Noninteracting Model Research Articles

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

Effects of renormalization and non-Hermiticity on nonlinear responses in strongly correlated electron systems

Nonlinear responses in condensed matter are intensively studied because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. While nonlinear responses in noninteracting models have been explored widely, the effect of strong correlations on the nonlinear response is still poorly understood, even though it has been suggested that correlations can enhance the nonlinear response. In this work, we first give an analytical derivation of nonlinear responses using Green's function methods at finite temperature. Then, we discuss the difficulties of considering dissipation using conventional methods, such as the reduced density matrix method. We reveal that the relaxation time approximation leads to severe limitations when considering optical responses. Finally, we demonstrate that correlation effects, such as the renormalization of the band structure and different lifetimes in orbitals or sublattices, can significantly enhance nonlinear responses and even change the sign of the nonlinear conductivity.

Tunable graphene plasmons in nanoribbon arrays: the role of interactions

Plasmons in patterned graphene have attracted much interest because of possible applications in sensing, nanophotonics, and optoelectronics. We perform mid and far-infrared optical studies of electrically doped graphene nanoribbon arrays as a function of the filling factor and compare results with the unpatterned graphene. We demonstrate that an increase in both the filling factor of nanoribbon arrays and the free carrier concentration intensifies the plasmon-plasmon and plasmon-radiation interactions. As a result, the free-carrier dynamics manifested itself in the strong plasmon redshift and increased radiative damping compared to non-interacting models for the transverse magnetic polarization. Similarly, signatures of interactions are identified for plasmons in transverse electric polarization. The obtained experimental and theoretical results provide the basis for better understanding and controlling graphene-based structures’ spectral properties, thus facilitating applications’ development.

Cosmological evolution via interacting/non-interacting holographic dark energy model for curved FLRW space–time in Rastall gravity

In this work, we explore the phenomenon of cosmic evolution using curved FLRW space–time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity (RG) and universe is assumed to be consists of interacting/ non-interacting dark energy (DE) and dark matter (DM). In both scenarios, we evaluate exact solutions of the dynamical equations and constraint the holographic parameter c2(z) assuming a slowly varying function of red-shift during non-interacting model. For interacting model, we consider c2 as a constant function of red-shift. Moreover, we analyze nature of the obtained results via deceleration parameter (q), statefinder pair (j,s) and Om(z)-diagnostic by constraining the involved model parameters using latest observational data. The graphical analysis showed that interacting model is very close to Λ cold DM (ΛCDM) model as compared to non-interacting case. We conclude that this holographic proposal is enough to describe the cosmic evolution at an accelerating rate.

Evapotranspiration simulation from a sparsely vegetated agricultural field in a semi-arid agro-ecosystem using Penman-Monteith models

Increased competition for water resources for agriculture calls for improved water productivities. Improved water productivities must start with accurate estimation of crop evapotranspiration (ET). Accurate estimation of ET has been a challenge for sparsely vegetated crops especially under varying soil water conditions. In this paper, we aim to improve estimation of ET using the Penman-Monteith (PM) method by (1) improved canopy resistance estimation by better representing soil water (2) improved surface resistance estimation by implementing a segmented approach of surface resistance calibration, and (3) investigating the performance of PM models over sparse vegetation by comparing four different solutions; the standard-PM model (PM-STD), the PM-Coupled (PM-CO) single-layer interactive model, the PM Shuttleworth-Wallace (PM-SW) dual-source interactive model and the PM Two-source Patch (PM-TSP) non-interactive model. The model results are evaluated against ET measurements from in-field Bowen ratio-energy balance observations. The results show that, under water-limiting conditions, correctly representing the soil moisture during the different crop development stages enhanced a PM model's ability to accurately estimate ET. The approach raised the Nash-Sutcliffe Efficiency (NSE) of a PM-STD from 0.72 to 0.75. Applying a segmented surface resistance further improved the PM-STD to an NSE of 0.77. When these improvements were implemented on the other PM models, the PM-SW and PM-CO performed superiorly with NSE of 0.83 and RMSE of 0.07 mm hr−1. The PM-TSP followed with an NSE of 0.79 and RMSE of 0.09 mm hr−1 while the PM-STD model trailed with an NSE of 0.77 and RMSE of 0.08 mm hr−1. The performance of all models highlighted the need to separate canopy and soil resistance terms during surface resistance calibration and the value of implementing a segmented approach for resistance calibration. High performance of PM-SW especially demonstrated the need to implement surface energy partitioning and surface aerodynamics interaction for canopy and soil surfaces in PM models

Probing band-center anomaly with the Kernel polynomial method

We investigate the anomalous behavior of localization length of a non-interacting one-dimensional Anderson model at zero temperature. We report numerical calculations of the Thouless expression of localization length, based on the Kernel polynomial method (KPM), which has an computational complexity, where N is the system size. The KPM results show excellent agreement with perturbative results in a large system size limit, confirming the validity of the Thouless formula. In the perturbative regime, we show that the KPM approximation of the Thouless expression produces the correct localization length at the band center in the thermodynamic limit. The Thouless expression relates localization length in terms of density of states in a one-dimensional disordered system. By calculating the KPM estimates of the density of states, we find a cusp-like behavior around the band center in the perturbative regime. This cusp-like singularity can not be obtained by approximate analytical calculations within the second-order approximations, reflects the band-center anomaly.

Rényi holographic dark energy in higher dimension Cosmology

Rényi holographic dark energy (RHDE) correspondence is discussed in higher dimensional cosmology, namely Kaluza–Klein (KK) cosmology. Both interacting and non-interacting cosmological scenario are considered here. It is found that the non-interacting model naturally leads to the late accelerated universe, unlike the standard Holographic Dark Energy models in 4D, which requires interaction to accommodate the late-time acceleration of the universe. The interacting model produces an accelerating universe at late time albeit failing to attain the estimated present value of the deceleration parameter. The evolution of different cosmologically relevant parameters have been estimated. We consider here two diagnostic tests namely, state-finder and Om diagnostics to study the non-interacting model which is more favoured in the light of recent cosmological observations. Classical stability of the cosmological models is also discussed.

Wigner–Weyl formalism for the lattice models

We discuss application of Wigner–Weyl formalism to the lattice models of condensed matter physics and relativistic quantum field theory. For the noninteracting models our technique relates Wigner transformation of the fermionic Green’s function with the Weyl symbol [Formula: see text] of lattice Dirac operator. We take as an example of the model defined on rectangular lattice the model of Wilson fermions. It represents the regularization of relativistic quantum field theory and, in addition, describes qualitatively certain topological materials in condensed matter physics. In this model we derive expression for [Formula: see text] in the presence of the most general case of external [Formula: see text] gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of [Formula: see text].

The Lagrangian Formulation and Gauge Theory of the Standard Model

Study of gauge symmetry is carried over the different interacting and non-interacting field theoretical models through a prescription based on Lagrangian formulation. And the prescription is capable of testing whether a given model possesses a gauge symmetry or not. It can successfully formulate the gauge transformation generator in all the cases whatever subtleties are involved in it. It is found that the prescription has the ability to show a direction how to extend the phase space using auxiliary fields to restore the gauge invariance of a theory. Like the usual phase space, the prescription is found to be equally powerful in the extended phase space of a theory.

Two-body metal-insulator transitions in the Anderson-Hubbard model

We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.

Superradiant Phase Transition in Electronic Systems and Emergent Topological Phases.

We derive a general criterion for determining the onset of superradiant phase transition in electronic bands coupled to a cavity field, with possibly electron-electron interactions. For longitudinal superradiance in 2D or genuine 1D systems, we prove that it is always prevented, thereby extending existing no-go theorems. Instead, a superradiant phase transition can occur to a nonuniform transverse cavity field and we give specific examples in noninteracting models, either through Fermi surface nesting or parabolic band touching. Investigating the resulting time-reversal symmetry breaking superradiant states, we find in the former case Fermi surface lifting down to four Dirac points on a square lattice model, with topologically protected zero modes, and in the latter case topological bands with nonzero Chern number on an hexagonal lattice.

Spin transport in a tunable Heisenberg model realized with ultracold atoms.

Simple models of interacting spins have an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, gauge theories, high-temperature superconductors, quantum spin liquids, and systems with exotic particles such as anyons and Majorana fermions1,2. To study and compare these models, a versatile platform is needed. Realizing such systems has been a long-standing goal in the field of ultracold atoms. So far, spin transport has only been studied in systems with isotropic spin-spin interactions3-12. Here we realize the Heisenberg model describing spins on a lattice, with fully adjustable anisotropy of the nearest-neighbour spin-spin couplings (called the XXZ model). In this model we study spin transport far from equilibrium after quantum quenches from imprinted spin-helix patterns. When spins are coupled only along two of three possible orientations (the XX model), we find ballistic behaviour of spin dynamics, whereas for isotropic interactions (the XXX model), we find diffusive behaviour. More generally, for positive anisotropies, the dynamics ranges from anomalous superdiffusion to subdiffusion, whereas for negative anisotropies, we observe a crossover in the time domain from ballistic to diffusive transport. This behaviour is in contrast with expectations from the linear-response regime and raises new questions in understanding quantum many-body dynamics far away from equilibrium.

On Sparse Linear Regression in the Local Differential Privacy Model

In this paper, we study the sparse linear regression problem under the Local Differential Privacy (LDP) model. We first show that polynomial dependency on the dimensionality <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> of the space is unavoidable for the estimation error in both non-interactive and sequential interactive local models, if the privacy of the whole dataset needs to be preserved. Similar limitations also exist for other types of error measurements and in the relaxed local models. This indicates that differential privacy in high dimensional space is unlikely achievable for the problem. With the understanding of this limitation, we then present two algorithmic results. The first one is a sequential interactive LDP algorithm for the low dimensional sparse case, called Locally Differentially Private Iterative Hard Thresholding (LDP-IHT), which achieves a near optimal upper bound. This algorithm is actually rather general and can be used to solve quite a few other problems, such as (Local) DP-ERM with sparsity constraints and sparse regression with non-linear measurements. The second one is for the restricted (high dimensional) case where only the privacy of the responses (labels) needs to be preserved. For this case, we show that the optimal rate of the error estimation can be made logarithmically dependent on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> (i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log p$ </tex-math></inline-formula> ) in the local model, where an upper bound is obtained by a label-privacy version of LDP-IHT. Experiments on real world and synthetic datasets confirm our theoretical analysis.

High folic acid or folate combined with low vitamin B-12 status: potential but inconsistent association with cognitive function in a nationally representative cross-sectional sample of US older adults participating in the NHANES

Potential safety concerns relative to impaired cognitive function may exist when high folic acid exposures are combined with low vitamin B-12 status. We aimed to examine the relation of the coexistence of high folate and low vitamin B-12 status with cognitive function, utilizing various definitions of "high" folate status. Cross-sectional data from older adults (≥60 y; n=2420) from the 2011-2014 NHANES were analyzed. High folate status was defined as unmetabolized serum folic acid (UMFA)>1 nmol/L or serum total folate>74.1 nmol/L, and low vitamin B-12 status as methylmalonic acid>271 nmol/L or serum vitamin B-12<150 pmol/L. Logistic regression models estimated ORs of scoring low on 1 of 4 cognitive tests: the Digit Symbol Substitution Test (DSST), the Consortium to Establish a Registry for Alzheimer's Disease Delayed Recall (CERAD-DR) and Word Learning tests, and the Animal Fluency test (AF). A significant interaction was observed relative to scoring low on the DSST (<34; UMFA; P-interaction=0.0071) and AF (serum folate; P-interaction=0.0078) for low vitamin B-12 and high folate status. Among those with low vitamin B-12, high UMFA or high serum total folate was associated with higher risk of scoring low on the DSST (OR: 2.16; 95% CI: 1.05, 4.47) and the AF (OR: 1.93; 95% CI: 1.08, 3.45). Among those with "normal" vitamin B-12, higher UMFA or serum total folate was protective on the CERAD-DR. In noninteraction models, when high folate and normal vitamin B-12 status was the reference group, low vitamin B-12 combined with high UMFA was associated with greater risk based on the DSST (<34, OR: 2.87; 95% CI: 1.85, 4.45; <40, OR: 2.22; 95% CI: 1.31, 3.75) and AF (OR: 1.97; 95% CI: 1.30, 2.97); but low vitamin B-12 and lower UMFA (OR: 1.69; 95% CI: 1.16, 2.47) was also significantly associated for DSST<40 risk. Low vitamin B-12 was associated with cognitive impairment both independently and in an interactive manner with high folate for certain cognitive performance tests among older adults.

Interacting ghost dark energy in complex quintessence theory

We employ a ghost model of interacting dark energy to obtain the equation of state omega for ghost energy density in an FRW universe in complex quintessence theory. We reconstruct the potential and study the dynamics of the scalar field that describes complex quintessence cosmology. We perform omega -omega ' analysis and stability analysis for both non-interacting and interacting cases and find that the same basic conclusion as for the real model, where omega ' = domega / d ln a. Taking account of the effect of the complex part and assuming the real part of the quintessence field to be a slow-rolling field, we conclude that the non-interacting model cannot describe the real universe since this will lead to fractional energy density Omega _D > 1, where Omega _D can be defined as the ratio of rho _D to rho _{cr}. However, for the interacting case, if we take present Omega _D =0.73, then we can determine that b^2 = 0.0849, where b^2 is the interaction coupling parameter between matter and dark energy. In the real quintessence model, Omega _D and b^2 are independent parameters, whereas in the complex quintessence model, we conclude that there is a relationship between these two parameters.

Bianchi type-III Tsallis holographic dark energy model in Saez\u2013Ballester theory of gravitation

In this paper, we have investigated Tsallis holographic dark energy (infrared cutoff is the Hubble radius) in homogeneous and anisotropic Bianchi type-III Universe within the framework of Saez–Ballester scalar–tensor theory of gravitation. We have constructed non-interaction and interaction dark energy models by solving the Saez–Ballester field equations. To solve the field equations, we assume a relationship between the metric potentials of the model. We developed the various cosmological parameters (namely deceleration parameter q, equation of state parameter omega _t, squared sound speed v_s^2, om-diagnostic parameter Om(z) and scalar field phi ) and well-known cosmological planes (namely omega _t-omega _t^{'} plane, where ' denotes derivative with respect to ln(a) and statefinders (r-s) plane) and analyzed their behavior through graphical representation for our both the models. It is also, quite interesting to mention here that the obtained results are coincide with the modern observational data.

Barrow holographic dark energy with hubble horizon as IR cutoff

In this work, we propose a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon. We study the evolutionary history of important cosmological parameters, in particular, deceleration parameter, equation of state (EoS) parameter, the BHDE and matter density parameter, and also observe satisfactory behaviors in the BHDE model. The stability of the BHDE model has been examined by squared sound speed [Formula: see text]. In addition, to describe the accelerated expansion of the Universe, the correspondence of the BHDE model with the quintessence scalar field has been reconstructed.

Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver

The accurate characterization of nonequilibrium strongly-correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, they feature correlated phenomena, including emergent energy scales and non-Fermi-liquid physics, requiring renormalization group treatment. This has typically been at odds with the description of their nonequilibrium steady-state under finite bias, which exposes their nature as open quantum systems. We present a novel numerically-exact method for obtaining the nonequilibrium state of a general quantum impurity coupled to metallic leads at arbitrary voltage or temperature bias, which we call "RL-NESS" (Renormalized Lindblad-driven NonEquilibrium Steady-State). It is based on coherently coupling the impurity to discretized leads which are treated exactly. These leads are furthermore weakly coupled to reservoirs described by Lindblad dynamics which impose voltage or temperature bias. Going beyond previous attempts, we exploit a hybrid discretization scheme for the leads together with Wilson's numerical renormalization group, in order to probe exponentially small energy scales. The steady-state is then found by evolving a matrix-product density operator via real-time Lindblad dynamics, employing a dissipative generalization of the time-dependent density matrix renormalization group. In the long-time limit, this procedure converges to the steady-state at finite bond dimension due to the introduced dissipation, which bounds the growth of entanglement. We test the method against the exact solution of the noninteracting resonant level model. We demonstrate its power using an interacting two-level model, for which it correctly reproduces the known limits, and gives the full $I$-$V$ curve between them.

On a Statistical Mechanics Approach to Some Problems of the Social Sciences

This work is a survey of some results on a statistical mechanics approach to the social sciences emerged in the last two decades. The pioneering work of Daniel McFadden, known as discrete choice theory, is interpreted in terms of a non-interacting model and extended along the lines of the Brock and Durlauf interacting systems. The generalization to the multi-populated model is presented and two specific case studies are reviewed with their phenomenological and theoretical analysis.

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength $U$ between particles. Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin components. The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases. We show that this phenomenon originates from the molecular or scattering-like nature of the pair states available at given energy $E$ and disorder strength $W$. The disorder-averaged density of states of the effective model for the pair is also investigated. Finally, we discuss the implications of our results for ongoing research on many-body localization.