Nearest-neighbor Interactions Research Articles

Finite temperature phases and excitations of bosons on a square lattice: a cluster mean field study

We study the finite temperature phases and collective excitations of hardcore as well as softcore bosons on a square lattice with nearest and next nearest neighbor interactions, focusing on the formation of various types of supersolid (SS) phases and their stability under thermal fluctuations. The interplay between the on-site, nearest, and next nearest neighbor interactions leads to various density ordering and structural transitions, which we have plotted out. Thermodynamic properties and phase diagrams are obtained by cluster mean field theory at finite temperatures, which includes quantum effects systematically, and they are compared with the single-site mean field (MF) results. We investigate the melting process of the SS phase to normal fluid (NF), which can occur in at least two steps due to the presence of two competing orders in the SS. A tetra-critical point exists at finite temperature and exhibits intriguing behavior, which is analyzed for different regimes of interactions. The phase diagrams reveal the different pathways of the thermal transition of SSs to the NF phase, for different interaction regimes, which can be accessible by thermal quench protocols used in recent experiments. We show how the phases and the transitions between them can be identified from the characteristic features of the excitation spectrum. We analyze the appearance of a low-energy gapped mode apart from the gapless sound mode in the SS phase, which is analogous to the gapped mode recently studied for dipolar SS phases. Finally, we discuss the relevance of the results of the present work in the context of ongoing experiments on ultracold atomic gases and newly observed SS phases.

Gutzwiller approximation for indistinguishable interacting Brownian particles on a lattice.

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equationfor Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equationfor interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.

Control of magnetic states and spin interactions in bilayer CrCl3 with strain and electric fields: an ab initio study

Using ab initio density functional theory, we demonstrated the possibility of controlling the magnetic ground-state properties of bilayer CrCl_{3} by means of mechanical strains and electric fields. In principle, we investigated the influence of these two fields on parameters describing the spin Hamiltonian of the system. The obtained results show that biaxial strains change the magnetic ground state between ferromagnetic and antiferromagnetic phases. The mechanical strain also affects the direction and amplitude of the magnetic anisotropy energy (MAE). Importantly, the direction and amplitude of the Dzyaloshinskii–Moriya vectors are also highly tunable under external strain and electric fields. The competition between nearest-neighbor exchange interactions, MAE, and Dzyaloshinskii–Moriya interactions can lead to the stabilization of various exotic spin textures and novel magnetic excitations. The high tunability of magnetic properties by external fields makes bilayer CrCl_{3} a promising candidate for application in the emerging field of two-dimensional quantum spintronics and magnonics.

Time-resolved single-particle spectrum of the one-dimensional extended Hubbard model after interaction quenches

We investigate the non-equilibrium dynamics of the one-dimensional extended Hubbard model after interaction quenches. In strong-coupling regime with large on-site interaction, the ground states of this model with small and large nearest-neighbor interactions are in spin-density-wave and charge-density-wave phases, respectively. Combining twisted boundary conditions with the time-dependent Lanczos method, we obtain snapshots of the time-dependent single-particle spectrum after quenches. We find that for quench within the same phase, the single-particle spectrum becomes close to that of the quenched Hamiltonian immediately after the quench. While for quench across the critical point, the afterward evolution process depends mainly on the distribution of the initial state among the eigenstates of the quenched Hamiltonian. Our finding may serve as a way to detect the phase transition in ultracold atom systems with interactions.

Prethermal Fragmentation in a Periodically Driven Fermionic Chain.

We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.

A Gibbsian Random Tree with Nearest Neighbour Interaction

We revisit the random tree model with nearest-neighbour interaction as described in Dunlop and Mardin (J Stat Phys 189:38, 2022), enhancing growth. When the underlying free Bienaymé–Galton–Watson (BGW) model is sub-critical, the (non-Markov) model with interaction exhibits a phase transition between sub- and super-critical regimes. In the critical regime, using tools from dynamical systems, we show that the partition function of the model approaches a limit at rate $$n^{-1}$$ in the generation number n. In the critical regime with almost sure extinction, we also prove that the mean number of external nodes in the tree at generation n decays like $$n^{-2}$$ . Finally, we give a spin representation of the random tree, opening the way to tools from the theory of Gibbs states, including FKG inequalities. We extend the construction in Dunlop and Mardin (J Stat Phys 189:38, 2022), when the law of the branching mechanism of the free BGW process has unbounded support.

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional 1H zigzag spin chains in hambergite (Be2BO3OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long 1H spin–lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

Extremal Inhomogeneous Gibbs States for SOS-Models and Finite-Spin Models on Trees

We consider $${\mathbb {Z}}$$ -valued p-SOS-models with nearest neighbor interactions of the form $$|\omega _v-\omega _w|^p$$ , and finite-spin ferromagnetic models on regular trees. This includes the classical SOS-model, the discrete Gaussian model and the Potts model. We exhibit a family of extremal inhomogeneous (i.e. tree automorphism non-invariant) Gibbs measures arising as low temperature perturbations of ground states (local energy minimizers), which have a sparse enough set of broken bonds together with uniformly bounded increments along them. These low temperature states in general do not possess any symmetries of the tree. This generalises the results of Gandolfo et al. (J. Stat. Phys. 148:999–1005, 2012) about the Ising model, and shows that the latter behaviour is robust. We treat three different types of extensions: non-compact state space gradient models, models without spin-symmetry, and models in small random fields. We give a detailed construction and full proofs of the extremality of the low-temperature states in the set of all Gibbs measures, analysing excess energies relative to the ground states, convergence of low-temperature expansions, and properties of cutsets.

Strong coupling between a photon and a hole spin in silicon.

Spins in semiconductor quantum dots constitute a promising platform for scalable quantum information processing. Coupling them strongly to the photonic modes of superconducting microwave resonators would enable fast non-demolition readout and long-range, on-chip connectivity, well beyond nearest-neighbour quantum interactions. Here we demonstrate strong coupling between a microwave photon in a superconducting resonator and a hole spin in a silicon-based double quantum dot issued from a foundry-compatible metal-oxide-semiconductor fabrication process. By leveraging the strong spin-orbit interaction intrinsically present in the valence band of silicon, we achieve a spin-photon coupling rate as high as 330 MHz, largely exceeding the combined spin-photon decoherence rate. This result, together with the recently demonstrated long coherence of hole spins in silicon, opens a new realistic pathway to the development of circuit quantum electrodynamics with spins in semiconductor quantum dots.

Robust formation of metachronal waves in directional chains of phase oscillators

Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest-neighbor interactions, connected in a loop and with rotational symmetry, so each oscillator resembles every other oscillator in the chain. Numerical integrations of the discrete phase oscillator systems and a continuum approximation show that directional models (those that do not obey reversal symmetry), can exhibit instability to short wavelength perturbations but only in regions where the slope in phase has a particular sign. This causes short wavelength perturbations to develop that can vary the winding number that describes the sum of phase differences across the loop and the resulting metachronal wave speed. Numerical integrations of stochastic directional phase oscillator models show that even a weak level of noise can seed instabilities that resolve into metachronal wave states.

Behavior of circular chains of nonlinear oscillators with Kuramoto-like local coupling

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units. Instead of global couplings, the nearest-neighbor interaction is assumed. Units are pairwise coupled by a Kuramoto term driven by their phase differences. The system exhibits a rich set of behaviors depending on the balance between the natural frequency of isolated units and the self-feedback. The case of two oscillators is solved analytically, while a numerical approach is used for N > 2. Building from Kuramoto, the approach to synchronization, when possible, is studied through a local complex order parameter. The system can eventually evolve as a set of coupled local communities toward a given phase value. However, the approach to the stationary state shows a non-monotonous non-trivial dynamic.

Activity and steady‐state kinetics of one‐dimensional kinetic Ising model

AbstractIn this work, we focused on the kinetics of a one‐dimensional Ising system (1DIS) with constant nearest‐neighbor interaction (NNI). The exact solution of both thermodynamics and kinetics of this system under quasi‐chemical approximation (QCA) had been shown in the literature, and the equilibrium solution was exact. In this work, it was discussed why QCA applied the best in the case of 1DIS with constant NNI. Furthermore, extension had been made to discuss that due to this special reason, perhaps the kinetics of the system under QCA is the correct steady‐state kinetics. Inspired by this observation, the activity and activity coefficients of the system was studied closely to re‐examine the form of the equation of motion under QCA. A novel concept—the instantaneous activities and the corresponding instantaneous activity coefficients—was introduced, and in terms of these quantities the kinetics seemed to be much simpler and physically more meaningful. The chevron plot of this system was also discussed and new way of looking at the rollover of chevron plots was presented.

Analysis of a Thermodynamic Determination of the Surface Tension of a Two-Component Vapor–Liquid System

A numerical analysis is performed of a thermodynamic determination of the surface tension (ST) of a vapor–liquid binary mixture and interfacial tension (IT) between two liquid phases as the excess value of free energy ΔF of a two-phase system with and without for a phase boundary. Calculations are made in the simplest version of the lattice gas model (LGM), allowing for the interaction of nearest neighbors in a quasi-chemical approximation. Each node of a two-component mixture in the LGM system can be occupied by mixture components A + B and vacancy V. The two main ways of calculating ST, expressed in terms of different partial contributions Miq to excess free energy ΔF (where i = A, B, V are vacancies; 1 ≤ q ≤ κ, q is the number of the monolayer inside the boundary; and κ is its width), are compared, as are calculations of ST and IT as excess free energy ΔF for a lattice model with no vacancies. The ambiguity of ST and IT values depending on the type of Miq functions is obtained by calculating the temperature dependence for a flat boundary and the dependence of ST and IT on droplet size at a fixed temperature. The role of vacancies in the LGM as the main mechanical characteristic of the system under the condition of strict phase equilibrium in three equilibria (mechanical, energy, and chemical) is discussed.

Superconducting transmon qubit-resonator quantum battery

Quantum battery (QB) is the miniature energy storage and release device and plays a crucial role in future quantum technology. Here an implementation scheme of a QB is proposed on a superconducting circuit, which is composed by $N$ coupled transmon qubits and a one-dimensional transmission line resonator. We derive the Hamiltonian of the QB system and investigate its charging performance by considering three decay channels. We find that the presence of the decay channels suppresses the high oscillation of the energy storage process, thereby realizing a stable and powerful QB. In particular, compared with the resonator decay and the qubit relaxation, the qubit dephasing shows a counterintuitive advantage in our QB. We show that the nearest-neighbor interaction always has a positive impact on the stable energy and the coupling only significantly influences the maximum charging power in the fully nondegenerate ground-state region. We also demonstrate the feasibility of our approach by evaluating the QB performance under experimental parameters.

Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction

We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion (V2) and the nearest-neighbor exchange interaction (J). We use the truncated unity functional renormalization group approach to determine a schematic ground-state phase diagram with higher resolution in the parameter space of V2 and J. In the absence of the on-site repulsion and presence of sizable next-nearest-neighbor repulsion and enhanced nearest-neighbor exchange interaction, we encounter the quantum spin Hall phase, the spin-Kekulé phase, and the three-sublattice and the incommensurate charge-density-wave phases. We propose a scheme for combining consistently the truncated unity functional renormalization group and the mean-field approximation, which is distinct from the conventional one that directly uses the renormalization-group results as an input for the mean-field calculation. This scheme is used to study in detail the quantum spin Hall phase, presenting some characteristics like the bulk gap, the Chern number and the helical edge states.

Theoretical Analysis of Magnetic Coupling in the Ti2C Bare MXene.

The nature of the electronic ground state of the Ti2C MXene is unambiguously determined by making use of density functional theory-based calculations including hybrid functionals together with a stringent computational setup providing numerically converged results up to 1 meV. All the explored density functionals (i.e., PBE, PBE0, and HSE06) consistently predict that the Ti2C MXene has a magnetic ground state corresponding to antiferromagnetic (AFM)-coupled ferromagnetic (FM) layers. A spin model, with one unpaired electron per Ti center, consistent with the nature of the chemical bond emerging from the calculations, is presented in which the relevant magnetic coupling constants are extracted from total energy differences of the involved magnetic solutions using an appropriate mapping approach. The use of different density functionals enables us to define a realistic range for the magnitude of each of the magnetic coupling constants. The intralayer FM interaction is the dominant term, but the other two AFM interlayer couplings are noticeable and cannot be neglected. Thus, the spin model cannot be reduced to include nearest-neighbor interactions only. The Néel temperature is roughly estimated to be in the 220 ± 30 K, suggesting that this material can be used in practical applications in spintronics and related fields.

Hierarchical compositional ordering in lead-based perovskite relaxors

Lead-based relaxor ferroelectric perovskites with the formula $\mathrm{Pb}({\mathrm{B}}_{1/3}{\mathrm{B}}_{2/3}^{\ensuremath{'}}){\mathrm{O}}_{3}$, such as $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$, can have different degrees of compositional ordering even for the same stoichiometry. Despite intensive investigation, determining the nature of the B and ${\mathrm{B}}^{\ensuremath{'}}$ ordering remains a challenging problem. Here, we reveal a hierarchical ordering in $\mathrm{Pb}({\mathrm{B}}_{1/3}{\mathrm{B}}_{2/3}^{\ensuremath{'}}){\mathrm{O}}_{3}$ on top of the well-known ${\ensuremath{\beta}}^{\text{I}}$ and ${\ensuremath{\beta}}^{\text{II}}$ sublattices, which is the first level of the proposed hierarchy. Such additional ordering, which is found by considering additional nearest neighboring interactions in the model enriches our understanding of the complex nature of the chemical ordering in lead-based ferroelectric relaxors. In addition, we show that $\mathrm{Pb}({\mathrm{Cd}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ has a higher degree of ordering than that of $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ or $\mathrm{Pb}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ in which antiphase domains exist, revealing the possible different degree of compositional ordering arising from intralattice ordering.

Universal logic with encoded spin qubits in silicon

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2–21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22–28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5–9,16,18,20,22,27,29,31–37, the all-electrical and low-crosstalk-control of partial swap operations1,22–28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.

Turing patterns in simplicial complexes.

The spontaneous emergence of patterns in nature, such as stripes and spots, can be mathematically explained by reaction-diffusion systems. These patterns are often referred as Turing patterns to honor the seminal work of Alan Turing in the early 1950s. With the coming of age of network science, and with its related departure from diffusive nearest-neighbor interactions to long-range links between nodes, additional layers of complexity behind pattern formation have been discovered, including irregular spatiotemporal patterns. Here we investigate the formation of Turing patterns in simplicial complexes, where links no longer connect just pairs of nodes but can connect three or more nodes. Such higher-order interactions are emerging as a new frontier in network science, in particular describing group interaction in various sociological and biological systems, so understanding pattern formation under these conditions is of the utmost importance. We show that a canonical reaction-diffusion system defined over a simplicial complex yields Turing patterns that fundamentally differ from patterns observed in traditional networks. For example, we observe a stable distribution of Turing patterns where the fraction of nodes with reactant concentrations above the equilibrium point is exponentially related to the average degree of 2-simplexes, and we uncover parameter regions where Turing patterns will emerge only under higher-order interactions, but not under pairwise interactions.

Fast-forward adiabatic quantum dynamics of XY spin model on three spin system

We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity function together with the original Hamiltonian give fast-forward driving for adiabatic states. We apply our method to XY spin model by considering three spin systems on the Kagome lattice. In this model, we obtained the XY pair-wise exchange interaction of nearest neighbors and next-nearest neighbors should be added to the original Hamiltonian as a driving interaction to accelerate the adiabatic motion. This pair-wise driving interaction in the fast-forward scheme guarantees the complete fidelity of accelerated states.