Possible reentrance of the fractional quantum Hall effect in the lowest Landau level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = 4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.     

Structure and melting of Morse solids

Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of the Morse pair potential. The structural properties of the liquid and solid phases vary significantly with the range. The longer range, softer potentials are associated with increased densities and cohesive energies in both the solid and liquid phases. The extent of local disorder associated with lattice sites in the solid phase, as measured by the Lindemann and bond orientational order parameters, increases with increasing range of the pair potential.     

Phase Dependence of the IR Spectra of Nitrobenzene

The IR spectra of nitrobenzene-d₀ and -d₅ were recorded in gas and liquid phases at 25°C and in amorphous solid phase at -170°C. The appearance of new bands and intensity changes going from liquid to solid phase spectrum, are interpreted in terms of molecular symmetry modifications. A normal coordinates analysis was performed and the potential energy distribution agrees well with previous assigments.     

Hybrid phase at the quantum melting of the Wigner crystal

We study the quantum melting of the two-dimensional Wigner crystal using a fixed node quantum Monte Carlo approach. In addition to the two already known phases (Fermi liquid at large density and Wigner crystal at low density), we find a third stable phase at intermediate values of the density. The third phase has hybrid behaviors in between a liquid and a solid. This hybrid phase has the nodal structure of a Slater determinant constructed out of the bands of a triangular lattice.     

Representation of the anisotropic pseudo-potential for nematogens

A semiclassical molecular dynamics method based on the approximate variational solution of the time-dependent Schrödinger equation with gaussian wave packets [1–3] has been applied to the simulation of liquid, solid and gaseous neon. The technique is computationally stable: the wave packets do not spread and the conservation of energy is excellent. With a suitable choice of the pair potential fairly satisfactory agreement with the experimental energy and pressure is obtained. The radial distribution functions exaggerate the quantum-mechanical broadening effect. Diffusion constants are in fair agreement with experiment and lower than those of the classical Lennard-Jones liquid.     

Quantum Theory of Solid State Plasma Dielectric Response

We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired “second quantized” creation and annhilation field operators of interacting quantum many‐body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron‐hole pair excitations and plasmons (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic phase diagram for CuMn

To study the magnetic phases of CuMn, we carry out a generalized perturbation expansion of the band energy across the composition range. We obtain the pair energy using the orbital peeling technique of Burke, based on the tight-binding linear muffin-tin orbital and augmented space recursion methods. We analyze the phases of the system by studying the probability distribution of the local staggered occupation ’fields’ within a mean-field approach. We show that our predicted phase boundaries agree well with experimental results.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

Monte Carlo values for the radial distribution function of a system of fluid hard spheres

The perturbation theory recently developed by Weeks, Chandler, and Andersen is applied to the solid phase of a rare gas near its melting line. The potential is separated into two parts: a reference part containing all the repulsive forces and a perturbation part containing all the attractions. We show that the expansion of the free energy in the perturbation potential is, as in the liquid phase, rapidly convergent for a temperature of the order of the triple-point temperature. On the contrary, the representation of the reference system by hard spheres with an appropriate diameter is less accurate than in the liquid phase. This representation requires the knowledge of the radial distribution functions of the hard-sphere solid for which we give a tabulation as well as an analytical representation. The perturbation theory is applied to the determination of the fluid-solid transition.     

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Thermodynamic calculation of the melting point of aluminum

The free energies of aluminum in the solid and liquid phases are calculated. The free energy in the solid state is determined in the quasiharmonic approximation. The radial distribution function of liquid aluminum is found by solving the Bogolyubov-Born-Green equation. The convergence of the series for finding the electrostatic energy of the liquid metal is discussed. The value obtained for the melting point agrees well with the experimental value.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.12, pp.29–32, December, 1980.     

Finite-temperature Wigner solid and other phases of ripplonic polarons on a helium film

Electrons on liquid helium can form different phases depending on density, and temperature. Also the electron-ripplon coupling strength influences the phase diagram, through the formation of so-called “ripplonic polarons”, that change how electrons are localized, and that shifts the transition between the Wigner solid and the liquid phase. We use an all-coupling, finite-temperature variational method to study the formation of a ripplopolaron Wigner solid on a liquid helium film for different regimes of the electron-ripplon coupling strength. In addition to the three known phases of the ripplopolaron system (electron Wigner solid, polaron Wigner solid, and electron fluid), we define and identify a fourth distinct phase, the ripplopolaron liquid. We analyse the transitions between these four phases and calculate the corresponding phase diagrams. This reveals a reentrant melting of the electron solid as a function of temperature. The calculated regions of existence of the Wigner solid are in agreement with recent experimental data.     

Grain Boundary Phase Transitions and their Influence on Properties of Polycrystals

Grain boundary (GB) phase transitions can change drastically the properties of polycrystals. The GB wetting phase transition can occur in the two-phase area of the bulk phase diagram where the liquid (L) and solid (S) phases are in equlibrium. Above the temperature of the GB wetting phase transition a GB cannot exist in equlibrium contact with the liquid phase. The experimental data on GB wetting phase transitions in numerous systems are analysed. The GB wetting tie-line can continue in the one-phase area of the bulk phase diagram as a GB solidus line. This line represents the GB premelting or prewetting phase transitions. The GB properties change drastically when GB solidus line is crossed by a change in the temperature or concentration. The experimental data on GB segregation, energy, mobility and diffusivity obtained in various systems both in polycrystals and bicrystals are analysed. In case if two solid phases are in equilibrium, the GB “solid state wetting” can occur. In this case the layer of the solid phase 2 has to substitute GBs in the solid phase 1. Such GB phase transition occurs if the energy of two interphase boundaries is lower than the GB energy in the phase 1.     

The role of the “Casimir force analogue” at the microscopic processes of crystallization and melting

Melting (crystallization), a phase transition from a crystalline solid to a liquid state, is a common phenomenon in nature. We suggest a new factor, “the Casimir force analogue”, to describe mechanisms of melting and crystallization. The Casimir force analogue is a force occurring between the surfaces of solid and liquid phases of metals caused by different energy density of phonons of these phases. It explains abrupt changes in geometry and thermodynamic parameters at a melting point. “The Casimir force analogue” helps to estimate latent melting heat and to gain an insight into a solid–liquid transition problem.     

谐振子系统的量子-经典轨道、Berry相及Hannay角

从量子-经典轨道和几何相两方面, 研究了二维旋转平移谐振子系统的量子-经典对应. 通过广义规范变换得到了Lissajous经典周期轨道和Hannay角. 另外, 使用含时规范变换解析推导了旋转平移谐振子系统Schrödinger方程的本征波函数和Berry相, 得出结论: 原规范中的非绝热Berry相是经典Hannay角的-n倍. 最后, 使用SU(2)自旋相干态叠加, 构造一稳态波函数, 其波函数的概率云很好地局域于经典轨道上, 满足几何相位和经典轨道同时对应.     

Thermodynamics of a dilute XX chain in a field

Gapless phases in ground states of low-dimensional quantum spin systems are rather ubiquitous. Their peculiarity is a remarkable sensitivity to external perturbations due to permanent criticality of such phases manifested by a slow (power-low) decay of pair correlations and the divergence of the corresponding susceptibility. A strong influence of various defects on the properties of the system in such a phase can then be expected. Here, we consider the influence of vacancies on the thermodynamics of the simplest quantum model with a gapless phase, the isotropic spin-1/2 XX chain. The existence of the exact solution of this model gives a unique opportunity to describe in detail the dramatic effect of dilution on the gapless phase—the appearance of an infinite series of quantum phase transitions resulting from level crossing under the variation of a longitudinal magnetic field. We calculate the jumps in the field dependences of the ground-state longitudinal magnetization, susceptibility, entropy, and specific heat appearing at these transitions and show that they result in a highly nonlinear temperature dependence of these parameters at low T. Also, the effect of enhancement of the magnetization and longitudinal correlations in the dilute chain is established. The changes of the pair spin correlators under dilution are also analyzed. The universality of the mechanism of the quantum transition generation suggests that similar effects of dilution can also be expected in gapless phases of other low-dimensional quantum spin systems.     

Quantum fluctuation driven first-order phase transition in weak ferromagnetic metals

In a local Fermi liquid (LFL), we show that there is a line of weak first-order phase transitions between the ferromagnetic and paramagnetic phases due to purely quantum fluctuations. We predict that an instability towards superconductivity is only possible in the ferromagnetic state. At T?=?0 we find a point on the phase diagram where all three phases meet and we call this a quantum triple point (QTP). A simple application of the Gibbs phase rule shows that only these three phases can meet at the QTP. This provides a natural explanation of the absence of superconductivity at this point coming from the paramagnetic side of the phase diagram, as observed in the recently discovered ferromagnetic superconductor, UGe ₂.