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Order and Disorder in Gauge Systems and Magnets
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Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
We report on the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study nonequilibrium energy and spin transport. We demonstrate that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast to clean integrable systems. This suggests that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wave functions are delocalized and a phase in which low-energy wave functions are quasilocalized (in a sense we specify). Both phases have ballistic transport; however, in the quasilocalized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.
Disorder, interactions, and their interplay in novel narrow-gap Dirac materials and Weyl semimetals
Progress of the modern day condensed matter physics is to a large extent driven by the synthesis of new materials, advances in their experimental characterization and theoretical description. Recent discoveries of novel gapless Weyl semimetals, such as NaBi,CdAs, and BiTe-based films, in which magnetic dopants essentially suppress the gap, have added to the family of graphene and topological insulators actively investigated over the past decade. With the field of novel semimetals rapidly maturing, its focus necessarily shifts from demonstrations of the feasibility of such materials to their quantitative characterization. While the transport and optical properties of graphene and topological insulators are well captured within the picture of free non-interacting electrons, gapless 3D Weyl semimetals and narrow-gap 2D semiconductors with Dirac spectrum are known to be extremely susceptible to disorder and electron-electron interactions. This susceptibility obscures the manifestations of nontrivial band structure -- like quantum anomalous Hall effect -- of the new topological materials. Among particular projects to be addressed are: 1) optical conductivity of 3D gapless Dirac fermions in the presence of smooth disorder, 2) interplay of disorder and Coulomb interactions in the spectral properties of such fermions, 3) formation and structure of the impurity band with Coulomb supercritical clusters, 4) Coulomb interaction-driven renormalization of the electron spectrum and of the transport response in the presence of strong magnetic field, 5) instanton approach to the disorder-induced fluctuation states in zero-gap 3D materials, and 6) the role of disorder in quantum anomalous Hall effect. The proposal relies upon the investigators' previous broad expertise in interacting and disordered electron systems. The methods to be employed include perturbative diagrammatic technique, non-perturbative instanton and self-consistent approximations, hydrodynamics of electron liquid. Both analytical as well as numerical approaches are to be employed. The anticipated broader outcome of the proposal includes gaining an in-depth understanding of the interplay of the disorder and interactions under the conditions when this interplay has the most dramatic impact on observables. Traditionally, interaction effects are among the most challenging and interesting problems of condensed matter physics. Similarly, disordered systems typically present very difficult but extremely rich problems in the description of various materials. Importantly, understanding the spectral and transport properties of such materials not only presents the fundamental objective, but is also of particular interest for many applications, such as computation, memory, optics, plasmonics. In particular realization of the quantum anomalous Hall effect may lead to the development of low-power-consumption electronics. Indeed, a major constraint for practical use of the quantum Hall effect is limited by the requirement of the quantizing magnetic field. At the same time, the quantum anomalous Hall effect samples exhibit non-dissipative edge quantum transport in a zero magnetic field.
Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder
Highlights: • Analytic results in disordered quantum systems are obtained. • Correlated disorder changes the universality class of quantum phase transitions. • The lower and upper bounds of the dynamical critical exponent are obtained. This study investigates the dynamical critical exponent of disordered Ising chains under transverse fields to examine the effect of a correlated disorder on quantum phase transitions. The correlated disorder, where the on-site transverse field depends on the nearest-neighbor coupling strengths connecting the site, gives a qualitatively different result from the uncorrelated disorder. In the uncorrelated disorder cases where the transverse field is either homogeneous over sites or random independently of the nearest-neighbor coupling strengths, the dynamical critical exponent is infinite. In contrast, in the presence of the correlated disorder, we analytically show that the dynamical critical exponent is finite. We also show that the dynamical critical exponent depends on the tuning process of the transverse field strengths.
Investigation of experimental signatures of spin glass transition temperature
We present a series of temperature and field-dependent magnetization studies of large single-crystal spin glass samples, focusing on both field-cooled (FC) and zero-field-cooled (ZFC) magnetization studies, as well as ac susceptibility measurements. Using the above experimental techniques we aim to understand the nature of spin glass transition in presence of a field, a key factor in understanding the properties of these systems. Building on previous studies that have explored magnetic signatures indicative of spin glass transitions, our research employs a systematic approach to refine the identification of this transition temperature. Through static and dynamic measurements, we aim to shed light on the open issues regarding the key markers of spin glass transitions, enhancing our understanding of these complex systems.
Topological prethermal strong zero modes on superconducting processors
Abstract Symmetry-protected topological phases 1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model 5 . They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations 1–4,6–8 . In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay 9–11 . Here we report the observation of a distinct type of topological edge mode 12–14 , which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach 15–18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.
Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems
In this work, we explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-Abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite-temperature spin autocorrelation function decays at long times as $t^{–β}$ with $\textit{β}$ < 0.5, indicating subdiffusive transport at strong disorders.
Effective theory of superconductivity in strongly coupled amorphous materials
A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusivelike transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $α^2F(ω)$ in comparison with experiments and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on the one hand, drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $ω_{\text{log}}$ in the Allen-Dynes formula. As a consequence, the nonmonotonicity of $T_c$ as a function of alloying (disorder) in Pb-based systems can be rationalized. Further, the case of Al-based systems, where disorder increases $T_c$ from the start, is also analyzed. General material-design principles for enhancing $T_c$ in amorphous superconductors are presented.
Molecular Mechanics Simulations and Improved Tight-Binding Hamiltonians for Artificial Light Harvesting Systems: Predicting Geometric Distributions, Disorder, and Spectroscopy of Chromophores in a Protein Environment
We present molecular mechanics and spectroscopic calculations on prototype artificial light harvesting systems consisting of chromophores attached to a tobacco mosaic virus (TMV) protein scaffold. These systems have been synthesized and characterized spectroscopically, but information about the microscopic configurations and geometry of these TMV-templated chromophore assemblies is largely unknown. We use a Monte Carlo conformational search algorithm to determine the preferred positions and orientations of two chromophores, Coumarin 343 together with its linker and Oregon Green 488, when these are attached at two different sites (104 and 123) on the TMV protein. The resulting geometric information shows that the extent of disorder and aggregation properties and therefore the optical properties of the TMV-templated chromophore assembly are highly dependent on both the choice of chromophores and the protein site to which they are bound. We use the results of the conformational search as geometric parameters together with an improved tight-binding Hamiltonian to simulate the linear absorption spectra and compare with experimental spectral measurements. The ideal dipole approximation to the Hamiltonian is not valid because the distance between chromophores can be very small. Finally, we found that using the geometries from the conformational search is necessary to reproduce the features of the experimental spectral peaks.
Dual-Gate Modulation of Carrier Density and Disorder in an Oxide Two-Dimensional Electron System
Carrier density and disorder are two crucial parameters that control the properties of correlated two-dimensional electron systems. Furthermore, in order to disentangle their individual contributions to quantum phenomena, independent tuning of these two parameters is required. By utilizing a hybrid liquid/solid electric dual-gate geometry acting on the conducting LaAlO 3 /SrTiO 3 heterointerface, we obtain an additional degree of freedom to strongly modify the electron confinement profile and thus the strength of interfacial scattering, independent from the carrier density. A dual-gate controlled nonlinear Hall effect is a direct manifestation of this profile, which can be quantitatively understood by a Poisson–Schrödinger sub-band model. In particular, the large nonlinear dielectric response of SrTiO 3 enables a very wide range of tunable density and disorder, far beyond that for conventional semiconductors. This study provides a broad framework for understanding various reported phenomena at the LaAlO 3 /SrTiO 3 interface.
Enhancing exciton diffusion by reducing energy disorder in organic solar cells
A highly crystalline, highly emissive, and wide-bandgap polymer AC174 with an extremely small Stokes shift is designed and synthesized in water, and is used to reduce system energetic disorder and increase the exciton diffusion length of the classical PM6:Y6 blend system. AC174 is incompatible with PM6 and Y6, improves molecular packing, and reduces system energetic disorder. The long-range Förster resonance energy transfer between the donor and acceptor is enhanced, and the exciton diffusion constant and exciton lifetime are increased, leading to a longer exciton diffusion length and more efficient exciton dissociation and charge generation. The addition of AC174 simultaneously improves the open-circuit voltage, short-circuit current density (J SC ) and fill factor of PM6:Y6 devices; especially the highest internal quantum efficiency approaches 100%, and the highest J SC is 28.4 mA cm –2 . Ternary devices with 5% AC174 in the donors achieve a power conversion efficiency of 17.2%, higher than those of the parent binary devices based on PM6:Y6 (15.9%) and AC174:Y6 (3.24%).
Detection of topology via entanglement oscillations
In this work, we introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an “entanglement gap,” showing that it is generally applicable to pure and disordered quantum systems. Using exact diagonalization and the strong disorder renormalization group method, we demonstrate that this approach gives results in agreement with the use of traditional topological invariants, especially in cases where topological order is known to persist in the presence of off-diagonal bond disorder. The entanglement gap is then used to analyze classes of quantum systems with alternating bond types, allowing us to construct their topological phase diagrams. The validity of these phase diagrams is verified in limiting cases of dominant bond types, where the solution is known.
Classical signatures of quenched and thermal disorder in the dynamics of correlated spin systems
Neutron scattering is frequently used to look for evidence of features indicative of quantum-entangled phases of matter such as continua from fractionalisation or quantised excitations. However, the non-specificity of these features and difficulty of both fully quantum treatments and semiclassical models of disorder, make the diagnosis of such states problematic. Here, we demonstrate the feasibility of semiclassical treatments of disordered systems for supercells of ~10 000 spins. By examining a number of classically disordered models we show the presence of quantised excitations, broad continua and anomalous damping originating from quenched disorder or large classical degeneracies.
Defect formation by pristine indenter at the initial stage of nanoindentation
Nano-indentation is a sophisticated method to characterize mechanical properties of materials. This method samples a very small amount of material during each indentation. Therefore, this method is extremely useful to measure mechanical properties of nano-materials. The measurements using nanoindentation is very sensitive to the surface topology of the indenter and the indenting surfaces. The mechanisms involved in the entire process of nanoindentation require an atomic level understanding of the interplay between the indenter and the substrate. In this paper, we have used atomistic simulation methods with empirical potentials to investigate the effect of various types of pristine indenter on the defect nucleation and growth. Using molecular dynamics simulations, we have predicted the load-depth curve for conical, vickers, and sperical tip. The results are analyzed based on the coherency between the indenter tip and substrate surface for a fixed depth of 20 Å. The depth of defect nucleation and growth is observed to be dependent on the tip geometry. A tip with larger apex angle nucleates defects at a shallower depth. However, the type of defect generated is dependent on the crystalline orientation of the tip and substrate. For coherent systems, prismatic loops were generated, which released into the substrate along the close-packed directions with continued indentation. For incoherent systems, pyramidal shaped dislocation junctions formed in the FCC systems and disordered atomic clusters formed in the BCC systems. These defect nucleation and growth process provide the atomistic mechanisms responsible for the observed load-depth response during nanoindentation.
Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations
Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H{sub 2} and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.
Distribution of interevent avalanche times in disordered and frustrated spin systems
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality, manifest in power-law distributions of avalanche sizes. Considerably less work has been done on the statistics of the times between avalanches. This paper considers this issue, generalizing the work of Nampoothiri et al. [Phys. Rev. E 96, 032107 (2017)] in one space dimension to higher space dimensions. In addition to the interevent statistics of all avalanches, we also consider what happens when events are restricted to those exceeding a certain threshold size. Doing so raises the possibility of altering the definition of time to count the number of small events between the large ones, which provides for an analog to the concept of natural time introduced by the geophysics community with the goal of predicting patterns in seismic events. Furthermore, we analyze the distribution of time and natural time intervals both in the case of models that include only nearest-neighbor interactions, as well as models with (sparse) long-range couplings.