Cluster phases of penetrable rods on a line

Emergence of an Ising critical regime in the clustering of one-dimensional soft matter revealed through string variables

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose interparticle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a nonmagnetic fluid.

Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a composite harmonic chain. Luttinger theory has to be adapted by changing the reference lattice density field. In both the liquid and cluster liquid phases, we find convincing evidence of a secondary mode, which becomes gapless only at the transition. In that region, we also measure the central charge and observe its increase towards c=3/2, as recently evaluated in a related extended Bose-Hubbard model, and we note a fast reduction of the Luttinger parameter. For two-particle clusters, we then interpret such observations in terms of the compresence of a Luttinger liquid and a critical transverse Ising model, related to the instability of the reference lattice density field towards coalescence of sites, typical of potentials which are flat at short distances. Even in the absence of a true lattice, we are able to evaluate the spatial correlation function of a suitable pseudospin operator, which manifests ferromagnetic order in the cluster liquid phase, exponential decay in the liquid phase, and algebraic order at criticality.

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.

Probing the existence of phase transitions in one-dimensional fluids of penetrable particles

Phase transitions in one-dimensional classical fluids are usually ruled out by using van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, e.g., the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, Phys. Rev. E 90, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however, also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically by use of three different and increasingly sophisticated approaches (i.e., a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum) to conclude that the alleged transitions of the one-dimensional GEM-4 system are likely just crossovers.