In this note, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two--dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three--dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically.
We study crystallization in a model system for eicosane (C20) by means of molecular dynamics simulation and we identify the microscopic mechanisms of homogeneous crystal nucleation and growth. For the nucleation process, we observe that chains first align and then straighten. Then the local density increases and finally the monomer units become ordered positionally. The subsequent crystal growth process is characterized by a sliding-in motion of the chains. Chains preferably attach to the crystalline cluster with one end and then move along the stems of already crystallized chains towards thei…
We consider the harmonic chain of oscillators with self-consistent stochastic reservoirs and give a new proof for the finitude of its thermal conductivity in the steady state. The approach, with involves an integral representation for the correlations (heat flow)and a perturbative analysis, is quite general and extendable to the study of anharmonic systems.
We simulate crystallization and melting with local Monte Carlo (LMC), event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD) in systems with up to one million three-dimensional hard spheres. We illustrate that our implementations of the three algorithms rigorously coincide in their equilibrium properties. We then study nucleation in the NVE ensemble from the fcc crystal into the homogeneous liquid phase and from the liquid into the homogeneous crystal. ECMC and EDMD both approach equilibrium orders of magnitude faster than LMC. ECMC is also notably faster than EDMD, es…
Time crystals appear when systems display a commensurate spontaneous breaking of the discrete time translational invariance imposed by an external periodic drive. No consensus on the definition has been reached as yet, but important aspects comprise robustness against small variations of the parameters and the initial quantum state. Often, disorder and interaction are thought to be essential ingredients for the occurrence of time crystals. We study a finite-length polarized XX spin chain engineered to display a spectrum of equidistant energy levels without drive and show that it keeps a spectr…
We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shape liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one containing fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexag…
The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir i…
An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the chain particles have random displacements and random velocities corresponding to a uniform initial temperature. An instant change of parameters of chain initiates a transient process. Analytical expressions for the chain temperature as a function of time are obtained from the statistical analysis of the dynamics equations. It is shown that the transition process is oscillatory and it converges non-monotonically to a new equilibrium state. Su…
The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is investigated using variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The investigated model has in a magnetic field an extraordinarily rich ground-state phase diagram, which includes the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin liquids and two bound magnon crystals in addition to the fully polarized ferro…
We investigate theoretically the crucial rôle of interstitialcies that trigger the melting of a boundary-free crystal. Based on an interstitialcy model that resembles the $J_1$-$J_2$ model of frustrated antiferromagnets with uniaxial anisotropy, we have calculated the exact partition function and correlation functions in a one-dimensional atom chain. The melting point and correlation behavior of this crystal model show the applicability of Lindemann criterion and Born criterion in the one-dimensional case.
Magnetic susceptibilities of spin-$(S,s)$ ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of $(S,s)$. Spin-$(S,s)$ ferrimagnetic chains behave like combinations of spin-$(S-s)$ ferromagnetic and spin-$(2s)$ antiferromagnetic chains provided $S=2s$.
We present a mean-field description of the zig-zag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential $r^{-n}e^{-r/λ}$, that are confined by a power-law potential ($y^α$). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of $α$ and $n$. Close to the transition point for the zig-zag phase transition, the scaling behavior of the order parameter is determined. For $α=2$ the zig-zag transition from a single to a double chain is of second order, while for $α>2$ the on…
We study a frustrated mixed spin chain with side chains, where the spin species and the exchange interactions are spatially varied. A nonlinear sigma model method is formulated for this model, and a phase diagram with two disordered spin-gap phases is obtained for typical cases. Among them we examine the case with a main chain consisting of an alternating array of spin-1 and spin-1/2 sites and side chains each of a single spin-1/2 site in great detail. Based on numerical, perturbational, and variational approaches, we propose a singlet cluster solid picture for each phase, where the ground sta…
We study the phase diagram of S=3/2 and S=2 bond-alternating spin chains numerically. In previous papers, the phase diagram of S=1 XXZ spin chain with bond-alternation was shown to reflect the hidden $Z_{2}\times Z_{2}$ symmetry. But for the higher S Heisenberg spin chain, the successive dimerization transition occurs, and for anisotropic spin chains the phase structure will be more colorful than the S=1 case. Using recently developed methods, we show directly that the phase structure of the anisotropic spin chains relates to the $Z_{2}\times Z_{2}$ symmetry.
We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg chains as well. In particular, we observe spinon confinement due to a next-nearest neighbor interaction in the SU(4) representation 10 spin chain.
A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations. A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases. The partially polarized ferrimagnetic phase has an incommensurate spin structure. Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases. Numerical results also suggest a series of almost cri…
A chiral-order parameter of spins in a crystal can not be inferred from measurements of Bragg reflections, although there are several claims in published literature to the contrary. Appropriate techniques use total scattering, of x-rays or neutrons, that yield the instantaneous value of a spin correlation related to an established measure of spin chirality.
Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the $\mathbb{Z}_2$ symmetry of the external periodic drive, while QMBS span a subspace of non-thermalizing eigenstates forming an su(2) algebra rep…
