Special Critical Points Research Articles

Manifestation of Luttinger liquid effects in a hybrid metal-semiconductor double-quantum dot device

We theoretically study the transport properties of a hybrid nanodevice comprised of two large metallic islands incorporated in a two-dimensional electron gas. The high-tunability of the conducting channels electrically connecting two islands to each other and to the leads allows us to treat the setup as a realization of a multi-channel two-site charge Kondo (2SCK) model. It is shown that the leading temperature dependence of the conductance in the 2SCK circuit satisfies the conductance scaling of a single-impurity problem in a Luttinger liquid, whose interaction parameter is fully determined by the number of conducting channels in the device. We demonstrate that the finite weak backscattering in all conducting channels features the appearance of the sub-leading temperature dependencies in linear conductance. At the special critical point, we predict an equivalency between the 2SCK nanodevice and a single-site two-channel charge Kondo problem, where one Kondo channel is implemented by a non-interacting electron gas and the second Kondo channel is attributed to the Luttinger liquid.

On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale. In previous works, the absence of traps for this problem was proved on various time scales. A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system. However, in case of a saddle, the numbers of negative and positive eigenvalues of the Hessian at this point and their magnitudes have not been studied. At the same time, these numbers and magnitudes determine the relative ease or difficulty for practical optimization in a vicinity of the critical point. In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point and, moreover, give estimates on magnitude of these eigenvalues. We also significantly simplify our previous proof of the theorem about this saddle point of the Hessian (Theorem 3 in [22]).

On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale. In previous works, the absence of traps for this problem was proven on various time scales. A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system. However, in the case of a saddle the numbers of negative and positive eigenvalues of the Hessian at this point and their magnitudes have not been studied. At the same time, these numbers and magnitudes determine the relative ease or difficulty for practical optimization in a vicinity of the critical point. In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point and, moreover, give estimates on magnitude of these eigenvalues. We also significantly simplify our previous proof of the theorem about this saddle point of the Hessian [Theorem 3 in B. O. Volkov, O. V. Morzhin, A. N. Pechen, J. Phys. A: Math. Theor. 54, 215303 (2021)]. Bibliography: 42 titles.

Critical points of warped AdS/CFT and higher-curvature gravity

WAdS/WCFT correspondence is an interesting realization of non-AdS holography. It relates 3-dimensional Warped-Anti-de Sitter (WAdS$_3$) spaces to a special class of 2-dimensional quantum field theory with chiral scaling symmetry that acts only on right-moving modes. The latter are often called Warped Conformal Field Theories (WCFT$_2$), and their existence makes WAdS/WCFT particularly interesting as a tool to investigate a new type of 2-dimensional conformal structure. Besides, WAdS/WCFT is interesting because it enables to apply holographic techniques to the microstate counting problem of non-AdS, non-supersymmetric black holes. Asymptotically WAdS$_3$ black holes (WBH$_3$) appear as solutions of topologically massive theories, Chern-Simons theories, and many other models. Here, we explore WBH$_3\times \Sigma_{D-3}$ solutions of $D$-dimensional higher-curvature gravity, with $\Sigma_{D-3}$ being different internal manifolds, typically given by products of deformations of hyperbolic spaces, although we also consider warped products with time-dependent deformations. These geometries are solutions of the second order higher-curvature theory at special (critical) points of the parameter space, where the theory exhibits a sort of degeneracy. We argue that the dual (W)CFT at those points is actually trivial. In many respects, these critical points of WAdS$_3 \times \Sigma_{D-3}$ vacua are the squashed/stretched analogs of the AdS$_D$ Chern-Simons point of Lovelock gravity.

Critical structure and emergent symmetry of Dirac fermion systems

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross–Neveu–Yukawa (GNY) model. Using the first-order ε expansion in dimensions, we study the critical structure and emergent symmetry of the O(N)-GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N) scalar field under a small O(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for on the basis of O(N)-GNY model. It turns out that the O(N)-GNY universality class is physically meaningful if and only if . On this premise, the small O(N)-symmetry breaking perturbation is always irrelevant in the O(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit , depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in Dirac systems with fermion flavor , and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor . Our result suggests some richer transitions with emergent- symmetry, and so on. Interestingly, in the O(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor .

KAJIAN STRUKTUR SOSIAL MASYARAKAT NELAYAN DI EKOSISTEM PESISIR (Study of Social Structure of the Fisherman Community in Coastal Ecosystem)

Research aim is to analyse any social changes and dynamic of space capacity and critical point of social structure in coastal ecosystem. The main factor of structural change is external factor of structural formation (individu , system), or increase of community access to the change of local social environment, and external social environment.
 Dynamics of space capacity of social structure in coastal ecosystem of Bungus Teluk Kabung Padang during periode of research can be explained through the two indicators, objective and subjective. There are a general critical point and a special critical point.
 This results explain that a evolution theory suggest a high possibility to be synthesized with any other theories, e.g. a conflict theory, an equilibrium theory, and a “timbul-tenggelam” theory. The synthesis process is an operational stage in a schematic mapping of theories by Appelbaum. Dynamics of social structure must be known bt any goverment and NGO, which have any development plans in the fisherman community.

Integrable quantum spin chains with free fermionic and parafermionic spectrum

We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,\ldots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z = (p+1)/N$ and specific-heat exponent $\alpha = \max\{0,1-(p+1)/N\}$.

Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.

Flat Bands and Salient Experimental Features Supportingthe Fermion Condensation Theory of Strongly Correlated Fermi Systems

The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence of resistivity in a large number of strongly correlated Fermi systems as well as normal metals. We show that the observed scattering rate is explained by the emergence of flat bands, while the so-called Planckian limit occurs accidentally since the normal metals exhibit the same scattering rate behavior. We also analyze recent challenging experimental data on tunneling differential conductivity collected under the application of magnetic field on the twisted graphene and the archetypical heavy fermion metal YbRh $${}_{2}$$ Si $${}_{2}$$ . Also we describe recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that these observations support the fermion condensation theory. Our theoretical results are in good agreement with corps of different and seemingly unrelated experimental facts. They show that the fermion-condensation quantum phase transition is an intrinsic property of strongly correlated Fermi systems and can be viewed as the universal agent explaining their core physics.

Kosterlitz-Thouless and Gaussian criticalities in a mixed spin-( 12, 52, 12 ) Heisenberg branched chain with exchange anisotropy

Density-matrix renormalization group calculations are used to determine the ground-state phase diagram of the mixed spin-(1/2, 5/2, 1/2) Heisenberg chain whose backbone consists of regularly alternating $s=1/2$ and $S=5/2$ spins, the latter of which are coupled to additional $s=1/2$ spins providing lateral branching. The proposed magnetic structure aims to describe the main characteristics of the heterotrimetallic coordination polymer $[{\mathrm{Cu}}^{\mathrm{II}}{\mathrm{Mn}}^{\mathrm{II}}({\mathrm{L}}^{1})][{\mathrm{Fe}}^{\mathrm{III}}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{ClO}}_{4}\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{H}}_{2}\mathrm{O}$. The full ground-state phase diagram in the parameter space exchange anisotropy versus magnetic field unveils special critical points, at which the intermediate magnetization plateaus emergent at 3/7 and 5/7 of the saturation magnetization vanish. A detailed description of the zero-temperature magnetization process and pair entanglement entropy is accomplished with the aim to distinguish the main coupling regimes. A scaling analysis is performed to accurately locate Kosterlitz-Thouless and Gaussian critical points. In particular, we introduce a new finite-size scaling protocol to properly extract the critical parameters from the size dependence of the magnetic-field range corresponding to the magnetization plateau in the close vicinity of the Gaussian point at which two gapped phases meet.

Flat bands and strongly correlated Fermi systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle-hole (C) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity dI/dV, where I is the current and V the bias voltage, is a symmetric function of V. Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn5 and . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition. An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T- and C-invariance, with the differential conductivity again becoming a symmetric function of V. This behavior has been observed in recent measurements of tunneling conductivity in both and graphene. Also within the FC framework, we describe and explain recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that the observed scaling is explained by the emergence of flat bands formed by fermion condensation.

DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Building on the constraints imposed on the dimers, we develop a Density Matrix Renormalization Group algorithm that takes full advantage of the relatively small Hilbert space that only grows as Fibonacci number. We further show that both models can be mapped rigorously onto a hard-boson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B 69, 075106 (2004)], and combining early results with recent results obtained with the present algorithm on this hard-boson model, we discuss the full phase diagram of these quantum dimer and quantum loop models, with special emphasis on the phase transitions. In particular, using conformal field theory, we fully characterize the Ising transition and the tricritical Ising end point, with a complete analysis of the boundary-field correspondence for the tricritical Ising point including partially polarized edges. Finally, we show that the Fibonacci anyon chain is exactly equivalent to special critical points of these models.

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

ABSTRACTThe fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.

Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis

We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan–Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel–Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU(2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.

Investigation of the spectroscopy properties of deformed nuclei by combining the X(3) and E(5) models

In this paper, we present a model which is composed of two parts related to the special critical points, E(5) (the phase transition between spherical oscillator and $ \gamma$ -soft) and X(3) (a $ \gamma$ -rigid version of X(5) . This model is studied to investigate the interplay situations by the free parameter $ \chi$ . These situations are cited between the $ \gamma$ -unstable and $ \gamma$ -rigid version of the Bohr Hamiltonian. The corresponding wave equation has been considered and the eigenvalues as well as eigenfunctions have been determined by solving this equation. Moreover, we have calculated the energy spectra and transition rates in order to compare our results with experimental data.

Entanglement and coherence in a spin-s XXZ system under non-uniform fields

We investigate entanglement and coherence in an XXZ spin s pair immersed in a non-uniform transverse magnetic field. The ground state and thermal entanglement phase diagrams are analyzed in detail in both the ferromagnetic and antiferromagnetic cases. It is shown that a non-uniform field can control the energy levels and the entanglement of the corresponding eigenstates, making it possible to entangle the system for any value of the exchange couplings, both at zero and finite temperatures. Moreover, the limit temperature for entanglement is shown to depend only on the difference between the fields applied at each spin, leading for to a separability stripe in the field plane such that the system becomes entangled above a threshold value of . These results are demonstrated to be rigorously valid for any spin s. On the other hand, the relative entropy of coherence in the standard basis, which coincides with the ground state entanglement entropy at T = 0 for any s, becomes non-zero for any value of the fields at , decreasing uniformly for sufficiently high T. A special critical point arising at T = 0 for non-uniform fields in the ferromagnetic case is also discussed.

Perpetual Points: New Tool for Localization of Coexisting Attractors in Dynamical Systems

Perpetual points (PPs) are special critical points for which the magnitude of acceleration describing the dynamics drops to zero, while the motion is still possible (stationary points are excluded), e.g. considering the motion of the particle in the potential field, at perpetual point, it has zero acceleration and nonzero velocity. We show that using PPs we can trace all the stable fixed points in the system, and that the structure of trajectories leading from former points to stable equilibria may be similar to orbits obtained from unstable stationary points. Moreover, we argue that the concept of perpetual points may be useful in tracing unexpected attractors (hidden or rare attractors with small basins of attraction). We show potential applicability of this approach by analyzing several representative systems of physical significance, including the damped oscillator, pendula, and the Henon map. We suggest that perpetual points may be a useful tool for localizing coexisting attractors in dynamical systems.

On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight

We study the asymptotics of recurrence coefficients for monic orthogonal polynomials $\pi_n(z)$ with the quartic exponential weight $\exp[-N(\frac 12 z^2+\frac 14 tz^4)]$, where $t\in {\mathbb C}$ and $N\in{\mathbb N}$, $N\to\infty$. Our goal is to describe these asymptotic behaviors globally for $t\in {\mathbb C}$ in different regions. We also describe the "breaking" curves separating these regions, and discuss their special (critical) points. All these pieces of information combined provide the global asymptotic "phase portrait" of the recurrence coefficients of $\pi_n(z)$, which was studied numerically in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321]. The main goal of the present paper is to provide a rigorous framework for the global asymptotic portrait through the nonlinear steepest descent analysis (with the $g$-function mechanism) of the corresponding Riemann-Hilbert problem (RHP) and the continuation in the parameter space principle. The latter allows to extend the nonlinear steepest descent analysis from some parts of the complex $t$-plane to all noncritical values of $t$. We also provide explicit solutions for recurrence coefficients in terms of the Riemann theta functions. The leading order behaviour of the recurrence coefficients in the full scaling neighbourhoods the critical points (double and triple scaling limits) was obtained in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321] and [Asymptotics of complex orthogonal polynomials on the cross with varying quartic weight: critical point behaviour and the second Painlev\'e transcendents, in preparation].

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h0/J), (D/J, T/J) and (K/J, T/J) planes, where T, h0, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.

Competing intramolecular vs. intermolecular hydrogen bonds in solution.

A hydrogen bond for a local-minimum-energy structure can be identified according to the definition of the International Union of Pure and Applied Chemistry (IUPAC recommendation 2011) or by finding a special bond critical point on the density map of the structure in the framework of the atoms-in-molecules theory. Nonetheless, a given structural conformation may be simply favored by electrostatic interactions. The present review surveys the in-solution competition of the conformations with intramolecular vs. intermolecular hydrogen bonds for different types of small organic molecules. In their most stable gas-phase structure, an intramolecular hydrogen bond is possible. In a protic solution, the intramolecular hydrogen bond may disrupt in favor of two solute-solvent intermolecular hydrogen bonds. The balance of the increased internal energy and the stabilizing effect of the solute-solvent interactions regulates the new conformer composition in the liquid phase. The review additionally considers the solvent effects on the stability of simple dimeric systems as revealed from molecular dynamics simulations or on the basis of the calculated potential of mean force curves. Finally, studies of the solvent effects on the type of the intermolecular hydrogen bond (neutral or ionic) in acid-base complexes have been surveyed.