Localized Ground State Research Articles

The Kondo effect in the quantum XX spin chain

We investigate the boundary phenomena that arise in a finite-size XX spin chain interacting through an XX interaction with a spin −12 impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using both Bethe Ansatz and exact diagonalization techniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling JimpJ . When the ratio falls below the critical value 2 , the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value 2 an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling Jimp exceeds the critical value 2J , the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site.

The nematic susceptibility of the ferroquadrupolar metal TmAg2 measured via the elastocaloric effect

Elastocaloric measurements of the ferroquadrupolar/nematic rare-earth intermetallic TmAg2 are presented. TmAg2 undergoes a cooperative Jahn-Teller-like ferroquadrupolar phase transition at 5K, in which the Tm3+ ion’s local 4f electronic ground state doublet spontaneously splits and develops an electric quadrupole moment which breaks the rotational symmetry of the tetragonal lattice. The elastocaloric effect, which is the temperature change in the sample induced by adiabatic strains the sample experiences, is sensitive to quadrupolar fluctuations in the paranematic phase which couple to the induced strain. We show that elastocaloric measurements of this material reveal a Curie-Weiss like nematic susceptibility with a Weiss temperature of T* ≈ 2.7K, in agreement with previous elastic constant measurements. Furthermore, we establish that a magnetic field along the c-axis acts as an effective transverse field for the quadrupole moments.

Self-consistent optimization of the trial wave function within the constrained path auxiliary field quantum Monte Carlo method using mixed estimators

We propose a scheme to implement the self-consistent optimization of the trial wave function within the constrained path auxiliary field quantum Monte Carlo (CP-AFQMC) method in the framework of natural orbitals. In this scheme, a new trial wave function in the form of a Slater determinant is constructed from the CP-AFQMC results by diagonalizing the mixed estimator of the one-body reduced density matrix. We compare two ways (from real and mixed estimators in CP-AFQMC) to calculate the one-body reduced density matrix in the self-consistent process and study the ground state of a doped two-dimensional Hubbard model to test the accuracy of the two schemes. By comparing the local density, occupancy, and ground state energy we find the scheme in which a one-body reduced density matrix is calculated from the mixed estimator is computationally more efficient and provides more accurate results with less fluctuation. The local densities from the mixed estimator scheme agree well with the numerically exact values. This scheme provides a useful tool for studying strongly correlated electron systems.

Boundary quantum phase transitions in the spin- 12 Heisenberg chain with boundary magnetic fields

We consider the spin $\frac{1}{2}$ Heisenberg chain with boundary magnetic fields and analyze it using a combination of Bethe ansatz and density matrix renormalization group (DMRG) techniques. We show that the system exhibits several different ground states which depend on the orientation of the boundary magnetic fields. When both the boundary fields take equal values greater than a critical field strength, each edge in the ground state accumulates a fractional spin which saturates to spin $\frac{1}{4}$, which is similar to systems exhibiting symmetry protected topological phases (SPT). Unlike in SPT systems, the fractional boundary spin in the Heisenberg spin chain is not a genuine quantum number since the variance of the associated operator does not vanish, this is due to the absence of a bulk gap. The system exhibits high energy bound states when the boundary fields take values greater than the critical field. All the excitations in the system can be sorted out into towers whose number depends on the number of bound states exhibited by the system. As the boundary fields are varied, in addition to the ground state phase transition, we find that the system may undergo an eigenstate phase transition (EPT) where the number of towers of the Hilbert space changes. We further inquire how the EPT reflects itself on local ground state properties by computing the magnetization profile $\langle S^z_j \rangle$ using DMRG. We identify a clear qualitative change from low edge fields to high edge fields when crossing the critical field. We though are unable to conclude on the basis of our data that EPT corresponds to a genuine phase transition in the ground state.

Ergotropy and entanglement in critical spin chains

A subsystem of an entangled ground state is in a mixed state. Thus, if we isolate this subsystem from its surroundings we may be able to extract work applying unitary transformations, up to a maximal amount which is called ergotropy. Once this work has been extracted, the subsystem will still contain some bound energy above its local ground state, which can provide valuable information about the entanglement structure. We show that the bound energy for half a free fermionic chain decays as the square of the entanglement entropy divided by the chain length, thus approaching zero for large system sizes, and we conjecture that this relation holds for all 1D critical states.

Ising spin glass on random graphs at zero temperature: Not all spins are glassy in the glassy phase

We investigate the replica symmetry broken (RSB) phase of spin glass (SG) models in a random field defined on Bethe lattices at zero temperature. From the properties of the RSB solution we deduce a closed equation for the extreme values of the cavity fields. This equation turns out not to depend on the parameters defining the RSB, and it predicts that the spontaneous RSB does not take place homogeneously on the whole system. Indeed, there exist spins having the same effective local field in all local ground states, exactly as in the replica symmetric (RS) phase, while the spontaneous RSB manifests only on the remaining spins, whose fraction vanishes at criticality. The characterization in terms of spins having fixed or fluctuating local fields can be extended also to the random field Ising model (RFIM), in which case the fluctuating spins are the only responsible for the spontaneous magnetization in the ferromagnetic phase. Close to criticality we are able to connect the statistics of the local fields acting on the spins in the RSB phase with the correlation functions measured in the paramagnetic phase. Identifying the two types of spins on given instances of SG and RFIM, we show that they participate very differently to avalanches produced by flipping a single spin. From the scaling of the number of spins inducing RSB effects close to the critical point and using the $M$-layer expansion we estimate the upper critical dimension $D_U \geq 8$ for SG.

Localized Spin Dimers and Structural Distortions in the Hexagonal Perovskite Ba3CaMo2O9.

Extended solid-state materials based on the hexagonal perovskite framework are typified by close competition between localized magnetic interactions and quasi-molecular electronic states. Here, we report the structural and magnetic properties of the new six-layer hexagonal perovskite Ba3CaMo2O9. Neutron diffraction experiments, combined with magnetic susceptibility measurements, show that the Mo2O9 dimers retain localized character down to 5 K and adopt nonmagnetic spin-singlet ground states. This is in contrast to the recently reported Ba3SrMo2O9 analogue, in which the Mo2O9 dimers spontaneously separate into a mixture of localized and quasi-molecular ground states. Structural distortions in both Ba3CaMo2O9 and Ba3SrMo2O9 have been studied with the aid of distortion mode analyses to elucidate the coupling between the crystal lattice and electronic interactions in 6H Mo5+ hexagonal perovskites.

Asymptotic stability of small ground states for NLS under random perturbations

We consider the cubic Schrödinger (NLS) equation on the Euclidean space perturbed by a short-range potential V . The presence of a negative simple eigenvalue for -\Delta+V gives rise to a curve of small and localized nonlinear ground states that yield some time-periodic solutions known to be asymptotically stable in the energy space. We study the persistence of these coherent states under rough perturbations. We shall construct a large measure set of small scaling-supercritical solutions below the energy space that display some asymptotic stability behaviors. The main difficulty is the need to handle the interactions of localized and dispersive terms in the modulation equations. To do so, we use a critical-weighted strategy to combine probabilistic nonlinear estimates in critical spaces based on U^p , V^q (controlling higher-order terms) with some local energy decay estimates (controlling lower-order terms). We also revisit in the perturbed setting the analysis of Bényi, Oh, and Pocovnicu (2015) on the probabilistic global well-posedness and scattering for small supercritical initial data. We use a distorted Fourier transform and semiclassical functional calculus to generalize probabilistic and bilinear Strichartz estimates.

Generalized universal equation of states for magnetic materials: A novel formulation for an interatomic potential in Fe

The development of quantitative models for understanding physical properties of alloys requires a proper treatment of magnetic interactions, which is of paramount importance for the microstructural stability, especially in steels and high-entropy alloys containing magnetic elements. These magnetic interactions also control the defects behavior which affects the mechanical properties and the response under irradiation. Current interatomic potentials for molecular dynamics (MD) simulations still lack an adequate formulation to include magnetism into the simulations. In this paper, the universal equation of states (UES) is revisited and generalized by including ferromagnetic (FM) and antiferromagnetic (AFM) configurations with the aim of proposing a new formulation to develop interatomic potentials with magnetic contribution. For the case of Fe, given a fixed magnetic configuration and magnitude of the magnetic moment, the energy of the system is calculated by means of three parameters, namely, the energy, volume, and corresponding scaling volume (directly related to the bulk modulus) at the local ground state of the corresponding lattice. These parameters depend on three terms: firstly, a distance-dependent function, which gathers the nonmagnetic influence of the surrounding atoms; secondly, a magnetically dependent function, contributing to the energy by means of the magnetic nature of the atom, irrespective of the magnetic moment magnitudes of its surrounding atoms; and finally, a term which is magnetically and distance dependent simultaneously, which describes the influence of the magnetic state of the surrounding atoms on the energy considering their interatomic distance. This latter term is built via two functions which cannot be disconnected: one dependent on the distance between two atoms (a decreasing function with the distance in absolute value) multiplied by another function which is dependent on the magnetic moment of these two atoms. In this way, the magnetic influence of a distant atom scales with its distance. The new formulation is tested for magnetic iron, where 18 240 spin polarized density functional theory (DFT) calculated energies for different lattices, volumes, and magnetic moments in FM and AFM configurations showed that the generalized UES (GUES) accurately describes the energy of the system. The root-mean-square error of the GUES is in the range of $5.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ over all DFT calculated energies, showing good accuracy and allowing us to propose a formulation for developing a magnetic interatomic potential (MIP) in Fe. The potential is developed for FM configuration in iron, aiming at studying the stability of the ferritic and austenitic phases but also defects and other configurations of special relevance as, for instance, in irradiation conditions for fusion or fission applications. The distance and magnetic functions of the GUES are tabulated to obtain a MIP, which describes the DFT calculated energies for different lattices, volumes, and magnetic moments in FM configuration. Further, the MIP has been validated in other crystal lattices (A15 and C15), elastic constants, stresses in the lattice, vacancies, interstitials, forces at different temperatures, transformation paths between body-centered cubic, face-centered cubic, hexagonal close-packed, and simple cubic structures as well as $\ensuremath{\gamma}$ surfaces. We conclude that the results in this paper pave the way to develop MIPs with accuracy and predictability beyond the state of the art in MD.

Creating a Ferromagnetic Ground State with Tc Above Room Temperature in a Paramagnetic Alloy through Non-Equilibrium Nanostructuring.

Materials with strong magnetostructural coupling have complex energy landscapes featuring multiple local ground states, thus making it possible to switch among distinct magnetic-electronic properties. However, these energy minima are rarely accessible by a mere application of an external stimuli to the system in equilibrium state. A ferromagnetic ground state, with Tc above room temperature, can be created in an initially paramagnetic alloy by nonequilibrium nanostructuring. By a dealloying process, bulk chemically disordered FeRh alloys are transformed into a nanoporous structure with the topology of a few nanometer-sized ligaments and nodes. Magnetometry and Mössbauer spectroscopy reveal the coexistence of two magnetic ground states, a conventional low-temperature spin-glass and a hitherto-unknown robust ferromagnetic phase. The emergence of the ferromagnetic phase is validated by density functional theory calculations showing that local tetragonal distortion induced by surface stress favors ferromagnetic ordering. The study provides a means for reaching conventionally inaccessible magnetic states, resulting in a complete on/off ferromagnetic-paramagnetic switching over a broad temperature range.

Strongly correlated doped hole carriers in the superconducting nickelates: Their location, local many-body state, and low-energy effective Hamiltonian

The families of high-temperature superconductors recently welcomed a new member: hole doped nickelate Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ with a $\sim$15K transition temperature. To understand its emergent low-energy behaviors and experimental properties, an immediate key question is whether the superconducting hole carriers reside in oxygen as in the cuprates, or in nickel as in most nickelates. We answer this crucial question via a ``(LDA+$U$)+ED'' scheme: deriving an effective interacting Hamiltonian of the hole carriers from density functional LDA+$U$ calculation, and studying its local many-body states via exact diagonalization. Surprisingly, distinct from the expected Ni$^{2+}$ spin-triplet state found in most nickelates, the local ground state of two holes is actually a Ni-O spin-singlet state with second hole greatly residing in oxygen. The emerged eV-scale model therefore resembles that of the cuprates, advocating further systematic experimental comparisons. Tracing the microscopic origin of this unexpected result to the lack of apical oxygen in this material, we proposed a route to increase superconducting temperature, and a possible quantum phase transition absent in the cuprates.

How real are liquid groundstates? Ultra-fast crystal growth and the susceptibility of energy minima in liquids

We calculate the degree to which the final structure of the local groundstate in a liquid is a function of the strength of a perturbing potential applied during energy minimization. This structural susceptibility is shown to correlate well with the observed tendency of the liquid adjacent to a crystal interface to exhibit a crystalline groundstate, a feature that has been strongly linked to the observation of ultra-fast crystal growth in pure metals and ionic melts. It is shown that the structural susceptibility increases dramatically as the interaction potential between atoms is softened.

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.

Quantum dynamical simulations of intra-chain exciton diffusion in an oligo (para-phenylene vinylene) chain at finite temperature.

We report on quantum dynamical simulations of exciton diffusion in an oligo(para-phenylene vinylene) chain segment with 20 repeat units (OPV-20) at finite temperature, complementary to our recent study of the same system at T = 0 K [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. Accurate quantum dynamical simulations are performed using the multi-layer multi-configuration time-dependent Hartree method as applied to a site-based Hamiltonian comprising 20 electronic states of Frenkel type and 460 vibrational modes, including site-local quinoid-distortion modes along with site-correlated bond-length alternation (BLA) modes, ring torsional modes, and an explicit harmonic-oscillator bath. A first-principles parameterized Frenkel-Holstein type Hamiltonian is employed, which accounts for correlations between the ring torsional modes and the anharmonically coupled BLA coordinates located at the same junction. Thermally induced fluctuations of the torsional modes are described by a stochastic mean-field approach, and their impact on the excitonic motion is characterized in terms of the exciton mean-squared displacement. A normal diffusion regime is observed under periodic boundary conditions, apart from transient localization features. Even though the polaronic exciton species are comparatively weakly bound, exciton diffusion is found to be a coherent-rather than hopping type-process, driven by the fluctuations of the soft torsional modes. Similar to the previous observations for oligothiophenes, the evolution for the most part exhibits a near-adiabatic dynamics of local exciton ground states (LEGSs) that adjust to the local conformational dynamics. However, a second mechanism, involving resonant transitions between neighboring LEGSs, gains importance at higher temperatures.

Projected cooling algorithm for quantum computation

In the current era of noisy quantum devices, there is a need for quantum algorithms that are efficient and robust against noise. Towards this end, we introduce the projected cooling algorithm for quantum computation. The projected cooling algorithm is able to construct the localized ground state of any Hamiltonian with a translationally-invariant kinetic energy and interactions that vanish at large distances. The term “localized” refers to localization in position space. The method can be viewed as the quantum analog of evaporative cooling. We start with an initial state with support over a compact region of a large volume. We then drive the excited quantum states to disperse and measure the remaining portion of the wave function left behind. For the nontrivial examples we consider here, the improvement over other methods is substantial. The only additional resource required is performing the operations in a volume significantly larger than the size of the localized state. These characteristics make the projected cooling algorithm a promising tool for calculations of self-bound systems such as atomic nuclei.

Mechanism of Color and Photoacidity Tuning for the Protonated Green Fluorescent Protein Chromophore.

The neutral or A state of the green fluorescent protein (GFP) chromophore is a remarkable example of a photoacid naturally embedded in the protein environment and accounts for the large Stokes shift of GFP in response to near UV excitation. Its color tuning mechanism has been largely overlooked, as it is less preferred for imaging applications than the redder anionic or B state. Past studies, based on site-directed mutagenesis or solvatochromism of the isolated chromophore, have concluded that its color tuning range is much narrower than its anionic counterpart. However, as we performed extensive investigation on more GFP mutants, we found that the color of the neutral chromophore can be more sensitive to protein electrostatics than can the anionic counterpart. Electronic Stark spectroscopy reveals a fundamentally different electrostatic color tuning mechanism for the neutral state of the chromophore that demands a three-form model as compared to that of the anionic state, which requires only two forms ( J. Am. Chem. Soc. 2019, 141, 15250-15265). Specifically, an underlying zwitterionic charge-transfer state is required to explain its sensitivity to electrostatics. As the Stokes shift is tightly linked to excited-state proton transfer (ESPT) of the protonated chromophore, we infer design principles of the GFP chromophore as a photoacid through the color tuning mechanisms of both protonation states. The three-form model could also be applied to similar biological and nonbiological dyes and complements the failure of the two-form model for donor-acceptor systems with localized ground-state electronic distributions.

Einstein-Maxwell-scalar black holes: The hot, the cold and the bald

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function f(ϕ), between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: f(Φ)=1+αΦ4. The domain of existence of the scalarised BHs, for fixed α, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myers-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.

Computational hardness of spin-glass problems with tile-planted solutions.

We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into edge-disjoint subgraphs and planting frustrated, elementary subproblems that share a common local ground state, which guarantees that the ground state of the entire problem is known a priori. Using population annealing Monte Carlo, we compare the typical hardness of problem classes over a large region of the multidimensional tuning parameter space. Our results show that the problems have a wide range of tunable hardness. Moreover, we observe multiple transitions in the hardness phase space, which we further corroborate using simulated annealing and simulated quantum annealing. By investigating thermodynamic properties of these planted systems, we demonstrate that the harder samples undergo magnetic ordering transitions which are also ultimately responsible for the observed hardness transitions on changing the sample composition.

Effects of power per pulse on reactive HiPIMS deposition of ZrO2 films: A time-resolved optical emission spectroscopy study

Time-resolved optical emission spectroscopy was carried out during controlled reactive high-power impulse magnetron sputtering of ZrO2 films in argon–oxygen gas mixtures. The effects of increased target power density (up to 3.0 kW cm−2) applied in voltage pulses shortened from 200 to 50 μs were studied at a nearly constant deposition-averaged target power density (close to 50 W cm−2) and a fixed repetition frequency of 500 Hz. The trends in time evolution of the local ground-state densities of Zr, Ar, and O atoms and that of the Zr+, Zr2+, Ar+, and O+ ions during a voltage pulse were deduced from the time evolution of the corresponding excited-state populations and the excitation temperature. It was found that the sputtered Zr atoms are much more ionized (with a high fraction of Zr2+ ions) and the Ar atom density is more decreased near the target during the shorter (50 μs) high-power pulses. These shorter pulses produce a four times higher pulse-averaged target power density oscillating between 1.7 and 2.1 kW cm−2 during deposition. Under these conditions, much higher densities of O atoms and Zr2+ ions were measured in the plasma bulk. The higher backward flux of the Zr+ and Zr2+ ions onto the target during this high-power discharge regime contributed significantly to a 34% decrease in the efficiency of the magnetron sputter deposition of ZrO2 films.

Unified View of the Local Cation-Ordered State in Inverse Spinel Oxides.

Cation ordering/disordering in spinel oxides plays an essential role in the rich physical and chemical properties which are hallmarks of the structural archetype. A variety of cation-ordering motifs have been reported for spinel oxides with multiple cations residing on the octahedral site (or B-site). This has attracted tremendous attention from both experimental and theoretical communities in the last few decades. However, no unified view has been reached, presumably due to the richness of cation species and corresponding complex arrangements emergent in this large family of compounds. In this report, local cation-ordered ground states of (inverse) spinel oxides with two different cations on the octahedral site have been thoroughly investigated using neutron and X-ray total scattering, and a comprehensive theory has been proposed to explain the commonly observed cation-ordered polymorphs. It is found that a cation-zigzag-ordered structure (space group P4122) is the ground state for inverse spinel oxides with a pure or strong ionic lattice, while a cation-linear-ordered arrangement (space group Imma) emerges when one of the B-site cations forms very strong directional covalent bonds with lattice oxygen. The degree and length scale of cation ordering is strongly correlated with the charge and ionic radius difference between the two octahedral site cations. More complicated cation ordering schemes can be formed when there is a concomitant charge and orbital ordering which fall on a similar energy scale. This can lead to the formation of orbital-driven cation clusters or the broad concept of "molecules" in solid- state compounds. It is expected these findings will help to better understand the observed physical properties of spinel oxides and thus facilitate design strategies for improved functional materials.