One-dimensional Lattice Model Research Articles

Development of Nascent Focal Adhesions in Spreading Cells

The eukaryotic cell develops organelles to sense and respond to the mechanical properties of its surroundings. These mechanosensing organelles aggregate into symmetry-breaking patterns to mediate cell motion and differentiation on substrate. The spreading of a cell plated onto a substrate is one of the simplest paradigms in which angular symmetry-breaking assemblies of mechanical sensors are seen to develop. We review evidence for the importance of the edge of the cell-extracellular matrix adhesion area in the aggregation of mechanosensors and develop a theoretical model for the clustering of mechanosensors into nascent focal adhesions on this contact ring. To study the spatial patterns arising on this topological feature, we use a one-dimensional lattice model with a nearest-neighbor interaction between individual integrin-mediated mechanosensors. We find the effective Ginzburg-Landau free energy for this model and determine the spectrum of spatial modes as the cell spreads and increases its contact area with the substrate. To test our model, we compare its predictions with measured distributions of paxillin in spreading fibroblasts.

Mechanics and thermodynamics of a new minimal model of the atmosphere

The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere.

New integrable 1D models of superconductivity

In this paper we find new integrable one-dimensional lattice models of electrons. We describe all such nearest-neighbour integrable models with symmetry by classifying solutions of the Yang–Baxter equation following the procedure first introduced in []. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models cannot be diagonalized using the standard nested Bethe Ansatz.

Exploring universal and nonuniversal regimes of trimers from three-body interactions in one-dimensional lattices

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbour two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\leq-2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\rightarrow \infty$, while both attractive $U\leq0$ and $V\leq0$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\rightarrow -\infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V>>t$, $U<-2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems

Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)S(α)=lntr(ρα)/(1−α) of the reduced density matrix \rhoρ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, S^{(2)}S(2) can be tightly bound—from above and below—by the much easier accessible Rényi number entropy S^{(2)}_N=-\ln \sum_n p^2(n)SN(2)=−ln∑np2(n) which is a function of the probability distribution p(n)p(n) of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth—albeit logarithmically slower—of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal (bond) disorder.

A modified two-dimensional triangular lattice model under honk environment

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

Bare-Excitation Ground State of a Spinless-Fermion-Boson Model and W-State Engineering in an Array of Superconducting Qubits and Resonators.

This Letter unravels an interesting property of a one-dimensional lattice model that describes a single itinerant spinless fermion (excitation) coupled to zero-dimensional (dispersionless) bosons through two different nonlocal coupling mechanisms. Namely, below a critical value of the effective excitation-boson coupling strength, the exact ground state of this model is the zero-quasimomentum Bloch state of a bare (i.e., completely undressed) excitation. It is demonstrated here how this last property of the lattice model under consideration can be exploited for a fast, deterministic preparation of multipartite W states in a readily realizable system of inductively coupled superconducting qubits and microwave resonators.

Entanglement front generated by an impurity traveling in an isolated many-body quantum system

We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front which never fades. We argue that these effects are valid for generic systems whose correlations propagate inside a light-cone. To assess the fully chaotic regime, we formulate a random circuit model which supports a moving impurity and a sharp lightcone. Although the qualitative behavior is similar to the integrable case, the endogenous regime is only visible at short times due to the onset of diffusive energy transport. Our predictions are supported by numerical simulations in the different regimes.

Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials

We study theoretically the localization properties of two distinct one-dimensional quasiperiodic lattice models with a single-particle mobility edge (SPME) separating extended and localized states in the energy spectrum. The first one is the familiar Soukoulis-Economou trichromatic potential model with two incommensurate potentials, and the second is a system consisting of two coupled 1D Aubry-Andre chains each containing one incommensurate potential. We show that as a function of the Hamiltonian model parameters, both models have a wide single-particle intermediate phase (SPIP), defined as the regime where localized and extended single-particle states coexist in the spectrum, leading to a behavior intermediate between purely extended or purely localized when the system is dynamically quenched from a generic initial state. Our results thus suggest that both systems could serve as interesting experimental platforms for studying the interplay between localized and extended states, and may provide insight into the role of the coupling of small baths to localized systems. We also calculate the Lyapunov (or localization) exponent for several incommensurate 1D models exhibiting SPME, finding that such localization critical exponents for quasiperiodic potential induced localization are nonuniversal and depend on the microscopic details of the Hamiltonian.

1D topological phases in transition-metal monochalcogenide nanowires.

The Su-Schrieffer-Heeger (SSH) model is a prototypical one-dimensional (1D) diatomic lattice model for non-trivial topological phases and topological excitations. Theoretically, many variations and extensions of the SSH model have been proposed and explored to better understand the novel aspects of topological physics in low dimensions on the nanoscale. However, the outstanding challenge remains to find real nanomaterials with robust structural stability for realizing the 1D topological states. Here, we develop an extended version of the SSH model with multi-atomic bases of four, six and eight atoms and an imposed screw rotation symmetry. Furthermore, based on first-principles calculations, we demonstrate the realization of this model in transition metal monochalcogenide M6X6 (M = Mo and W; X = S, Se and Te) nanowires. The topological features of the doped M6X6 nanowires are confirmed with non-trivial edge modes and e/2 fractional charges, representative of the 1D non-trivial Zak phase. Our finding not only sheds new light on our fundamental understanding of 1D topological physics, but also significantly extends the scope of 1D topological materials that will attract immediate experimental interest, since isolated M6X6 nanowires have already been synthesized in experiments.

Unraveling the excitation spectrum of many-body systems from quantum quenches

Quenches are now routinely used in synthetic quantum systems to study a variety of fundamental effects, including ergodicity breaking, light-cone-like spreading of information, and dynamical phase transitions. It was shown recently that the dynamics of equal-time correlators may be related to ground-state phase transitions and some properties of the system excitations. Here, we show that the full low-lying excitation spectrum of a generic many-body quantum system can be extracted from the after-quench dynamics of equal-time correlators. We demonstrate it for a variety of one-dimensional lattice models amenable to exact numerical calculations, including Bose and spin models, with short- or long-range interactions. The approach also applies to higher dimensions, correlated fermions, and continuous models. We argue that it provides an alternative approach to standard pump-probe spectroscopic methods and discuss its advantages.

Superconducting Correlations in the One-Dimensional Kondo Lattice Models under Magnetic Fields

We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.

Large deviations in renewal models of statistical mechanics

In Zamparo (2019 (arXiv:1903.03527)) the author has recently established sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a separable Banach space. The renewal model has been there identified with constrained and non-constrained pinning models of polymers, which amount to Gibbs changes of measure of a classical renewal process. In this paper we show that the constrained pinning model is the common mathematical structure to the Poland–Scheraga model of DNA denaturation and to some relevant one-dimensional lattice models of statistical mechanics, such as the Fisher–Felderhof model of fluids, the Wako–Saitô–Muñoz–Eaton model of protein folding, and the Tokar–Dreyssé model of strained epitaxy. Then, in the framework of the constrained pinning model, we develop an analytical characterization of the large deviation principles for cumulative rewards corresponding to multivariate deterministic rewards that are uniquely determined by, and at most of the order of magnitude of, the time elapsed between consecutive renewals. In particular, we outline the explicit calculation of the rate functions and successively we identify the conditions that prevent them from being analytic and that underlie affine stretches in their graphs. Finally, we apply the general theory to the number of renewals. From the point of view of equilibrium statistical physics and statistical mechanics, cumulative rewards of the above type are the extensive observables that enter the thermodynamic description of the system. The number of renewals, which turns out to be the commonly adopted order parameter for the Poland–Scheraga model and for also the renewal models of statistical mechanics, is one of these observables.

Weak coupling magnetism of the ionic Kondo lattice model

We consider a one-dimensional ionic Kondo lattice model, which consists of a hopping term, a local spin-spin interaction, and an alternating one-particle potential. With this model, which is feasible with cold atom setups, we show that it is possible to obtain a quasi-long-range magnetic order for small local couplings, using the density matrix renormalization group method. We found a quasi-long-range antiferromagnetic phase, which is absent in the original model but common for Kondo lattice materials. For weak local couplings and potentials of great strength, we found a quasi-long-range ferromagnetic-antiferromagnetic ground state crossover when the global commensurate density increases.

Crystallization Kinetics of Poly(ethylene oxide) under Confinement in Nanoporous Alumina Studied by in Situ X-ray Scattering and Simulation.

While a relatively complete understanding of the nucleation and orientation of polymers under confinement in one-dimensional nanochannels has been achieved, crystallization kinetics investigation of confined polymers is still rare. In this work, we investigated the crystallization kinetics of poly(ethylene oxide) confined in anodic alumina oxide templates with different pore sizes using in situ wide-angle X-ray scattering (WAXS). The crystallization kinetics results were fitted with the Avrami equation. The Avrami index was determined by both "isothermal step crystallization" and in situ WAXS. The crystallization process of polymers under one-dimensional nanopore confinement was simulated by a "one-dimensional lattice model". Based on this model, it is shown that homogeneous nucleation with the simultaneous growth of multiple crystal planes with drastically different growth rates could result in Avrami indexes lower than 1.

Non-Markovian stochastic Schrödinger equation in k-space toward the calculation of carrier dynamics in organic semiconductors.

A non-Markovian stochastic Schrödinger equation developed in our former work [Y. Ke and Y. Zhao, J. Chem. Phys. 147, 184103 (2017)] is extended to the reciprocal (k-) space to calculate the carrier dynamics in organic semiconductors with both local and nonlocal carrier-phonon interactions taken into account. The validity of this approach is examined by comparing with numerically exact benchmark results. As an application, the carrier mobilities are calculated within a one-dimensional periodic lattice model. The results reveal an inversion in the magnitude of the mobility as the nonlocal carrier-phonon interaction varies from weak to strong strengths, indicating a transition of the transport mechanism. This is also demonstrated by a variation in the temperature dependence of the mobility. In addition, a transient localization diffusive behavior caused by intramolecular vibrations is also found.

Spin-current diode with a monoaxial chiral magnet

Monoaxial chiral magnets exhibit a chiral conical magnetic state in a magnetic field parallel to the chiral axis. The conical spins carry the potential for nonreciprocal transport phenomena, as they break both spatial inversion and time reversal symmetries. Here, we study the spin-dependent transport in the chiral conical magnetic state, using the Landauer method based on Green's functions for a one-dimensional Kondo lattice model. We show that the system exhibits nonreciprocal spin transport, which depends on the chirality, period, cone angle, and polarization of the spin current. In particular, we find the distinct cone angle dependence between the spin textures with long and short periods. We also show that the nonreciprocity is related to the spin states of itinerant electrons near the leads. Our results indicate that the chiral cone acts as a spin-current diode, which can be flexibly controlled by a magnetic field.

Ground-State Phase Diagram of theS= 1 One-Dimensional Kondo Lattice Model with a Uniaxial Anisotropy under Transverse Fields

We study the effects of transverse magnetic fields on the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy using the density matrix renormalization group. The model can be regarded as a simplified one for analyzing the Ising ferromagnetic superconductor URhGe. We find various phases such as ferromagnetic and antiferromagnetic phases, Kondo plateau (KP) phases, Tomonaga-Luttinger liquids, and fully polarized phases. In the KP phase, a pseudoplateau emerges in the magnetization due to strongly bound pairs between the local and the conduction electron spins. This is why we call this phase the Kondo plateau. At the critical field between the ferromagnetic and KP phases, we find metamagnetic behavior in the magnetization curve. We discuss various correlation functions and the Friedel oscillations in detail, and the experimental data under transverse magnetic fields in URhGe are discussed on the basis of the present results.

Normal modes of a spin cycloid or helix

Although spin cycloids and helices are quite common, remarkably little is known about the normal modes of a spin cycloid or helix with finite length on a discrete lattice. Based on simple one-dimensional lattice models, we numerically evaluate the normal modes of a spin cycloid or helix produced by either Dzyaloshinskii-Moriya (DM) or competing exchange (CE) interactions. The normal modes depend on the type of interaction and on whether the nearest-neighbor exchange is antiferromagnetic (AF) or ferromagnetic (FM). In the AF/DM and FM/DM cases, there is only a single Goldstone mode; in the AF/CE and FM/CE cases, there are three. For FM exchange, the spin oscillations produced by non-Goldstone modes contain a mixture of tangential and transverse components. For the DM cases, we compare our numerical results with analytic results in the continuum limit. Examples are given of materials that fall into all four cases.

The effect of boundaries and impurity on a system with non-local hop dynamics

We study a one-dimensional lattice model of particles which interact with each other via hard-core repulsion, and which can make long hops in addition to the usual nearest neighbour hopping dynamics. The parameter p gives the probability for long hops and the p = 0 limit leads to the well studied totally asymmetric simple exclusion process (TASEP). The first part of this study describes the combined effect of open boundaries and long hops on the steady state of the system. Apart from the usual low density (LD), high density (HD) and maximum current (MC) phases, the introduction of a finite p leads to a new possibility-an empty road (ER) phase with particles clearing out faster than they enter. The variation in the phase diagram with p is interesting, with the LD and MC phases vanishing at large values of p while the ER and HD phases divide the parameter space into 1/2. In the second part of this study, we look at the combined effect of long hops and static/dynamic impurities. The boundaries are taken to be periodic for simplicity. We see that the system with a static impurity and with 0 < p < 1 shows a phase transition from a shock phase characterised by finite densities on either side of the shock (HD–LD phase) to a phase where the density on one side of the shock is zero (HD-ER phase). We also study the effect of a dynamic impurity, introduced via a slow particle. Here, the system undergoes a phase transition from a homogeneous phase to a shock phase depending on the density, the speed of the particle, as well as the probability p. The shock phase dominates the phase diagram at large values of p. All our studies involve numerical simulations which are supported by mean field theory arguments. The mean field approximation works well qualitatively and correctly identifies the possible phases, while the quantitative agreement with numerics varies, depending on parameter values.