Critical Point Of Phase Transition Research Articles

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.

The magnetic phase transition in Mn2-xFexB alloys: First-principles calculations

Based on the density-functional theory (DFT) and the generalized gradient approximation (GGA), Mn2-xFexB (0 ≤ x ≤ 2) alloys are investigated for their magnetic, electronic and structural properties by the first principles calculations with the virtual crystal approximation (VCA). Two extremes at x = 0 and 2, respectively, show that anti-ferromagnetic Mn2B and ferromagnetic Fe2B have the same electronic structure as I4/mcm but with different lattice constants. There is a critical point for phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) at x = 0.5 according to calculations under the condition of the lowest energy for the four states of non-magnetic (NM), FM, AFM1 and AFM2. It is in agreement with the Stoner model in the range of the FM state.

Analytical studies on holographic superconductor in the probe limit

We investigate the holographic superconductor model constructed in the (2[Formula: see text]+[Formula: see text]1)-dimensional AdS soliton background in the probe limit. With analytical methods, we obtain the formula of critical phase transition points with respect to the scalar mass. We also generalize this formula to higher-dimensional space–time. We mention that these formulas are precise compared to numerical results. In addition, we find a correspondence between the value of the charged scalar field at the tip and the scalar operator at infinity around the phase transition points.

Multipartite entanglement from matrix-product states and a quantum phase transition

We investigate multipartite entanglement and a quantum phase transition for spin chain systems by making use of the density-matrix renormalization-group method in the form of matrix-product states. It is found that multipartite entanglement changes dramatically near the critical region and the residual-to-global entanglement ratio reaches its maximum at the critical point of the quantum phase transition. These results indicate that multipartite entanglement as well as the residual-to-global entanglement ratio can serve as good indicators to detect a quantum phase transition. We also demonstrate a linear relation between the next-nearest-neighbor interaction strength and the critical magnetic field for an $XYZ$ spin chain by using multipartite entanglement and quantum coherence.

Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths☆☆Project supported by National Basic Research Program of China (Grant No. 2013CBA01702) and National Natural Science Foundation of China (Grant Nos. 61377016, 61575055, 10974039, 61307072, 61308017, and 61405056).

We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.

Simple Universal Kelvin Equation Valid in Critical Point Vicinity and its Application to Carbon Dioxide Capillary Condensation in Mesoporous Silica

A new simple universal form of the Kelvin equation that can be used even near the gas-liquid phase transition critical point is shown. The correction of the chemical potential, pressure, and density outside the porous medium is presented and taken into account for the CO2 meniscus curvature radius calculation at capillary condensation in mesoporous silica MCM-41, known [1] for its wide range of applications.

Effect of the exchange interaction anisotropy on the magnetic quantum phase transitions in dimerized antiferromagnets

We present a theoretical description of a quantum phase transition in a dimerized antiferromagnet, induced by an external magnetic field. The description of such transitions is constructed by determining the minimum of the Lagrange function which depends on the parameters of the ground-state crystal wavefunction. We determine that during a crystal transition from the singlet state of the dimer to the state with a noncollinear spin orientation, an order-order type phase transition occurs. We show that in the case of a single-axis character of the exchange anisotropy, the location of the quantum phase transition critical point is affected by the spin-spin interactions inside the dimer. Additionally, analogous to the classical Néele antiferromagnets, single-axis type anisotropic spin-spin interactions between dimers, shift the point of the spin-flip transition from the noncollinear antiferromagnetic phase to the ferromagnetic phase.

Quantum sensing close to a dissipative phase transition: Symmetry breaking and criticality as metrological resources

We study the performance of a single qubit-laser as a quantum sensor to measure the amplitude and phase of a driving field. By using parameter estimation theory we show that certain suitable field quadratures are optimal observables in the lasing phase. The quantum Fisher information scales linearly with the number of bosons and thus the precision can be enhanced by increasing the incoherent pumping acting on the qubit. If we restrict ourselves to measurements of the boson number observable, then the optimal operating point is the critical point of the lasing phase transition. Our results point out to an intimate connection between symmetry breaking, dissipative phase transitions and efficient parameter estimation.

Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors

We study a general flat space/boson star transition model in quasi-local ensemble through approaches familiar from holographic superconductor theories. We manage to find a parameter ψ2, which is proved to be useful in disclosing properties of phase transitions. In this work, we explore effects of the scalar mass, scalar charge and Stückelberg mechanism on the critical phase transition points and the order of transitions mainly from behaviors of the parameter ψ2. We mention that properties of transitions in quasi-local gravity are strikingly similar to those in holographic superconductor models. We also obtain an analytical relation ψ2 ∝ (μ − μc)1/2, which also holds for the condensed scalar operator in the holographic insulator/superconductor system in accordance with mean field theories.

Quantum coherence of an XY spin chain with Dzyaloshinskii-Moriya interaction and quantum phase transition

We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.

Effect of the Coulomb interaction on the liquid-gas phase transition of nuclear matter

We investigate the role of the Coulomb interaction on the liquid-gas phase transition of nuclear matter with three different values of proton fraction ($Y_p$=0.5,0.3 and 0.1), relevant for heavy-ion physics as well as various astrophysical scenarios, within the framework of quantum molecular dynamics. We perform simulations for a wide range of density and temperature with and without the Coulomb interaction and calculate the two-point correlation functions of nucleon density fluctuations for all the configurations to determine the phase transition region. We also determine the critical end point of the liquid-gas phase transition for all three values of proton fraction considered. We observe that the Coulomb interaction reduces the transition temperature by about 2 MeV for nuclear matter with $Y_p$=0.5 and 0.3 and by about 1 MeV for nuclear matter with $Y_p$=0.1. However, the critical density is found to be more or less insensitive to the Coulomb interaction.

Evidence for the ferromagnetic frustration in a classical spin-[formula omitted] system with multisite interaction in external magnetic field: Exact results

We investigate the influence of the multisite interaction among sites within elementary triangles of the kagome-like recursive lattice on the properties of the classical spin-1∕2 ferromagnetic Ising model in the external magnetic field. The exact solution of the model is found and it is shown that the model exhibits a nontrivial structure of the first order as well as second order phase transitions in nonzero external magnetic fields related to the multisite interaction. The equation for the exact determination of the positions of the critical points of the second order phase transitions is derived. The thermodynamic properties of the model are investigated in detail and it is shown that the competition between the ferromagnetic interaction and the multisite interaction leads to the appearance of strong ferromagnetic frustration effects represented by the formation of a nontrivial system of macroscopically degenerated plateau-like and single-point-like ground states. The residual entropies of all ground states are found and the kagome spin-ice-like highly macroscopically degenerated plateau state with nonzero magnetization is identified with the exact residual entropy per site s∕kB=ln(4∕3)∕3≈0.095894. The properties of the specific heat are investigated, its Schottky-type behavior near the single-point ground state values of the magnetic field is identified, the existence of large magnetocaloric effect is discussed, and the existence of the first order phase transitions without the specific heat capacity change is demonstrated.

Dynamical correlation functions of the quadratic coupling spin-Boson model**Project supported by the National Key Basic Research Program of China (Grant No. 2012CB921704), the National Natural Science Foundation of China (Grant No. 11374362), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 15XNLQ03).

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions , with the operator taken as , , and , respectively. In the weak-coupling regime , these functions show power law ω-dependence in the small frequency limit, with the powers 1+2s, 1+2s, and s, respectively. At the critical point of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as and , respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Probing quantum critical points by Fisher information at finite temperature

We study the quantum Fisher information (QFI) of a one-dimensional anisotropic XY chain in a transverse field with three-spin interaction. It is shown that the QFI, computed at a finite temperature, can be used to estimate the critical point (CP) of the quantum phase transition (QPT) at zero temperature. The accuracy of the obtained result depends on both the anisotropy parameter of the chain and the local observable used in the computation of QFI.

Shape phase mixing in critical point nuclei

Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid collective conditions through a rigidity parameter. The model in the lower and upper limits of the rigidity parameter recovers the X(5) and X(3) solutions respectively, while in the equally mixed case it corresponds to the X(4) critical point symmetry. Numerical applications of the model on nuclei from regions known for critical behavior reveal a sizable shape phase mixing and its evolution with neutron or proton numbers. The model also enables a better description of energy spectra and electromagnetic transitions for these nuclei.

One-norm geometric quantum discord and critical point estimation in the XY spin chain

In contrast with entanglement and quantum discord (QD), we investigate the thermal quantum correlation in terms of Schatten one-norm geometric quantum discord (GQD) in the XY spin chain, and analyze their capabilities in detecting the critical point of quantum phase transition. We show that the one-norm GQD can reveal more properties about quantum correlation between two spins, especially for the long-range quantum correlation at finite temperature. Under the influences of site distance, anisotropy and temperature, one-norm GQD and its first derivative make it possible to detect the critical point efficiently for a general XY spin chain.

Glassy features of crystal plasticity

Crystal plasticity occurs by deformation bursts due to the avalanche-like motion of dislocations. Here we perform extensive numerical simulations of a three-dimensional dislocation dynamics model under quasistatic stress-controlled loading. Our results show that avalanches are power-law distributed, and display peculiar stress and sample size dependence: The average avalanche size grows exponentially with the applied stress, and the amount of slip increases with the system size. These results suggest that intermittent deformation processes in crystalline materials exhibit an extended critical-like phase in analogy to glassy systems, instead of originating from a non-equilibrium phase transition critical point.