Novel phenomena in dilute electron systems in two dimensions

Based on theory and experiments in weakly interacting electron systems, it was believed for many years that no metallic phase is possible in two dimensions. The unexpected observation of metallic-like behavior in strongly interacting electron systems has thus drawn considerable attention. Following background material and a brief history, we review the dramatic response of these 2D systems to in-plane magnetic fields, and the evidence this provides for a possible quantum phase transition.Received: 30 January 2004, Published online: 20 July 2004PACS: 71.30. + h Metal-insulator transitions and other electronic transitions - 73.40.Qv Metal-insulator-semiconductor structures (including semiconductor-to-insulator) - 73.50.Jt Galvanomagnetic and other magnetotransport effects (including thermomagnetic effects)     

Direct observation of geometrical phase transitions in mesoscopic superconductors by scanning tunneling microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.     

Effects of boundaries on structure formation in low-dimensional colloid model systems near the liquid-solid-transition in equilibrium and in external fields and under shear

A brief review focusing on low-dimensional colloidal model systems is given describing both simulation studies and complementary experiments, elucidating the interplay between phase behavior, geometric structures, and transport phenomena. These studies address the response of these very soft colloidal systems to perturbations such as uniform or uniaxial compression, laser fields, randomly quenched disorder, and shear deformation caused by moving boundaries. Binary hard-disk mixtures are studied by Monte Carlo simulation, to investigate ordering on surfaces or in monolayers, modeling the effect of a substrate by an external potential. By weak external laser fields the miscibility of the mixture can be controlled, and the underlying mechanism (laser-induced demixing) is clarified. The stability of various space-filling structures is discussed only for the case where no laser fields are present.Hard spheres interacting with repulsive screened Coulomb or dipolar interaction confined in 2D and 3D narrow constrictions are investigated by Brownian Dynamics simulation. With respect to the structural behavior, it is found that layers or planes throughout the microchannel are formed. The arrangement of the particles is disturbed by diffusion, and can also be modified by an external driving force causing a density gradient along the channel. Then the number of layers or planes gets reduced, adjusting to the density gradient, and this self-organized change of order also shows up in the particle velocities. The experimental work that is reviewed here addresses dipolar colloidal particles confined by gravity on a solid substrate on which a set of pinning sites has been randomly distributed. The dynamics of the system is studied by tracking the trajectories of individual particles, and it is found that the mean square displacements of particles that are nearest neighbors of pinned particles are strongly affected by these defects. The influence of the pinning sites on the order and microscopic mechanism of phase transitions in two dimensions is investigated.     

The diffusion of macroparticles and criteria of phase transitions for dust structures in weakly ionized plasma

The dynamics of charged particles is investigated under conditions close to those of experiments in a weakly ionized laboratory gas-discharge dust plasma. The existing phenomenological criteria of phase transitions for dust structures in such a plasma are treated, and new criteria are suggested. The parameters responsible for the order and scaling of dynamic processes in Yukawa dissipative systems are determined. The relation for the diffusion coefficient D of macroparticles in strongly correlated liquid structures is derived.     

Phase separation transition in a driven diffusive system with anti-ferromagnetic interaction

One-dimensional non-equilibrium systems with short-range interaction can undergo phase transitions from homogeneous states to phase separated states as interaction (?) among particles is increased. One of the model systems where such a transition has been observed is the extended Katz-Lebowitz-Spohn (KLS) model with ferromagnetically interacting particles at ?=4/5. Here, the system remains homogeneous for small interaction strength (?<4/5), and for anti-ferromagnetic interactions (?<0). We show that the phase separation transitions can also occur in anti-ferromagnetic systems if interaction among particles depends explicitly on the size of the block (n) they belong to. We study this transition in detail for a specific case ?=δ/n, where phase separation occurs for δ<−1.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

Possible links between the liquid-gas and deconfinement-hadronization phase transitions

It is commonly accepted that strongly interacting matter has several phase transitions in different domains of temperature and baryon density. In this contribution I discuss two most popular phase transitions which, in principle, can be accessed in nuclear collisions. One of them, the liquid-gas phase transition, is well established theoretically and studied experimentally in nuclear multifragmentation reactions at intermediate energies. The other one, the deconfinement-hadronization phase transition, is at the focus of present and future experimental studies with relativistic heavy-ion beams at SPS, RHIC and LHC. Possible links between these two phase transitions are identified from the viewpoint of their manifestation in violent nuclear collisions.     

Statistics of internal excitations of atomic systems

The character of internal excitations is compared for phase transitions and chemical transitions in atomic systems. Although the temperature dependences of some physical parameters of atomic systems have resonance-like structures with maxima in both cases, the dependences of the partition functions on the number of elementary excitations or the excitation energy differ because of the difference in the numbers of interactions that govern the transitions. The phase changes of condensed rare gases are considered in the case where the external pressure is small and the differences between phases are predominantly associated with differences in configurations. Important energy parameters of rare gases are determined by the attractive part of the pairwise interaction potential between atoms. The statistical analysis shows the existence of a “freezing limit” temperature for these systems, below which the liquid state becomes unstable. The kinetics of decay of such unstable states is analyzed in terms of the diffusion of voids.     

Nonadiabatic preparation of spin crystals with ultracold polar molecules

We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using a dipole blockade of microwave excitations, we map the system onto an interacting spin-1/2 model possessing ground states with crystalline order, and describe a way to prepare these states by nonadiabatically driving the transitions between molecular rotational levels. The proposed technique bypasses the need to cross a phase transition and allows for the creation of ordered domains of considerably larger size compared to approaches relying on adiabatic preparation.     

Reentrant transitions in colloidal or dusty plasma bilayers

The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic, and triangular structures are found to be stable including a first-order transition between two different rhombic structures. For varied screening length at fixed density, one of these rhombic phases exhibits both a single and even a double reentrant transition. Our predictions can be verified experimentally in strongly confined charged colloidal suspensions or dusty plasma bilayers.     

Analysis of phase transitions in two-dimensional Coulomb clusters by the dynamic entropy method

The dynamics of two-dimensional clusters consisting of 7 and 18 particles whose interaction is described by a screened Coulomb potential has been numerically simulated by the Langevin molecular dynamics method. With the use of the data obtained for the displacements and velocities of particles, the functions of the “mean first-passage time” dynamic entropy have been obtained for clusters having different kinetic temperatures close to the conditions of laboratory experiments with macroparticles in a gas-discharge plasma. Three phase states of the small systems under consideration—crystal, liquid, and transient—have been observed. A mechanism of phase transitions under consideration has been described. The method proposed to analyze the dynamics of systems can be used for extremely small structures.     

Aspects of Entanglement in Quantum Many-Body Systems

Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions.     

Simulation of mass transfer in systems with isotropic pair correlation of particles

Results of a numerical analysis of mass transfer in systems of macroscopic particles with various isotropic interaction potentials are presented. Parameters that determine transport properties of nonideal dissipative systems are obtained for a broad class of model potentials. An approximate expression for the diffusivity of interacting particles is proposed. The relationship between diffusivity and viscosity is analyzed for strongly nonideal systems.     

A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi-integrable systems

We investigate numerically the stable and unstable manifolds of the hyperbolic manifolds of the phase space related to the resonances of quasi-integrable systems in the regime of validity of the Nekhoroshev and KAM theorems. Using a model of weakly interacting resonances we explain the qualitative features of these manifolds characterized by peculiar ‘flower-like’ structures. We detect different transitions in the topology of these manifolds related to the local rational approximations of the frequencies. We find numerically a correlation among these transitions and the speed of Arnold diffusion.     

Stability and phase coherence of trapped 1D Bose gases

We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as three-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. "Fermionization" of the system reduces the phase coherence length, and at T=0 the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime.     

On the new universal possibility to detect phase transitions in correlated electron systems

We investigate temperature and concentration driven phase transitions (structural and reentrant phase transitions included) in magnetic and superconducting systems with the use of a wide class of model Hamiltonians applied to rare earth (Re) based compounds and alloys (integer and fluctuating valence systems). Studying the temperature or concentration dependence of the chemical potential we observe small but distinct and well localized kinks at all critical points as evidence for phase transitions. For systems with, at least, two kinds of interacting electrons the kinks at critical temperatures or concentrations occur also in the electronic average occupation numbers (critical electron redistribution). These observations suggest a direct and universal experimental application of the chemical potential as a detector of phase transitions for temperature and concentration driven phase transitions, as well as, for pressure-or external field-induced transitions in solids. The agreement between the calculated critical temperature behaviour of the chemical potential, presented in this paper, and experimental measurements for high-temperature superconductor YBa₂Cu₃O_7-δ entirely supports these general observations.     

Anomalous latent heat in nonequilibrium phase transitions

We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc.) are well defined. The sign of the latent heat is found to be counterintuitive: it is positive when going from the phase where the temperatures and the entropy are higher to the one where these quantities are lower. The effect exists only out of equilibrium and requires conflicting interactions. It is displayed on a lattice gas model of ferromagnetically interacting spin-1/2 particles.     

Temperature dependence of the magnetic susceptibility of magnetic dispersed nanosystems

The temperature dependence of the complex magnetic susceptibility of different magnetic nano-colloids and finely dispersed magnetite powder is studied. The results are explained with allowance for the magnetic moment relaxation in single-domain particles and phase transitions in a system of interacting dipoles.     

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.