Hard-core System Research Articles

Driven transport of soft Brownian particles through pore-like structures: Effective size method

Single-file transport in pore-like structures constitutes an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here, we study how softness in the particle interaction affects the emergent transport behavior. To this end, we investigate the driven Brownian motion of particles in a periodic potential. The particles interact via a repulsive softcore potential with a shape corresponding to a smoothed rectangular barrier. This shape allows us to elucidate effects of mutual particle penetration and particle crossing in a controlled manner. We find that even weak deviations from the hardcore case can have a strong impact on the particle current. Despite this fact, knowledge about the transport in a corresponding hardcore system is shown to be useful to describe and interpret our findings for the softcore case. This is achieved by assigning a thermodynamic effective size to the particles based on the equilibrium density functional of hard spheres.

Quantum phase transitions in a ν=12 bosonic fractional Chern insulator

Interacting quantum many-body systems often generate exotic orders, either topological or conventional competing orders. Understanding these phases and the phase transitions between them are common issues in condensed-matter physics. How to characterize these states in a convincing and convenient way remains ambiguous. Here, we report our numerical study on the interacting $\ensuremath{\nu}=\frac{1}{2}$ hard-core boson system with topological flat bands based on the infinite density matrix group algorithm. We explicitly show that the entanglement spectral flow can be used to diagnose the quantum phases emerging in the hard-core boson systems. In particular, the subsequent charge pumping exhibits a linear, sinelike, and indiscernible dependence by the flux threading in the fractional Chern insulator, supersolid, and solid state, respectively. The real-space boson occupancy in the thermodynamic limit is further calculated for a better understanding of the respective state. We compare the phase diagram obtained here with that obtained by the previously exact diagonalization method, and qualitative differences are observed. Therefore, the infinite density matrix group algorithm provides a convincing and convenient way to study the phase transition in such a strongly correlated topological system.

ϕ4theory Hamiltonian for fluids: Application to the surface tension near the critical point

We show that the surface tension of fluid near the critical point may be correctly described by taking into consideration the microscopic structure of the system using a {\phi}4 field theory. We revise the theory of the surface tension near criticality to take into account a microscopic structure of the fluid. Focusing on the case of the Lennard-Jones fluid, we express the surface tension in terms of the compressibility of the reference hard-core system and its derivatives with respect to density. We demonstrate that the obtained analytical microscopic expression for the surface tension near the critical point is in a good agreement with numerical experiments, which emphasizes the impact of microscopic structure on the critical behavior of the surface tension in fluids. Our analysis provides a basis for studying the surface tension in small-volume systems important in many technological applications.

Survival of current in a periodically driven hard-core bosonic system

We study the survival of the current induced initially by applying a twist at the boundary of a chain of hard-core bosons (HCBs), subject to a periodic double $\delta$-function kicks in the staggered on-site potential. We study the current flow and the work-done on the system at the long-time limit as a function of the driving frequency. Like a recent observation in the HCB chain with single $\delta$-function kick in the staggered on-site potential, here we also observe many dips in the current flow and concurrently many peaks in the work-done on the system at some specific values of the driving frequency. However, unlike the single kicked case, here we do not observe a complete disappearance of the current in the limit of a high driving frequency, which shows the absence of any dynamical localization in the double $\delta$-functions kicked HCB chain. Our analytical estimations of the saturated current and the saturated work-done, defined at the limit of a large time together with a high driving frequency, match very well with the exact numerics. In the case of the very small initial current, induced by a very small twist $\nu$, we observe that the saturated current is proportional to $\nu$. Finally, we study the time-evolution of the half-filled HCB chain where the particles are localized in the central part of the chain. We observe that the particles spread linearly in a light-cone like region at the rate determined by the maximum value of the group velocity. Except for a very trivial case, the maximum group velocity never vanishes, and therefore we do not observe any dynamical localization in the system.

Many-body localization with synthetic gauge fields in disordered Hubbard chains

We analyze the localization properties of the disordered Hubbard model in the presence of a synthetic magnetic field. An analysis of level spacing ratios shows a clear transition from ergodic to many-body localized phase. The transition shifts to larger disorder strengths with increasing magnetic flux. Study of dynamics of local correlations and entanglement entropy indicates that charge excitations remain localized whereas spin degree of freedom gets delocalized in the presence of the synthetic flux. This residual ergodicity is enhanced by the presence of the magnetic field with dynamical observables suggesting incomplete localization at large disorder strengths. Furthermore, we examine the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed as opposed to the fermionic case.

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion.

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by the use of the random sequential adsorption with a surface diffusion model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage.

Randomness of Eigenstates of Many-Body Quantum Systems.

The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.

Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas

The scaling of the largest eigenvalue $\lambda_0$ of the one-body density matrix of a system with respect to its particle number $N$ defines an exponent $\mathcal{C}$ and a coefficient $\mathcal{B}$ via the asymptotic relation $\lambda_0 \sim \mathcal{B}\,N^{\mathcal{C}}$. The case $\mathcal{C}=1$ corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well known result also confirmed by bosonization gives instead $\mathcal{C}=1/2$. Here we investigate the inhomogeneous case, initially addressing the behaviour of $\mathcal{C}$ in presence of a general external trapping potential $V$. We argue that the value $\mathcal{C}= 1/2$ characterises the hard-core system independently of the nature of the potential $V$. We then define the exponents $\gamma$ and $\beta$ which describe the scaling with $N$ of the peak of the momentum distribution and the natural orbital corresponding to $\lambda_0$ respectively, and we derive the scaling relation $\gamma + 2\beta= \mathcal{C}$. Taking as a specific case the power-law potential $V(x)\propto x^{2n}$, we give analytical formulas for $\gamma$ and $\beta$ as functions of $n$. Analytical predictions for the coefficient $\mathcal{B}$ are also obtained. These formulas are derived exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent.

Charge order–superfluidity transition in a two-dimensional system of hard-core bosons and emerging domain structures

We have used high-performance parallel computations by NVIDIA graphics cards applying the method of nonlinear conjugate gradients and Monte Carlo method to observe directly the developing ground state configuration of a two-dimensional hard-core boson system with decrease in temperature, and its evolution with deviation from a half-filling. This has allowed us to explore unconventional features of a charge order—superfluidity phase transition, specifically, formation of an irregular domain structure, emergence of a filamentary superfluid structure that condenses within of the charge-ordered phase domain antiphase boundaries, and formation and evolution of various topological structures.

Supercritical fluid of particles with a Yukawa potential: A new approximation for the direct correlation function and the Widom line

We propose an approximation of a direct correlation function corresponding to the linearization with respect to −βϕ(r) of a generalized mean spherical approximation for a hard-core multi-Yukawa system of particles. We use the results to study the behavior of maximums of thermodynamic response functions in the supercritical region of a fluid with a two-term Yukawa potential imitating the Lennard-Jones potential.

Membrane curvature generated by asymmetric depletion layers of ions, small molecules, and nanoparticles.

Biomimetic and biological membranes consist of molecular bilayers with two leaflets that are typically exposed to different aqueous solutions. We consider solutions of "particles" that experience effectively repulsive interactions with these membranes and form depletion layers in front of the membrane leaflets. The particles considered here are water-soluble, have a size between a few angstrom and a few nanometers as well as a rigid, more or less globular shape, and do neither adsorb onto the membranes nor permeate these membranes. Examples are provided by ions, small sugar molecules, globular proteins, or inorganic nanoparticles with a hydrophilic surface. We first study depletion layers in a hard-core system based on ideal particle solutions as well as hard-wall interactions between these particles and the membrane. For this system, we obtain exact expressions for the coverages and tensions of the two leaflets as well as for the spontaneous curvature of the bilayer membrane. All of these quantities depend linearly on the particle concentrations. The exact results for the hard-core system also show that the spontaneous curvature can be directly deduced from the planar membrane geometry. Our results for the hard-core system apply both to ions and solutes that are small compared to the membrane thickness and to nanoparticles with a size that is comparable to the membrane thickness, provided the particle solutions are sufficiently dilute. We then corroborate the different relationships found for the hard-core system by extensive simulations of a soft-core particle system using dissipative particle dynamics. The simulations confirm the linear relationships obtained for the hard-core system. Both our analytical and our simulation results show that the spontaneous curvature induced by a single particle species can be quite large. When one leaflet of the membrane is exposed, e.g., to a 100 mM solution of glucose, a lipid bilayer can acquire a spontaneous curvature of ±1/(270 nm). Our theoretical results can be scrutinized by systematic experimental studies using a large variety of different types of particles.

Effect of inter-species selective interactions on the thermodynamics and nucleation free-energy barriers of a tessellating polyhedral compound.

The phase behavior and the homogeneous nucleation of an equimolar mixture of octahedra and cuboctahedra are studied using thermodynamic integration, Gibbs-Duhem integration, and umbrella sampling simulations. The components of this mixture are modeled as polybead objects of equal edge lengths so that they can assemble into a space-filling compound with the CsCl crystal structure. Taking as reference the hard-core system where the compound crystal does not spontaneously nucleate, we quantified the effect of inter-species selective interactions on facilitating the disorder-to-order transition. Facet selective and facet non-selective inter-species attractions were considered, and while the former was expectedly more favorable toward the target tessellating structure, the latter was found to be similarly effective in nucleating the crystal compound. Ranges for the strength of attractions and degree of supersaturation were identified where the nucleation free-energy barrier was small enough to foretell a fast process but large enough to prevent spinodal fluctuations that can trap the system in dense metastable states lacking long-range order. At those favorable conditions, the tendency toward the local orientational order favored by packing entropy is amplified and found to play a key role seeding nuclei with the CsCl structure.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics.

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

Polymorph selection in the crystallization of hard-core Yukawa system

Colloid-colloid interactions in charge-stabilized dispersions can to some extent be represented by the hard-core Yukawa model. The crystallization process and polymorph selection of hard-core Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic (fcc) phase. The contact value of hard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed (hcp) structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic (bcc). The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald's step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.

Phase separation in one-dimensional hard-core boson system with two- and three-body interactions

We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optic lattice. When these two interactions are comparable and increasing the hopping rate, physically intuitive analysis indicates that there exists an exotic phase separation regime between the solid phase with charge density wave order and superfluid phase. We identify these phases and phase transitions by numerically analyzing the density distribution, structure factor of density-density correlation function, three-body correlation function and von Neumann entropy estimator obtained by density matrix renormalization group method. These exotic phases and phase transitions are expected to be observed in the ultra-cold polar molecule experiments by properly tuning interaction parameters, which is constructive to understand the physics of ubiquitous insulating-superconducting phase transitions in condensed matter systems.

Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

Vibrational density of states in the disordered solid using classical density functional model

Abstract The inhomogeneous density n ( x ) of an amorphous solid is expressed as a sum of Gaussian profiles. Average width of these profiles represents a characteristic length l signifying the degree of mass localization in the system. We demonstrate that as l spreads beyond a critical value l 0 , the corresponding vibrational density of states g ( ω ) deviates from the Debye form g D ( ω ) . We estimate the g ( ω ) assuming a single peak form similar to the boson peak. For a hard core system of diameter σ we obtain l 0 ≈ 0.2 σ . At an optimum l = l h the boson peak height h B of g ( ω ) reaches a maximum.

Auxetic Materials and Related Systems

to mechanical metamaterials and related systems with particular emphasis on auxetic systems. Such materials show counter-intuitive, negative behaviours. For example, auxetic materials exhibit negative Poisson’s ratios which mean that these systems get fatter rather than thinner when stretched. Due to the superior properties exhibited by these systems, their study and characterisation has experienced a signifi cant increase, particularly in the last decade, something which may be perceived from the always increasing number of publications and patents in these areas. In fact, this issue is the seventh in a series of special issues published in physica status solidi (b) dedicated to auxetic materials and related systems (see [1–6]).

Pair supersolid with atom-pair hopping on the state-dependent triangular lattice

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.

Partially auxetic behavior in fcc crystals of hard-core repulsive Yukawa particles

Elastic properties of the face centered cubic (fcc) phase of particles, interacting through hard-core repulsive Yukawa potential are determined by Monte Carlo (MC) simulations in the NpT ensemble with variable shape of the periodic box. The effects of the Debye screening length () and contact value of the potential () on elastic properties of the system are studied. It is found that the hard-core repulsive Yukawa system is partially auxetic. The Poisson's ratio of the system in the direction is negative and decreases with increasing the Debye screening length. Poisson's ratio of the hard-core repulsive Yukawa system measured in the directions at versus density.