Localized Ground State Research Articles

Flat-band ferromagnetism of SU(N) Hubbard model on Tasaki lattices

We investigate the para-ferro magnetic transition of the repulsive SU(N) Hubbard model on a type of one- and two-dimensional decorated cubic lattices, referred as Tasaki lattices, which feature massive single-particle ground state degeneracy. Under certain restrictions for constructing localized many-particle ground states of flat-band ferromagnetism, the quantum model of strongly correlated electrons is mapped to a classical statistical geometric site-percolation problem, where the nontrivial weights of different configurations must be considered. We prove rigorously the existence of para-ferro transition for the SU(N) Hubbard model on one-dimensional Tasaki lattice and determine the critical density by the transfer-matrix method. In two dimensions, we numerically investigate the phase transition of SU(3), SU(4) and SU(10) Hubbard models by Metropolis Monte Carlo simulation. We find that the critical density exceeds that of standard percolation, and increases with spin degrees of freedom, implying that the effective repulsive interaction becomes stronger for larger N. We further rigorously prove the existence of flat-band ferromagnetism of the SU(N) Hubbard model when the number of particles equals to the degeneracy of the lowest band in the single-particle energy spectrum.

Coherent Charge Transfer Exciton Formation in Regioregular P3HT: A Quantum Dynamical Study.

The ultrafast formation of charge transfer excitons (CTXs) in regioregular poly(3-hexyl thiophene) (rrP3HT) domains is elucidated by electronic structure and quantum dynamical studies of an aggregate model system comprising five stacked quaterthiophene units. Using a multistate vibronic coupling Hamiltonian parametrized by TDDFT calculations for 13 electronic states of Frenkel and CTX type, along with 78 vibrational modes, quantum dynamical simulations are carried out using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method. In line with time-resolved spectroscopic results [ De Sio , A. ; et al. Nat. Commun. 2016 , 7 , 13742 ], it is found that CTX formation occurs immediately upon photoexcitation, accompanied by sustained regular oscillations with a ∼22 fs periodicity. These coherent features, whose presence may seem surprising in a high-dimensional aggregate or thin film material, can be traced back to a dominant vibronic signature of CC stretch-type high-frequency modes. These vibrational signatures are found to be enhanced due to a collective vibronic response that is prompted by the initial generation of a delocalized bright exciton and its subsequent relaxation, by internal conversion, to a polaronic local exciton ground state.

Kibble-Zurek mechanism with a single particle: Dynamics of the localization-delocalization transition in the Aubry-André model

The Aubry-Andr\'e 1D lattice model describes a particle hopping in a pseudo-random potential. Depending on its strength $\lambda$, all eigenstates are either localized ($\lambda>1$) or delocalized ($\lambda<1$). Near the transition, the localization length diverges like $\xi\sim(\lambda-1)^{-\nu}$ with $\nu=1$. We show that when the particle is initially prepared in a localized ground state and the potential strength is slowly ramped down across the transition, then -- in analogy with the Kibble-Zurek mechanism -- it enters the delocalized phase having finite localization length $\hat\xi\sim\tau_Q^{\nu/(1+z\nu)}$. Here $\tau_Q$ is ramp/quench time and $z$ is a dynamical exponent. At $\lambda=1$ we determine $z\simeq2.37$ from the power law scaling of energy gap with lattice size $L$. Even though for infinite $L$ the model is gapless, we show that the gap relevant for excitation during the ramp remains finite. Close to the critical point it scales like $\xi^{-z}$ with the value of $z$ determined by the finite size scaling. It is the gap between the ground state and the lowest of those excited states that overlap with the ground state enough to be accessible for excitation. We propose an experiment with a non-interacting BEC to test our prediction. Our hypothesis is further supported by considering a generalized version of Aubry-Andr\'{e} model possessing an energy-dependent mobility edge.

Synthesis, structural characterization, and computational study of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide

An efficient synthesis of the new (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide is described. Its molecular structural features have been characterized by FTIR, 1H NMR, 13C NMR and MS, then have been confirmed by single crystal X-ray diffraction. Quantum chemical calculations including molecular geometry, intermolecular H-bonds and vibrational frequencies were carried out for the structures to explain stability and geometry using the hybrid density functional (DFT/B3LYP) in conjunction with 6-311 + G(d,p) basis set. The calculated structural and vibrational parameters are presented and compared with their experimental X-ray and FTIR counterparts. The global minimum and local minima ground states characteristics of the title compound and its rotamers have been theoretically established through 2D potential energy scan and vibrational frequencies. Computational analysis predicted that head-to-tail E/E-dimer of the observed E-isomer has significantly stronger intermolecular hydrogen bonding in solution rather than in the gaseous state. It is found that NH and CO vibrational bands suffering blue-shift due to intermolecular hydrogen bonds (IHBs). Weak intramolecular hydrogen bonds that have been detected in the monomeric form in the gaseous state and in solution are lacking in trimers and tetramers due to loss of planarity in the molecular structure. Optimization in solution clearly shows that the strength of the IHBs decreased exponentially with dielectric continuum of the solvent used. Inexistence of solvent/monomer intermolecular hydrogen bonds has been explained in terms of Condensed Fukui Functions.

Many-body localization as a large family of localized ground states

Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian $\mathcal{H}_0$ is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to $\mathcal{H}_0$ but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to $L=256$ sites.

Localization studies for ground states of the Gross‐Pitaevskii equation

AbstractFor oscillatory high‐amplitude potentials it is known that the linear Schrödinger operator leads to exponentially localized ground states. This localization result can be quantified explicitly in terms of geometric parameters and the degree of disorder within the potential. In the present paper we study the influence of the amplitude and the importance of the periodicity in the nonlinear setting of the Gross‐Pitaevskii equation which models ultracold bosonic gases.

Recombination from polar InGaN/GaN quantum well structures at high excitation carrier densities

In this paper we report on the emergence of a high energy band at high optically excited carrier densities in the low temperature photoluminescence spectra from polar InGaN/GaN single quantum well structures. This high energy band emerges at carrier densities when the emission from the localized ground states begins to saturate. We attribute this high energy band to recombination involving higher energy less strongly localized electron and hole states that are populated once the localized ground states become saturated; this assignment is supported by the results from an atomistic tight-binding model. A particular characteristic of the recombination at the high carrier densities is that the overall forms of the photoluminescence decay curves bear great similarity to those from semiconductor quantum dots. The decay curves consist of plateaus where the photoluminescence intensity is constant with time as a result of Pauli state blocking in the high energy localized states followed by a rapid decrease in intensity once the carrier density is sufficiently low that the states involved are no longer saturated.

Violation of the Bell inequality in quantum critical random spin-1/2 chains

We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same universality class for a certain range of randomness.

Investigation of the vanadium L23 -edge x-ray absorption spectrum of SrVO3 using configuration interaction calculations: Multiplet, valence, and crystal-field effects

Configuration interaction cluster calculations have been performed to investigate the electronic structure of orthorhombic distorted ${\mathrm{SrVO}}_{3}$ compound, where a considerable tetragonal crystal-field splitting of larger than $180\phantom{\rule{4.pt}{0ex}}\text{meV}$ for ${t}_{2g}$ orbital levels is suggested for the good consistence between the simulated and the experimental spectral line shape. This supports the crystal-field splitting scenario for the metal-insulator transition mechanism. We further calculate V ${L}_{23}$-edge absorption spectra of vanadium oxides with similar ${\mathrm{VO}}_{6}$ octahedral environment for formal $d$ electrons varying from $3{d}^{0}$ to $3{d}^{3}$, where we obtain energy parameters representing the local ground-state properties and provide the theoretical guidance for identifying the chemical valence and the crystal-field strength of a particular vanadium oxide. Our simulated polarization-dependent spectra at different tetragonal crystal-field values reveal a nonlinear orbital-lattice interaction. The orbital polarization $P$ reflecting the electron occupations in different ${d}_{xy}$ and ${d}_{xz(yz)}$ orbital symmetries shows strong sensitivity to small tetragonal crystal field, indicating the strongly correlated electron effect and further addressing the efficiency of strain engineering in functional SVO-based thin films and heterostructures.

Investigation of the multiplet features of SrTiO3 in X-ray absorption spectra based on configuration interaction calculations.

Synchrotron-based L2,3-edge absorption spectra show strong sensitivities to the local electronic structure and chemical environment. However, detailed physical information cannot be extracted easily without computational aids. Here, using the experimental Ti L2,3-edges absorption spectrum of SrTiO3 as a fingerprint and considering full multiplet effects, calculations yield different energy parameters characterizing local ground state properties. The peak splitting and intensity ratios of the L3 and L2 set of peaks are carefully analyzed quantitatively, giving rise to a small hybridization energy around 1.2 eV, and the different hybridization energy values reported in the literature are further addressed. Finally, absorption spectra with different linearly polarized photons under various tetragonal crystal fields are investigated, revealing a non-linear orbital-lattice interaction, and a theoretical guidance for material engineering of SrTiO3-based thin films and heterostructures is offered. Detailed analysis of spectrum shifts with different tetragonal crystal fields suggests that the eg crystal field splitting is a necessary parameter for a thorough analysis of the spectra, even though it is not relevant for the ground state properties.

The interplay between frustration and entanglement in many-body systems

Frustration of classical many-body systems can be used to distinguish ferromagnetic interactions from anti-ferromagnetic ones via the Toulouse conditions. A quantum version of the Toulouse conditions provides a similar classification based on the local ground states. We compute the global ground states for a family of models with Heisenberg-like interactions and analyse their behaviour with respect to frustration, entanglement and degeneracy. For that we develop analytical and numerical analysing tools capable of quantifying the interplay between those three quantities. We find that the quantum Toulouse conditions provide a proper classification, however, refinements can be found. Our results show how the different local ground states affect the interplay and pave the way for further generalisation and possible applications to other quantum many-body systems.

Open quantum random walk in terms of quantum Bernoulli noise

In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897–1908, 2016) as a special case.

Properties of Heavy Fermion in an Impurity Anderson Model with f2 Local Singlet Ground State

The Fermi-liquid properties of a two-orbital impurity Anderson model with an f2 local singlet ground state is studied by the numerical renormalization group method. It is shown that a heavy-fermion (HF) state with a vanishingly small Wilson ratio is realized in the vicinity of the quantum critical point (QCP) between the local-singlet and Kondo-singlet phases. The parameter area in which the HF behavior appears is remarkably enlarged with increasing the excitation energy from the local singlet to triplet states. It is also clarified that the HF state takes place with an intermediate average occupancy of f electrons, reflecting the existence of the QCP under strong valence fluctuation. The possible application of these theoretical results to an unconventional HF state in Sm compounds is discussed.

On the co-operative formation of local ground states and frustration fields in the structural glass As2Se3

A microscopic free energy model with an order parameter was introduced earlier that included a local frustration gauge field with U1 symmetry. Ad hoc values of this field were introduced to fit the NQR distribution of a powdered sample of As2Se3 glass and predict the glass and Kauzmann temperatures. Here we derive initial values of the local frustration force amplitudes from an associated molecular free energy. We show that these amplitudes as calculated solely as gradients of the free energy are too large, and that a force term derived from energy leaving the glass and entering the bath must be included to give the correct magnitude. The modification to the bath also acts as a U1 gauge transformation of the frustration field, and insures that the “freezing” process is irreversible, non-equilibrium, and approximately steady state.

Local Nodal Cooper Pairs in Multiorbital Systems

We show the emergence of a new class of superconductivity in multiorbital systems, focusing on non-Kramers f$^2$ states. The Cooper pairs in this class of superconductivity mainly consist of local pairs with the same symmetry as the local f$^2$ ground states. When the local ground state is an anisotropic representation, the superconducting gap has nodes on the Fermi surface. This nodal superconductivity is mediated by the strong onsite inter-orbital attractions as a consequence of negative-$U$ physics generalized to multiorbital systems. We show that this is indeed realized in a simple two-orbital model with antiferro Hund's coupling and enhanced inter-orbital interaction derived via a systematic local down folding. Finally, we briefly discuss superconductivity in Pr-1-2-20 compounds, UBe$_{13}$, and PrOs$_4$Sb$_{12}$ in view of the present mechanism.

Large exchange anisotropy in quasi-one-dimensional spin- 12 fluoride antiferromagnets with a d(z2)1 ground state

Hybrid density functional calculations are performed for a variety of systems containing d9 ions (Cu2+, Ag2+), and exhibiting quasi-one-dimensional magnetic properties. In particular we study fluorides containing these ions in a rarely encountered compressed octahedral coordination which forces the unpaired electron in the d(z2) orbital. We predict that such systems should exhibit magnetic anisotropies surpassing that of Sr2CuO3 - one of the best realizations of an one-dimensional system known to date. In particular we predict that the inter-chain coupling in the Ag2+ containing [AgF][BF4] should be nearly five orders of magnitude smaller than the intra-chain interaction. Our results indicate that quasi-one-dimensional spin-1/2 systems containing chains with spin sites in a d(z2)1 local ground state could constitute a versatile model for testing modern theories of quantum many-body physics in the solid state.

Optical emission spectroscopy during the deposition of zirconium dioxide films by controlled reactive high-power impulse magnetron sputtering

Time-resolved optical emission spectroscopy was performed near the sputtered Zr target and in a plasma bulk during a controlled high-rate reactive high-power impulse magnetron sputtering of stoichiometric ZrO2 films in argon-oxygen gas mixtures at the argon pressure of 2 Pa. The repetition frequency was 500 Hz at the deposition-averaged target power density of 52 W cm−2 with a peak target power density of 1100 W cm−2. The voltage pulse duration was 200 μs. From the time evolutions of the excited-state populations for the chosen atoms (Zr, Ar, and O) and ions (Zr+, Zr2+, Ar+, and O+), and of the excitation temperature during a voltage pulse, the trends in a time evolution of the local ground-state densities of these atoms and ions during the voltage pulse were derived. Near the target, a decrease in the ground-state densities of Ar and O atoms, caused by a gas rarefaction and intense electron-impact ionization, was observed in the first half of the voltage pulse. Simultaneous, very effective electron-impact ionization of sputtered Zr atoms was proved. A composition of particle fluxes onto the substrate during a film deposition was found almost independent of the instantaneous oscillating oxygen partial pressure.

Proper modelling of ligand binding requires an ensemble of bound and unbound states.

Although noncovalent binding by small molecules cannot be assumed a priori to be stoichiometric in the crystal lattice, occupancy refinement of ligands is often avoided by convention. Occupancies tend to be set to unity, requiring the occupancy error to be modelled by the B factors, and residual weak density around the ligand is necessarily attributed to `disorder'. Where occupancy refinement is performed, the complementary, superposed unbound state is rarely modelled. Here, it is shown that superior accuracy is achieved by modelling the ligand as partially occupied and superposed on a ligand-free `ground-state' model. Explicit incorporation of this model of the crystal, obtained from a reference data set, allows constrained occupancy refinement with minimal fear of overfitting. Better representation of the crystal also leads to more meaningful refined atomic parameters such as the B factor, allowing more insight into dynamics in the crystal. An outline of an approach for algorithmically generating ensemble models of crystals is presented, assuming that data sets representing the ground state are available. The applicability of various electron-density metrics to the validation of the resulting models is assessed, and it is concluded that ensemble models consistently score better than the corresponding single-state models. Furthermore, it appears that ignoring the superposed ground state becomes the dominant source of model error, locally, once the overall model is accurate enough; modelling the local ground state properly is then more meaningful than correcting all remaining model errors globally, especially for low-occupancy ligands. Implications for the simultaneous refinement of B factors and occupancies, and for future evaluation of the limits of the approach, in particular its behaviour at lower data resolution, are discussed.

Single-atom edgelike states via quantum interference

We demonstrate how quantum interference may lead to the appearance of robust edge-like states of a single ultracold atom in a two-dimensional optical ribbon. We show that these states can be engineered either within the manifold of local ground states of the sites forming the ribbon, or of states carrying one unit of angular momentum. In the former case, we show that the implementation of edge-like states can be extended to other geometries, such as tilted square lattices. In the latter case, we suggest to use the winding number associated to the angular momentum as a synthetic dimension.

Encoding the structure of many-body localization with matrix product operators

Anderson insulators are non-interacting disordered systems which have localized single particle eigenstates. The interacting analogue of Anderson insulators are the Many-Body Localized (MBL) phases. The natural language for representing the spectrum of the Anderson insulator is that of product states over the single-particle modes. We show that product states over Matrix Product Operators of small bond dimension is the corresponding natural language for describing the MBL phases. In this language all of the many-body eigenstates are encode by Matrix Product States (i.e. DMRG wave function) consisting of only two sets of low bond-dimension matrices per site: the $G_i$ matrix corresponding to the local ground state on site $i$ and the $E_i$ matrix corresponding to the local excited state. All $2^n$ eigenstates can be generated from all possible combinations of these matrices.