Evolution of order and chaos across a first-order quantum phase transition

We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.     

Effect of a fermion on quantum phase transitions in bosonic systems

The effect of a fermion with angular momentum j on quantum phase transitions of a (s,d) bosonic system is investigated. It is shown that the presence of a fermion strongly modifies the critical value at which the transition occurs, and its nature, even for small and moderate values of the coupling constant. The analogy with a bosonic system in an external field is mentioned. Experimental evidence for precursors of quantum phase transitions in bosonic systems plus a fermion (odd-even nuclei) is presented.     

Quantum phase transitions in Bose–Fermi systems

Quantum phase transitions in a system of N bosons with angular momentum L = 0, 2 (s, d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)–SU(3) (spherical to axially-deformed) transition in odd–even nuclei is presented.     

Partial dynamical symmetries

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.     

Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.     

Excited-state quantum phase transitions in systems with two degrees of freedom: Level density,level dynamics,thermal properties

Quantum systems with a finite number of freedom degrees f$f$ develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f$f$, particularly f=2$f=2$, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition.     

Optical line shapes for polymethine dyes and their aggregates: Novel theory of quantum transitions and its correlation with experiment

This work reports how a proper theoretical definition of electron-nuclear(-phonon) coupling in the dynamics of the transient state in quantum transitions enables an explanation for the basic experimental data on the optical line shapes for polymethine dyes and their dimers as well as H-, H*-, and J-aggregates, which defied understanding for many decades.     

Structural relative stabilities and pressure-induced phase transitions for lanthanide trihydrides REH3 (RE=Sm,Gd, Tb,Dy, Ho,Er, Tm,and Lu)

The structures, structural relative stabilities, pressure-induced phase transitions, and equations of state for lanthanide trihydrides REH₃ (RE=Sm, Gd, Tb, Dy, Ho, Er, Tm, and Lu) are systematically studied using ab initio calculations under a core state model (CSM). The obtained ground-state parameters, such as lattice constants and bulk modulus, agree well with the available data. Among the P6₃/mm, P3?c1, and P6₃cm structures, the P6₃cm structure is found to be the most stable structure for lanthanide trihydride via the comparison of the calculated total energies. With the help of Birch–Murnaghan equation of state, the structural transitions from hexagonal to cubic for REH₃ (RE=Sm, Gd, Ho, Er, and Lu) under pressure are affirmed; especially, the similar behavior of REH₃ (RE= Tb, Dy, and Tm) is reasonably predicted for the first time by this means. For the transitions, the repulsive interactions of H–H atoms may play an important role in terms of the analysis of the structures in the vicinity of the theoretical phase transition.     

Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-T<Subscript>c</Subscript> copper oxides

In this paper a mean-field theory for the spin-liquid paramagnetic non-superconducting phase of the p- and n-type high-T_c cuprates is developed. This theory applied to the effective t-t'-t′′-J^* model with the ab initio calculated parameters and with the three-site correlated hoppings. The static spin-spin and kinematic correlation functions beyond Hubbard-I approximation are calculated self-consistently. The evolution of the Fermi surface and band dispersion is obtained for the wide range of doping concentrations x. For p-type systems the three different types of behavior are found and the transitions between these types are accompanied by the changes in the Fermi surface topology. Thus a quantum phase transitions take place at x = 0.15 and at x = 0.23.Due to the different Fermi surface topology we found for n-type cuprates only one quantum critical concentration, x = 0.2. The calculated doping dependence of the nodal Fermi velocity and the effective mass are in good agreement with the experimental data.     

Revisiting novel symmetries in coupled ${ \mathcal N }=2$ supersymmetric quantum systems: examples and supervariable approach

We revisit the novel symmetries in ${ \mathcal N }=2$ supersymmetric quantum mechanical models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.     

Tl/Ge(1 0 0) system: Phase formation and phase transitions

Using scanning tunneling microscopy, phase formation and temperature-driven phase transitions in Tl/Ge(1 0 0) system have been studied. Evolution of Tl overlayer structure has been considered for three temperature ranges, including around room temperature (RT), high-temperature (HT) (350-450 K) and low-temperature (LT) (20-100 K) ranges. Upon RT growth, a 2 × 1-Tl phase develops in submonolayer range and is completed at around 1 ML of Tl. Cooling of the RT-deposited Tl overlayer results in formation of a set of various LT structures. These are 1D chains, 5 × 4-Tl and “stroked” phases observed in submonolayer range and a long-period c(12 × 14)-Tl phase developed at around 1 ML. All transitions between these RT and LT structures are reversible. At doses beyond 1 ML, RT deposition of Tl onto Ge(1 0 0) leads to the growth of second-layer Tl stripes, forming arrays with a 1 × 4 periodicity. Meanwhile, structure of the first layer also changes and it displays a set of various reconstructions, c(2 × 8), c(10 × 6) and c(10 × 7). All these structures remain unchanged upon cooling to LT. Growth at HT as well as heating of RT-deposited Tl overlayer irreversibly produces 3 × 2-Tl phase whose rows become decorated by second-layer Tl stripes at prolonged Tl deposition.     

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport

We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions (determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample boundaries. Received 19 August 2002 Published online 19 November 2002     

Raman light scattering,infrared absorption and DSC studies of the phase transition and vibrational and reorientational dynamics of H2O ligands and ClO4– anions in [Ba(H2O)3](ClO4)2

[Ba(H₂O)₃](ClO₄)₂ between 90 and 300 K possesses two solid phases. One phase transition of the first‐order type at: = 211.3 K (on heating) and = 204.6 K (on cooling) was determined by differential scanning calorimetry. The entropy change value (ΔS ≈ 15 Jmol^–1 K^–1), associated with the observed phase transition, indicates a moderate degree of molecular dynamical disorder. Both, vibrational and reorientational motions of H₂O ligands and ClO₄^– anions, in the high‐temperature and low‐temperature phases, were investigated by Fourier transform far‐infrared and middle‐infrared and Raman light scattering spectroscopies. The temperature dependences of the full‐width at half‐maximum values of the bands associated with ρ_w(H₂O) mode, in both infrared (~570 cm^–1) and Raman light scattering (~535 cm^–1) spectra, suggest that the observed phase transition is not associated with a sudden change of a speed of the H₂O reorientational motions. Ligands reorient fast, with correlation time of the order of several picoseconds, with a mean activation energy value E_a = 5.1 kJ mol^–1 in both high and low temperature phases. On the other hand, measurements of temperature dependences of full‐width at half‐maximum values of the infrared band at ~460 cm^–1, associated with δ_d(OClO)E mode, and Raman band at ~1105 cm^–1, associated with ν_as(ClO)F₂ mode, revealed the existence of a fast ClO₄^– reorientation in phase I and in phase II, with the E_a(I) and E_a(II) values equal to 8.0 and 6.5 kJ mol^–1, respectively. These reorientational motions of ClO₄^– are slightly distorted at the T_C. Fourier transform far‐infrared and middle‐infrared spectra with decreasing of temperature indicated characteristic changes at the vicinity of PT at T_C, which suggested lowering of the crystal structure symmetry. All these experimental facts suggest that the discovered phase transition is associated with small change of H₂O ligands and somewhat major change of ClO₄^– anions reorientational dynamics, and with insignificant change of the crystal structure, too. Copyright © 2012 John Wiley & Sons, Ltd.     

The dense α-√3 × √3Pb/Si(1 1 1) phase: A comprehensive STM and SPA-LEED study of ordering, phase transitions and interactions

The T-θ phase diagram for the system Pb/Si(1 1 1) was determined in the coverage range 6/5 ML < θ < 4/3 ML from complementary STM and SPA-LEED experiments. This coverage is within the range where a “Devil’s Staircase” (DS) has been realized. The numerous DS phases answer conflicting information in the Pb/Si(1 1 1) literature and update the previously published phase diagram. The measurements reveal the thermal stability of the different linear DS phases with the transition temperature found to be a function of phase period. Because of additional complexity in the experimental system (i.e. two-dimensionality and 3-fold symmetry) the linear DS phases transform at higher temperature into commensurate phases of 3-fold symmetry HIC (historically named “hexagonal incommensurate phase”). Different types of HIC phases have been discovered differing in the size of the supercell built out of √3 × √3 domains separated by domain walls of the √7 × √3 phase. The detailed structures of these HIC phases (coverage, binding site, twist angle, etc.) have been deduced from the comparison of STM images and diffraction patterns. After heating the system to even higher temperature the HIC phase transforms into the disordered phase. For sufficiently high coverage a SIC (“striped incommensurate phase” which is also built from √3 × √3 domains but meandering √7 × √3 domain walls) is observed which also disorders at high temperatures.     

Dual model for magnetic excitations and superconductivity in UPd 2 Al 3

The Heavy Fermion state in UPd₂Al₃ may be approximately described by a dual model where two of the three U-5 f electrons are in a localized state split by the crystalline electric field into two low lying singlets with a splitting energy Δ≃ 6 meV. The third 5 f electron has itinerant character and forms the Heavy Electron bands. Inelastic neutron scattering and tunneling experiments suggest that magnetic excitons, the collective propagating crystal field excitations of the localized 5 f electrons, mediate superconducting (sc) pairing in UPd₂Al₃. A theory for this novel mechanism is developed within a nonretarded approach. A model for the magnetic exciton bands is analyzed and compared with experiment. The sc pair potential which they mediate is derived and the gap equations are solved. It is shown that this mechanism favors an odd parity state which is nondegenerate due to the combined symmetry breaking by the crystalline electric field and the AF order parameter. A hybrid model including the spin fluctuation contribution to the pairing is also discussed. Received 22 October 2001 and Received in final form 28 February 2002     

Exact ground-state for the periodic Anderson model in dimensions at finite value of the interaction and absence of the direct hopping in the correlated f-band

We report for the first time exact ground-states deduced for the D = 2 dimensional generic periodic Anderson model at finite U, the Hamiltonian of the model not containing direct hopping terms for f-electrons ( t ^f = 0). The deduced itinerant phase presents non-Fermi liquid properties in the normal phase, emerges for real hybridization matrix elements, and not requires anisotropic unit cell. In order to deduce these results, the plaquette operator procedure has been generalised to a block operator technique which uses blocks higher than an unit cell and contains f-operator contributions acting only on a single central site of the block. Received 1st July 2002 / Received in final form 16 September 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: gulacsi@heavy-ion.atomki.hu