Nearest-neighbor Interactions Research Articles

Exactly solvable inhomogeneous fermion systems

Abstract 15 exactly solvable inhomogeneous (spinless) fermion systems on one-dimensional lattices are constructed explicitly based on the discrete orthogonal polynomials of Askey scheme, e.g. the Krawtchouk, Hahn, Racah, Meixner, q-Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground state two point correlation functions are derived explicitly. The multi point correlation functions are obtained by Wick’s Theorem. Corresponding 15 exactly solvable XX spin systems are also displayed. They all have nearest neighbour interactions. The exact solvability of Schrödinger equation means that of the corresponding Fokker-Planck equation. This leads to 15 exactly solvable Birth and Death fermions and 15 Birth and Death spin models. These provide plenty of materials for calculating interesting quantities, e.g. entanglement entropy, etc.

Model-free distributed state estimation with local measurements.

In this paper, the state estimation problem of physical plants with unknown system dynamic is revisited from the perspective of limited output information measurement, which corresponds to those with characteristics of high-dimensional, wide-area coverage and scatter. Given this fact, a network of sensors are used to carry out the measurement with each one accessing only partial outputs of the targeted systems and a novel model-free state estimation approach, named distributed stochastic variational inference state estimation, is proposed. The key idea of this method is to compensate for the impacts of local output measurements by adding nearest-neighbor rule-based information interaction among estimators to complete the state estimation. It finds from the numerical experiments that the proposed method has clear advantages in both estimation accuracy and speed, and it also provides guidance on how to improve the efficiency of state estimation under local measurements.

Generalized hydrodynamics and approach to generalized Gibbs equilibrium for a classical harmonic chain

Abstract We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two generalized Gibbs ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the generalized hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as ∼ 1 / t to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady-state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as ∼ 1 / t for the densities and as ∼ 1 / t 2 for the currents. We compare the analytical results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

Chemical Design of Spin Frustration to Realize Topological Spin Glasses.

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal-organic framework (MOF) platform, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin-spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Pairing correlation of the kagome-lattice Hubbard model with the nearest-neighbor interaction

Abstract A recently discovered family of kagome lattice materials, AV3Sb5 (A = K,Rb,Cs), has attracted great interest, especially in the debate over their dominant superconducting pairing symmetry. To explore this issue, we study the superconducting pairing behavior within the kagome-lattice Hubbard model through the constrained path Monte Carlo method. It is found that doping around the Dirac point generates a dominant next-nearest-neighbor-d pairing symmetry driven by on-site Coulomb interaction U. However, when considering the nearest-neighbor interaction V, it may induce nearest-neighbor-p pairing to become the preferred pairing symmetry. Our results provide useful information to identify the dominant superconducting pairing symmetry in the AV3Sb5 family.

Signatures of spin-liquid-like state and spin-phonon coupling in square lattice Sr2CuTe0.5W0.5O6

A spin-liquid state can be induced by uncompensated interactions in the spin lattice due to disorder or randomness in exchange pathways. Sr2CuTeO6 and Sr2CuWO6 are square-lattice antiferromagnetic double perovskites (A2BB′O6) with dominant nearest-neighbor (Néel-type) and next-nearest neighbor (Columnar-type) magnetic interactions, respectively. Random distribution of these interactions in a system has been theoretically predicted to be a way to induce the spin-liquid state. Here, we have synthesized a spin-liquid candidate Sr2CuTe0.5W0.5O6 with B′-site mixing of its parent systems (Sr2CuTeO6 and Sr2CuWO6) to explore the phonon properties and their correlations with the liquid-like magnetic interactions. Our measurements reveal the presence of a broad continuum in the Raman spectrum of Sr2CuTe0.5W0.5O6, instead of the well-defined spin-wave excitations (magnon) observed in the parent systems. Observation of continuum feature in the Raman spectrum in conjunction with the lack of long-range magnetic order provide the signatures of liquid-like correlations. On the other hand, phonon anomalies are observed below the short-ranged magnetic ordering temperature indicating the onset of spin-phonon coupling.

Signatures of the attractive interaction in spin spectra of one-dimensional cuprate chains

Identifying the minimal model for cuprates is crucial for explaining the high-Tc pairing mechanism. Recent photoemission experiments have suggested a significant near-neighbor attractive interaction V in cuprate chains, favoring pairing instability. To determine its strength, we systematically investigate the dynamical spin structure factors S(q,ω) using the density matrix renormalization group. Our analysis quantitatively reveals a notable softening in the two-spinon continuum, particularly evident in the intense spectrum at large momentum. This softening is primarily driven by the renormalization of the superexchange interaction, as determined by a comparison with the slave-boson theory. We also demonstrate the feasibility of detecting this spectral shift in thin-film samples using resonant inelastic x-ray scattering. Therefore, this provides a distinctive fingerprint for the attractive interaction, motivating future experiments to unveil essential ingredients in cuprates. Published by the American Physical Society 2024

Condensate formation in a chiral lattice gas

Abstract We investigate the formation of condensates in a binary lattice gas in the presence of chiral interactions. These interactions differ between a given microscopic configuration and its mirror image. We consider a two dimensional lattice gas with nearest-neighbour interactions to which we add interactions involving favoured local structures that are chiral. We focus on favoured local structures that have the shape of the letter L and explore condensate formation through simulations and analytical calculations. At low temperature, this model can exhibit four different phases that are characterised by different periodic tiling patterns, depending on the strength of interactions and the chemical potential. When particle numbers are conserved, some of these phases can coexist. We analyse the structure and surface tension of interfaces between coexisting phases and determine the shapes of minimal free energy of crystalline condensates. We show that these shapes can be quadrilaterals or octagons of different orientation and symmetry.

Theoretical Investigations and Comparisons of the Amorphous Structures of Adamantane-like Cluster Materials Utilizing Molecular Dynamics Simulations.

Cluster materials of the composition AdR4 (Ad = adamantane, R = organic substituent) and [(RT)4E6] (R = organic substituent; T = Si, Ge, Sn; and E = S, Se, Te) exhibit directional white light emission or produce second harmonics when irradiated with a continuous wave infrared laser source. The nature of the nonlinear optical properties correlates with the macroscopic structures of the cluster materials. The desired white light emission predominantly occurs in amorphous materials. It is therefore crucial to understand the geometric structures of the materials and the order within the materials. Here, we investigate the geometric structures of 12 different adamantane-like cluster materials by molecular dynamics simulations using a nonperiodic particle approach. The comparison of the calculated structure factors for two cluster materials with the corresponding experimental data obtained from diffraction and EXAFS measurements shows very good agreement. Our computations revealed that, on the one hand, larger, more flexible core structures (Ad < {Si4S6} < {Ge4S6} < {Sn4S6}) tend to lead to amorphous solids. On the other hand, larger substituents (methyl < phenyl < naphthyl) lead to more defined nearest neighbor interactions, with a tendency toward crystalline solids. Overall, our results show that a beginning order in the material results from a combination of the degree of flexibility of the core structure and the variation of the nearest neighbor interaction determined by the substituents.

A statistical-physics approach for codon usage optimisation

The concept of “codon optimisation” involves adjusting the coding sequence of a target protein to account for the inherent codon preferences of a host species and maximise protein expression in that species. However, there is still a lack of consensus on the most effective approach to achieve optimal results. Existing methods typically depend on heuristic combinations of different variables, leaving the user with the final choice of the sequence hit. In this study, we propose a new statistical-physics model for codon optimisation. This model, called the Nearest-Neighbour interaction (NN) model, links the probability of any given codon sequence to the “interactions” between neighbouring codons. We used the model to design codon sequences for different proteins of interest, and we compared our sequences with the predictions of some commercial tools. In order to assess the importance of the pair interactions, we additionally compared the NN model with a simpler method (Ind) that disregards interactions. It was observed that the NN method yielded similar Codon Adaptation Index (CAI) values to those obtained by other commercial algorithms, despite the fact that CAI was not explicitly considered in the algorithm. By utilising both the NN and Ind methods to optimise the reporter protein luciferase, and then analysing the translation performance in human cell lines and in a mouse model, we found that the NN approach yielded the highest protein expression in vivo. Consequently, we propose that the NN model may prove advantageous in biotechnological applications, such as heterologous protein expression or mRNA-based therapies.

One dimensional lattice fluid mixture with nearest neighbour interactions

We present an exact derivation of the free energy functional of a fluid mixture of hard rods with arbitrary sizes on a one-dimensional lattice. Our approach is based on the Wertheim cluster theory which consists of mapping a system with finite range interactions to the system with pure hard-core interaction but with modified activities. We show that the free energy functional has the same form as the fundamental measure functional. The interactions part of the free energy has two contributions, one from the one-particle cavity restricted to the hard rod or hard-sphere diameter and a second from the two-particle cavity which includes the finite range of the interaction. In the limit of a one-component system, our results reduce to the one derived using the Markov chain approach. For vanishing interactions, the density functionals coincide exactly with the previously derived for the mixture of hard rods with pure hard-core interaction.

Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers

We present the quantum simulation of the frustrated quantum spin-12 antiferromagnetic Heisenberg spin chain with competing nearest-neighbor (J1) and next-nearest-neighbor (J2) exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era. Published by the American Physical Society 2024

Phase diagram and ground state of a decorated antiferromagnetic Ising model on a triangular lattice with nearest and next nearest neighbor interactions

The static critical behavior of the two-dimensional decorated Ising model on a triangular lattice is studied using computational physics methods. The exchange interaction between the nearest nodal neighbors and between the next nearest nodal neighbors was antiferromagnetic. The exchange interaction between nodal and decorated spins varied over a wide range from antiferromagnetic to ferromagnetic. The ground state of the model is determined, critical temperatures are calculated, and the phase diagram is constructed for the entire range of exchange interactions between nodal and decorated spins. Our results showed that decoration can lead to frustration effects, the appearance of new phases, and change the type of phase transition depending on the value and sign of the decorated exchange interaction.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Study of Concentration Quenching and Energy Transfer Mechanism in Ce Doped Y2O3 Nanomaterials.

We study concentration quenching and energy transfer mechanisms of yttrium oxide (Y2O3) nanomaterials doped with different concentrations (0-5mol%) of cerium (Ce). Photoluminescence (PL) spectra recorded under an excitation wavelength of 350nm show a broad emission band at ∼ 406nm and a feeble emission band at ∼ 463nm in the undoped Y2O3 sample. The doping of Ce in Y2O3 induced multiple PL peaks within the blue-green region of the spectrum in all the doped samples with the peak at ∼ 466nm being notably the prominent one. This prominent emission band exhibits a decrease in intensity with increasing Ce concentration due to concentration quenching. Analysis of Time-resolved photoluminescence (TRPL) spectra reveal that the average emission lifetime of Ce-doped Y2O3 is shorter than that of the undoped Y2O3 sample. The concentration quenching effect and the decrease of average emission lifetime of the dominant emission band are explained on the basis of energy transfer from the host Y2O3 to the Ce3+ ion centres. The critical quenching concentration of Ce3+ ion in Y2O3:Ce phosphor was identified to be 1mol% and the critical transfer distance was estimated to be 23.74 Å. Analysis reveal that the concentration quenching mechanism involves nearest-neighbour interaction.

Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices

We investigate the frustrated J 1–J 2 Ising model with nearest-neighbor interaction J 1 and next-nearest-neighbor interaction J 2 in two kinds of generalized triangular lattices (GTLs) employing the Wang–Landau Monte Carlo method and finite-size scaling analysis. In the first GTL (GTL1), featuring anisotropic properties, we identify three kinds of super-antiferromagnetic ground states with stripe structures. Meanwhile, in the second GTL (GTL2), which is non-regular in next-nearest-neighbor interaction, the ferrimagnetic 3×3 and two kinds of partial spin liquid (PSL) ground states are observed. We confirm that residual entropy is proportional to the number of spins in the PSL ground states. Additionally, we construct finite-temperature phase diagrams for ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. In GTL1, the transition into the ferromagnetic phase is continuous, contrasting with the first-order transition into the stripe phase. In GTL2, the critical temperature into the ferromagnetic ground state decreases as antiferromagnetic next-nearest-neighbor interaction intensifies until it meets the 3×3 phase boundary. For intermediate values of the next-nearest-neighbor interaction, two successive transitions emerge: one from the paramagnetic phase to the ferromagnetic phase, followed by the other transition from the ferromagnetic phase to the 3×3 phase.

Large magnetocaloric refrigeration performance near room temperature in monolayer transition metal dihalides

Magnetocaloric effect (MCE) exhibits highly efficient and ecological cooling abilities for solid-state refrigeration in contrast to traditional vapor-compression refrigeration. Successive emerging two-dimensional (2D) magnetic materials provide a fertile platform for exploring low-dimensional MCE systems. Here, we focus on a series of 2D transition metal dihalides MX2 (M = Fe, Ru, Os; X = Cl, Br) to explore the maximum isothermal magnetic entropy change (−ΔSmagmax) and adiabatic temperature change (ΔTadmax) under external magnetic field. It is found that FeCl2, FeBr2, and RuCl2 have intrinsically sizable −ΔSmagmax, ΔTadmax, and high thermal conductivity near room temperature, demonstrating superior comprehensive refrigeration performance in comparison with other 2D magnets. It is revealed that strong nearest-neighbor ferromagnetic exchange interaction plays a decisive role in −ΔSmagmax, and the high lattice thermal conductivities of FeCl2 and RuCl2 are attributed to the longer phonon lifetime and larger group velocity of low-frequency acoustic branch. Moreover, moderate strain and carriers doping are able to effectively regulate Curie temperature and magnetocrystalline anisotropy energy and correspondingly enhance −ΔSmagmax. The present work provides important insights for the exploration of 2D magnets for magnetocaloric refrigeration near room temperature.

Modeling public opinion control by a charismatic leader

We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature T models an idealized social climate, representing an authoritarian regime if T is low or a liberal one if T is high. We derive a mean-field solution for the average magnetization m, the “social mood”, and investigate how m and the super spin magnetization vary as a function of T. We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.

Manipulating and investigating the room-temperature magnetic memory phenomenon: The impact of rare-earth ion doping on nickel oxide nanoparticles

This study investigates the relationship between point defect density and magnetic properties in nickel oxide (NiO) nanoparticles (NPs). Specifically, we explore the effects of 0.5 % trivalent rare-earth ion (RE3+: Ce3+, Pr3+, Nd3+, Sm3+, and Dy3+) doping on NiO NPs, considering the influence of RE3+ ionic radius on structural modulation and magnetic properties. Our findings reveal important trends: increased microstrain (0.08 %–0.17 %) and decreased crystalline size (36–17 nm) with increasing ionic radius (r = 0.91 to 1.01 Å), along with a preference for growth along the (1 1 1) plane over (2 0 0). Additionally, multivalent point defects increase with the increase of ionic radius. Substituting Ni2+ site with RE3+ ion promotes nearest-neighbor weak ferromagnetic interaction over next-nearest-neighbor strong antiferromagnetic (AF) interaction. This leads to a redshift of two magnons (2 M) frequency by 50 cm−1 and enhanced room temperature (RT) magnetization (0.23–0.43 emu/g) with increasing ionic radius. Ce-doped NiO (r = 1.01 Å) shows the smallest crystalline size (17 nm), maximum 2 M redshift, and enhanced RT magnetization (0.43 emu/g) based on interacting bound magnetic polaron model. Ce-, Pr-, Nd-, and Sm-doped NiO NPs exhibit RT magnetic memory effects, while Dy-doped NiO NPs (r = 0.912 Å) display AF properties. Our analysis provides valuable insights for designing RT magnetic memory materials with tailored properties through suitable RE3+ ion substitutions.

Thermally induced localization of dopants in a magnetic spin ladder

I unveil an emergent localization phenomenon pertaining to the motion of a dopant in a thermal spin lattice. This is rendered localized by thermal spin fluctuations, whereby it is in stark constrast to the intrinsic origin of Anderson localization for quenched disorder. The system of interest consists of spin-1/2 particles organized in a two-leg ladder with nearest-neighbor Ising interactions J. The motion of a hole—the dopant—is initialized by suddenly removing a spin from the thermal spin ensemble, which then moves along the ladder via nearest-neighbor hopping t. I find that the hole remains for all values of J/t and for nonzero temperatures. The origin is an effective disorder potential seen by the hole and induced by thermal spin fluctuations. Its length scale is found to match with the underlying spin-spin correlation length at low temperatures. For ferromagnetic couplings (J&lt;0), the associated localization length of the hole increases with decreasing temperature and becomes proportional to the correlation length at low temperatures, asymptotically delocalizing at low temperatures. For antiferromagnetic couplings (J&gt;0), there is a smooth crossover between thermal localization at high temperatures to localization driven by the antiferromagnetic order at low temperatures. At infinite temperatures, the dynamics becomes independent of the sign of the spin coupling, whereby the localization length is a universal function of |J|/t, diverging as (t/J)2 for |J|≪t. Finally, I analyze a setup with Rydberg-dressed atoms, which naturally realizes finite-range Ising interactions, accessible in current experimental setups. I show that the discovered localization phenomenon can be probed on experimentally accessible length- and timescales, providing a strong testing ground for my predictions. Published by the American Physical Society 2024