Critical Point Of Phase Transition Research Articles

Monolayer Mg2C : Negative Poisson's ratio and unconventional two-dimensional emergent fermions

Novel two-dimensional (2D) emergent fermions and negative Poisson's ratio in 2D materials are fascinating subjects of research. Here, based on first-principles calculations and theoretical analysis, we predict that the hexacoordinated Mg$_{2}$C monolayer hosts both exotic properties. We analyze its phonon spectrum, reveal the Raman active modes, and show that it has small in-plane stiffness constants. Particularly, under the tensile strain in the zigzag direction, the Mg$_{2}$C monolayer shows an intrinsic negative Poisson's ratio $\sim -0.023$, stemming from its unique puckered hinge structure. The material is metallic at its equilibrium state. A moderate biaxial strain can induce a metal-semimetal-semiconductor phase transition, during which several novel types of 2D fermions emerge, including the anisotropic Dirac fermions around 12 tilted Dirac points in the metallic phase, the $2$D double Weyl fermions in the semimetal phase where the conduction and valence bands touch quadratically at a single Fermi point, and the 2D pseudospin-1 fermions at the critical point of the semimetal-semiconductor phase transition where three bands cross at a single point on the Fermi level. In addition, uniaxial strains along the high-symmetry directions break the three-fold rotational symmetry and reduce the number of Dirac points. Interestingly, it also generates 2D type-II Dirac points. We construct effective models to characterize the properties of these novel fermions. Our result reveals Mg$_{2}$C monolayer as an intriguing platform for the study of novel 2D fermions, and also suggests its great potential for nanoscale device applications.

Application quantum renormalization group to optimal dense coding in transverse Ising model

We have merged the object of renormalization group(RG) with quantum dense coding for one-dimensional Ising model in a transverse field. At first, we have shown how the dynamic quantum discord(QD) evolves in present intrinsic decoherence when the size of the system becomes large, i.e., the finite size scaling is obtained. By considering that the generation of highly entangled quantum states is a fundamental requirement for quantum information, the main purpose of this work is to answer the following question: how the valid optimal dense coding can be determined by RG in many body systems? We find that the optimal dense coding capacity depends on the normalization group. It has been found that valid dense coding can exist with the increasing of RG steps. Moreover, the results show that by increasing of RG steps, valid dense coding capacity suddenly occurs near the critical point of the quantum phase transition in present intrinsic decoherence. Using this approach, identifying a critical point of the transverse Ising model in dense coding capacity quality can be very effective.

Maximum cumulant method for studying condensation-evaporation phase transitions

In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 073211] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates ($k$-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions ${g}_{1}(\ensuremath{\theta})$ and ${g}_{2}(\ensuremath{\theta})$ with zero overlap and mean values ${\ensuremath{\theta}}_{1}$ and ${\ensuremath{\theta}}_{2}$, respectively; and (ii) ${g}_{1}(\ensuremath{\theta})$ and ${g}_{2}(\ensuremath{\theta})$ are unimodal distributions that are symmetric with respect to the middle point $({\ensuremath{\theta}}_{1}+{\ensuremath{\theta}}_{2})/2$. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear $k$-mers on square and triangular lattices, $S$-shaped $k$-mers on square lattices and ${k}^{2}$-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.

Generalization of Laughlin’s theory for the fractional quantum Hall effect

Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor (m odd), I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin’s quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory, without a priori assumption of the presence of CFs. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for 1/m state. Each of these wave functions is interpreted as expelling an electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions , respectively, can be constructed as coherent superposition of n coupled Laughlin condensates and their ‘conjugates’, formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transition between two topologically distinct phases each corresponding to a family of states: one consists of large number of coupled Laughlin condensates of filling factor 1/3 and the other corresponds to large number of coupled conjugate Laughlin condensates of filling factor 1, which may be distinguished, respectively, by the absence and presence of upstream edge modes.

Polarization of the spontaneous magnetic field and magnetic fluctuations in s+is anisotropic multiband superconductors

We show that multiband superconductors with broken time-reversal symmetry can produce spontaneous currents and magnetic fields in response to the local variations of pairing constants. Considering the iron pnictide superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ as an example we demonstrate that both the point-group symmetric $s+is$ state and the C$_4$-symmetry breaking $s+id$ states produce in general the same magnitudes of spontaneous magnetic fields. In the $s+is$ state these fields are polarized mainly in ab crystal plane, while in the $s+id$ state their ab-plane and c-axis components are of the same order. The same is true for the random magnetic fields which are produced by the order parameter fluctuations near the critical point of the time-reversal symmetry breaking phase transition. Our findings can be used as a direct test of the $s+is/s+id$ dichotomy and the additional discrete symmetry breaking phase transitions with the help of muon spin relaxation experiments.

Critical point of nuclear matter and beam-energy dependence of net-proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $S\sigma$ and kurtosis $\kappa\sigma^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $\kappa\sigma^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

Transport theory is the key foundation of the theoretical design of metamaterials-metamaterial is artificial phase transition

This is a revisit of my PhD thesis work is which I coined the term transport theory. In 1966. This is the first introduction of transport theory into condensed matter physics. Transport theory is today the key foundation of the theoretical design of materials. Since metamaterial is a new material, naturally it will fall under this category of work. Recently I discovered that metamaterial is in fact, artificial phase transition. Permeability, permittivity, effective bulk modulus, effective mass density are transport properties. The transport property also shows a singularity behavior at the critical point of phase transition in metamaterial same as that of the singularity behavior of transport property during condensation at phase transition. The successful fabrication of quantum metamaterial producing artificial superconductivity and metamaterial interpretation of high temperature superconductivity further confirms that metamaterial is artificial phase transition. Being artificial phase transition, one is able to control the degree of phase transition by tuning the resonance frequency of the transport properties.

Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates

We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is swept linearly. Three distinct dynamical regions are identified for different sweeping time scales ($\tau$), when compared to the time scale $\tau_{\rm KZ}\sim N^{(1+\nu z)/\nu d}$ decided by external driving in a system with finite size $N$ ($\nu,z$ are critical exponents and $d$ the dimensionality). They are manifested by the excitation probability $\mathcal{P}$ and the excess heat density $\mathcal{Q}$. The adiabatic region of $\,\mathcal{P}\sim\mathcal{Q}\sim\tau^{-2}\,$ follows from the adiabatic perturbation theory when $\tau >\tau_{\rm KZ}$, while the non-adiabatic universal region of $\,\mathcal{P}\sim\mathcal{Q}\sim\tau^{-1}\,$ in the thermodynamic limit is described by the Kibble-Zurek mechanism when $\tau_{\rm KZ}>\tau >$ the time scale given by initial gap. The Kibble-Zurek scaling hypothesis is augmented with finite-size scaling in the latter region and several experimentally falsifiable features for the finite system we consider are predicted. The region of the fastest sweeping is found to be non-universal and far-from-equilibrium with $\mathcal{P}$ and $\mathcal{Q}$ essentially being constants independent of $\tau$.

Lévy-stable two-pion Bose-Einstein correlations in sNN=200 GeV Au+Au collisions

We present a detailed measurement of charged two-pion correlation functions in 0%-30% centrality $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from L\'evy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the L\'evy index of stability $\alpha$ and the L\'evy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same L\'evy-stable source functions. The $\lambda(m_T)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The L\'evy length scale parameter $R(m_T)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the L\'evy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha=2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.

Double-hump solitons in fractional dimensions with a 𝒫𝒯-symmetric potential.

We investigate the properties of double-hump solitons supported by the nonlinear Schrödinger equation featuring a combination of parity-time symmetry and fractional-order diffraction effect. Two classes of nonlinear states, i.e., out-of-phase and in-phase solitons are found. Each class contains two families of solitons originating from the same linear mode in both focusing and defocusing nonlinear Kerr media. The critical phase-transition point increases monotonously with increasing Lévy index. For strong gain and loss, out-of-phase solitons in focusing media are stable in a wide parameter window and are almost completely unstable in media with a defocusing nonlinearity. The stability of in-phase solitons is opposite to that of out-of-phase solitons. In-phase solitons in defocusing media are stable in their entire existence domains provided that the gain-loss strength is below a critical value. Meanwhile, the stability region shrinks with the decrease of Lévy index. We, thus, put forward the first example of spatial solitons in fractional dimensions with a parity-time symmetry.

Quantum phase transitions in spin-1 XXZ chains with rhombic single-ion anisotropy

We explore the fidelity susceptibility and the quantum coherence along with the entanglement entropy in the ground-state of one-dimensional spin-1 XXZ chains with the rhombic single-ion anisotropy. By using the techniques of density matrix renormalization group, effects of the rhombic single-ion anisotropy on a few information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the Y-N\'{e}el phase to the Large-$E_x$ or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap can be used to detect the critical points of quantum phase transitions. Conclusions drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy $\Delta$ and the rhombic single-ion anisotropy $E$.

On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box

We study the asymptotically flat quasi-local black hole/hairy black hole model with nonzero mass of the scalar field. We disclose effects of the scalar mass on transitions in a grand canonical ensemble with condensation behaviors of the parameter psi _{2}, which is similar to approaches in holographic theories. We find that a more negative scalar mass makes the phase transition easier. We also obtain the analytical relation psi _{2}varpropto (T_{c}-T)^{1/2} around the critical phase transition points, implying a second order phase transition. Besides the parameter psi _{2}, we show that metric solutions can be used to disclose properties of the transitions. In this work, we observe that phase transitions in a box are strikingly similar to holographic transitions in AdS gravity and the similarity provides insights into holographic theories.

Characterizing real-space topology in Rice-Mele model by thermodynamics.

The thermodynamic quantities which are related to energy-level statistics are used to characterize the real-space topology of the Rice-Mele model. Through studying the energy spectrum of the model under different boundary conditions, we found that the non-normalizable wave function for the infinite domain is reduced to the edge state adhered to the boundary. For the finite domain with symmetric boundary condition, the critical point for the topological phase transition is equal to the inverse of the domain length. In contrast, the critical point is zero for the semi-infinite domain. Additionally, the symmetry of the energy spectrum is found to be sensitive to the boundary conditions of the Rice-Mele model, and the emergence of the edge states as well as the topological phase transition can be reflected in the thermodynamic properties. A potentially practical scheme is proposed for simulating the Rice-Mele model and detecting the relevant thermodynamic quantities in the context of Bose-Einstein condensate.

QCD critical end point from a realistic PNJL model

With parameters fixed by critical temperature and equation of state at zero baryon chemical potential, a realistic Polyakov-Nambu-Jona-Lasinio (rPNJL) model predicts a critical end point of chiral phase transition at (μEB = 720MeV; TE = 93MeV). The extracted freeze-out line from heavy ion collisions is close to the chiral phase transition boundary in the rPNJL model, and the kurtosis kσ2 of baryon number fluctuations from the rPNJL model along the experimental freeze-out line agrees well with the BES-I measurement. Our analysis shows that the dip structure of measured kσ2 is determined by the relationship between the freeze-out line and chiral phase transition line at low baryon density region, and the peak structure can be regarded as a clean signature for the existence of CEP.

Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth

A solution for the Bohr-Mottelson Hamiltonian with an anharmonic oscillator potential of sixth order, obtained through a diagonalization in a basis of Bessel functions, is presented. The potential is consid- ered to have simultaneously spherical and deformed minima of the same depth separated by a barrier (a local maximum). This particular choice is appropriate to describe the critical point of the nuclear phase transition from a spherical vibrator to an axial rotor. Up to a scale factor, which can be cancelled by a corresponding normalization, the energy spectra and the electromagnetic E2 transition probabilities depend only on a single free parameter related to the height of the barrier. Investigations of the numerical data revealed that the model represents a good tool to describe this critical point.

Quasi-single-crystalline CoO hexagrams with abundant defects for highly efficient electrocatalytic water oxidation.

Defects and structural long-range ordering have been recognized as two crucial characters for advanced electrocatalysts. However, these two features have rarely been achieved together. Herein, we report the preparation of single-crystalline CoO hexagrams and demonstrate their exceptional electrocatalytic properties for water oxidation. The quasi-single-crystalline CoO hexagrams, prepared at the critical phase transition point of β-Co(OH)2/Co(OH)F hexagrams, possess both abundant oxygen vacancies as defects and structural long-range ordering. The matching between the b-axis of Co(OH)F crystals and the a-axis of β-Co(OH)2 crystals is critical for the formation of the CoO hexagram single crystals. The quasi-single-crystalline CoO hexagrams with abundant defects are highly efficient for water oxidation by delivering a 10 mA cm-2 current density at a low overpotential of 269 mV in a 1 M KOH aqueous solution.

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing points with linear dispersion, around which the quasiparticles resemble the relativistic Dirac Fermions. It can be described by a 4 * 4 massless Dirac Hamiltonian which can be decomposed into a pair of Weyl points or gaped into an insulator. Thus, crystal symmetry is critical to guarantee the stable existence. On the contrary, by breaking crystal symmetry, a DSM may transform into a Weyl semimetal (WSM) or a topological insulator (TI). Here, by taking hexagonal LiAuSe as an example, we find that it is a starfruit shaped multiple nodal chain semimetal in the absence of spin-orbit coupling(SOC). In the presence of SOC, it is an ideal DSM naturally with the Dirac points locating at Fermi level exactly, and it would transform into WSM phase by introducing external Zeeman field or by magnetic doping with rare-earth atom Sm. It could also transform into TI state by breaking rotational symmetry. Our studies show that DSM is a critical point for topological phase transition, and the conclusion can apply to most of the DSM materials, not limited to the hexagonal material LiAuSe.

Bohr model description of the critical point for the first order shape phase transition

The critical point of the shape phase transition between spherical and axially deformed nuclei is described by a collective Bohr Hamiltonian with a sextic potential having simultaneous spherical and deformed minima of the same depth. The particular choice of the potential as well as the scaled and decoupled nature of the total Hamiltonian leads to a model with a single free parameter connected to the height of the barrier which separates the two minima. The solutions are found through the diagonalization in a basis of Bessel functions. The basis is optimized for each value of the free parameter by means of a boundary deformation which assures the convergence of the solutions for a fixed basis dimension. Analyzing the spectral properties of the model, as a function of the barrier height, revealed instances with shape coexisting features which are considered for detailed numerical applications.

Adiabatic Mach–Zehnder interferometer in a dipolar spin-1 condensate

We propose and analyze a realizable scheme for performing a Heisenberg-limited Mach–Zehnder interferometry with a dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach–Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also study the spin squeezing of the state generated in the beam splitter and show that the spin squeezing exhibits an extremum near the critical point of phase transition.

Quantum sensing of rotation velocity based on transverse field Ising model

We study a transverse-field Ising model (TFIM) in a rotational reference frame. We find that the effective Hamiltonian of the TFIM of this system depends on the system's rotation velocity. Since the rotation contributes an additional transverse field, the dynamics of TFIM sensitively responses to the rotation velocity at the critical point of quantum phase transition. This observation means that the TFIM can be used for quantum sensing of rotation velocity that can sensitively detect rotation velocity of the total system at the critical point. It is found that the resolution of the quantum sensing scheme we proposed is characterized by the half-width of Loschmidt echo of the dynamics of TFIM when it couples to a quantum system S. And the resolution of this quantum sensing scheme is proportional to the coupling strength \delta between the quantum system S and the TFIM, and to the square root of the number of spins N belonging the TFIM.