glass-forming liquids time-reversal symmetry is expressed as a nonlinear field transformation that leaves the action invariant. Because of this nonlinearity, standard perturbation theories generically do not preserve time-reversal symmetry and in particular fluctuation–dissipation relations. We show how one can cure this problem and set up symmetry preserving perturbation theories by introducing some auxiliary fields. As an outcome we obtain Schwinger–Dyson dynamical equations that automatically preserve FDR and that serve as a basis for carrying out symmetry-preserving approximations. We apply our results to the mode-coupling theory of the glass transition, revisiting previous field theory derivations of MCT equations and showing that they generically violate FDR. We obtain symmetry-preserving mode-coupling equations and discuss their advantages and drawbacks. Furthermore, we show, contrary to previous works, that the structure of the dynamic equations is such that the ideal glass transition is not cut off at any finite order of perturbation theory, even in the presence of coupling between current and density. The opposite results found in previous field theoretical works, such as the ones based on nonlinear fluctuating hydrodynamics, were only due to an incorrect treatment of time-reversal symmetry.

Compact localized states and flat-band generators in one dimension

Flat bands (FB) are strictly dispersionless bands in the Bloch spectrum of a periodic lattice Hamiltonian, recently observed in a variety of photonic and dissipative condensate networks. FB Hamiltonians are finetuned networks, still lacking a comprehensive generating principle. We introduce a FB generator based on local network properties. We classify FB networks through the properties of compact localized states (CLS) which are exact FB eigenstates and occupy

Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy

U

Artificial flat band systems: from lattice models to experiments

unit cells. We obtain the complete two-parameter FB family of two-band

Chiral flat bands: Existence, engineering, and stability

d=1

Random perfect lattices and the sphere packing problem

networks with nearest unit cell interaction and

Avalanches and hysteresis in frustrated superconductors and XY spin glasses.

U=2

Interacting ultracold atomic kicked rotors: loss of dynamical localization

. We discover a novel high symmetry sawtooth chain with identical hoppings in a transverse dc field, easily accessible in experiments. Our results pave the way towards a complete description of FBs in networks with more bands and in higher dimensions.

Random Coulomb antiferromagnets: From diluted spin liquids to Euclidean random matrices

In the spectrum of many-body quantum systems, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of non-equilibrium questions. Wave functions of interacting lattice quantum systems can be characterized either by local observables, or by global properties such as the participation ratio (PR) in a many-body basis or the entanglement between various partitions. We present a study of the PR and of the entanglement entropy (EE) between two roughly equal spatial partitions of the system, in all the eigenfunctions of local Hamiltonians. Motivated by the similarity of the PR and EE - both are generically larger in the bulk and smaller near the edges of the spectrum - we quantitatively analyze the correlation between them. We elucidate the effect of (proximity to) integrability, showing how low-entanglement and low-PR states appear also in the middle of the spectrum as one approaches integrable points. We also determine the precise scaling behavior of the eigenstate-to-eigenstate fluctuations of the PR and EE with respect to system size, and characterize the statistical distribution of these quantities near the middle of the spectrum.

Incommensurate helical spin ground states on the hollandite lattice

Abstract Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned coupling. These flat bands display remarkable strongly interacting phases of matter. Originally considered as a theoretical convenience useful for obtaining exact analytical solutions of ferromagnetism, flat bands have now been observed in a variety of settings, ranging from electronic systems to ultracold atomic gases and photonic devices. Here we review the design and implementation of flat bands and chart future directions of this exciting field. Graphical Abstract