Diagonal Order Research Articles

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.

Superfluid, Supersolid, and Checkerboard Solid in Two-Component Bosons in an Optical Lattice: Study by Means of Gross–Pitaevskii Theory and Monte-Carlo Simulations

The bosonic t–J model is a strong-on-site repulsion limit of the two-component Bose–Hubbard model and is expected to be realized by experiments of cold atoms in an optical lattice. In previous papers, we studied the bosonic t–J model by both analytical methods and numerical Monte-Carlo (MC) simulations. However, in the case of finite Jz, where Jz is the z-component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t–J model using both the Gross–Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as Jz is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.

Magnetic phases in the S=1 Shastry-Sutherland model with uniaxial anisotropy

We explore the field-induced magnetic phases of an $S=1$ $XXZ$ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry-Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground-state phases are characterized in detail in terms of their thermodynamic properties, and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the $S=1$ spins results in several ground state phases that are not realized for $S=1/2$ spins. These include the quantum paramagnetic state that is ubiquitous to $S=1$ spins with single-ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering), and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for $S=1/2$ spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.

Composite Orders and Lifshitz Transition of Heavy Electrons

Magnetic and other unconventional electronic orders are discussed for heavy electrons. In addition to the ordinary Kondo lattice, we consider non-Kramers systems taking the two-channel Kondo lattice, and another lattice that consists of a singlet–triplet f2 configuration. The latter gives a scalar order with staggered sublattices of crystalline-electric-field (CEF) and Kondo singlets, which accounts for the observed order in PrFe4P12. In the two-channel Kondo lattice, an odd-frequency pairing is realized that becomes degenerate at half-filling with a diagonal composite order involving both localized and conduction electrons. The degeneracy is interpreted in terms of a hidden SO(5) symmetry. For the ordinary Kondo lattice with exchange interaction J, we take insulating ground states as reference. The metallic states are approached by infinitesimal doping of carriers either from the Kondo insulator or from the antiferromagnetic insulator. By adding intersite exchange we find that location of the band extremum of the heavy band depends on the value of J. The change of J gives topological change of the Fermi surface, which corresponds to a generalized version of the Lifshitz transition, and occurs separately from the quantum critical point of the antiferromagnetic order.

Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach— Part 1: The Over-Sampled Case

In Abramovich [“Bounds on Maximum Likelihood Ratio-Part I: Application to Antenna Array Detection-Estimation With Perfect Wavefront Coherence,” IEEE Trans. Signal Process., vol. 52, pp. 1524-1536, June 2004], it was demonstrated, for multivariate complex Gaussian distribution, that the probability density function (p.d.f.) of the likelihood ratio (LR) for the (unknown) actual covariance matrix R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> does not depend on this matrix and is fully specified by the matrix dimension M and the number of independent training samples T. This invariance property hence enables one to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically “as likely” as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . This “expected likelihood” quality assessment allowed significant improvement of MUSIC DOA estimation performance in the so-called “threshold area,” and for diagonal loading and TVAR model order selection in adaptive detectors. Recently, the so-called complex elliptically symmetric (CES) distributions have been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario (T ≥ M) while Part II deals with the undersampled scenario (T ≤ M).

Minimal primes of ideals arising from conditional independence statements

We study ideals whose primary decomposition specifies the relevant structural zeros of certain conditional independence models. The ideals we study generalize the class of ideals considered by Fink (2011) [5] in a way distinct from the generalizations of Herzog, Hibi, Hreinsdottir, Kahle, and Rauh (2010) [10] and Ay and Rauh (2011) [1]. We introduce switchable sets to give a combinatorial description of the minimal prime ideals, and for some classes we describe the minimal components. We discuss possible interpretations of the ideals we study, including as 2×2 minors of generic hypermatrices. We also introduce a definition of diagonal monomial orders on generic hypermatrices to compute some Gröbner bases.

Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice.

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order—2kF charge correlations—to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phonon frequencies. The crossover can hence be interpreted in terms of preformed pairs corresponding to bipolarons, which are essentially localized in the Peierls phase, and ‘condense’ with increasing phonon frequency to generate dominant pairing correlations.

Valence bond crystal and possible orbital pinball liquid in at2gorbital model

We study a model for orbitally degenerate Mott insulators, where localized electrons possess t_2g degrees of freedom coupled by several, competing, exchange mechanisms. We provide evidence for two distinct strongly fluctuating regimes, depending on whether superexchange or direct exchange mechanism predominates. In the superexchange-dominated regime, the ground state is dimerized, with nearest neighbor orbital singlets covering the lattice. By deriving an effective quantum dimer model and analyzing it numerically, we characterize this dimerized phase as a valence bond crystal stabilized by singlet resonances within a large unit cell. In the opposite regime, with predominant direct exchange, the combined analysis of the original model and another effective model adapted to the local constraints, shows that subleading perturbations select a highly resonating ground state, with coexisting diagonal and off-diagonal long-range orbital orders.

Quantum and thermal transitions out of the pair-supersolid phase of two-species bosons on a square lattice

We investigate two-species bosons in a two-dimensional square lattice by quantum Monte Carlo method. We show that the inter-species attraction and nearest-neighbor intra-species repulsion results in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occurs in two steps. Upon heating, first the pair-superfluid is destroyed via a KT transition then the solid order melts via an Ising transition

The far infrared spectrum of trans-formic acid: An extension up to 175 cm−1

The far infrared spectrum of HCOOH was recorded at a high resolution (0.0009cm−1) and long path length (72m) at the far-infrared beamline, Canadian Light Source. Spectra were recorded in the region 62–300cm−1, showing transitions from the trans-isomer.Ground state rotational transitions with Ka up to 30, were identified up to 175cm−1, extending the observation reported in the literature. A total of 3321 transitions were assigned and fitted together with previous (4149) published data. An improved set of rotational parameters was obtained adopting the symmetric top (A) reduction of the rotational Hamiltonian in the Ir representation. The newly measured far infrared transitions allowed the determination of all diagonal and off diagonal 8th order parameters L and of some of the diagonal 10th order parameters P.

Diagonal Composite Order in a Two-Channel Kondo Lattice

A novel type of symmetry breaking is reported for the two-channel Kondo lattice where conduction electrons have spin and orbital (channel) degrees of freedom. Using the continuous-time quantum MonteCarlo and the dynamical mean-field theory, a spontaneous breaking of the orbital symmetry is observed. The tiny breakdown of orbital occupation number, however, vanishes if the conduction electrons have the particle-hole symmetry. The proper order parameter instead is identified as a composite quantity representing the orbital-selective Kondo effect. The single-particle spectrum of the selected orbital shows insulating property, while the other orbital behaves as a Fermi liquid. This composite order is the first example of odd-frequency order other than off-diagonal order (superconductivity), and is a candidate of hidden order in f-electron systems.

Application of electron conformational–genetic algorithm approach to 1,4-dihydropyridines as calcium channel antagonists: pharmacophore identification and bioactivity prediction

Two different approaches, namely the electron conformational and genetic algorithm methods (EC-GA), were combined to identify a pharmacophore group and to predict the antagonist activity of 1,4-dihydropyridines (known calcium channel antagonists) from molecular structure descriptors. To identify the pharmacophore, electron conformational matrices of congruity (ECMC)-which include atomic charges as diagonal elements and bond orders and interatomic distances as off-diagonal elements-were arranged for all compounds. The ECMC of the compound with the highest activity was chosen as a template and compared with the ECMCs of other compounds within given tolerances to reveal the electron conformational submatrix of activity (ECSA) that refers to the pharmacophore. The genetic algorithm was employed to search for the best subset of parameter combinations that contributes the most to activity. Applying the model with the optimum 10 parameters to training (50 compounds) and test (22 compounds) sets gave satisfactory results (R(2)(training)= 0.848, R(2)(test))= 0.904, with a cross-validated q(2) = 0.780).

Spontaneous formation and optical manipulation of extended polariton condensates

Cavity exciton-polaritons (polaritons) are bosonic quasi-particles offering a unique solid-state system to investigate interacting condensates. Up to now, disorder induced localization and short lifetimes have prevented the establishment of long range off diagonal order needed for any quantum manipulation of the condensate wavefunction. In this work, using a wire microcavity with polariton lifetimes ten times longer than in all previously existing samples, we show that polariton condensates can propagate over macroscopic distances outside the excitation area, while preserving their spontaneous spatial coherence. An extended condensate wave-function builds-up with a degree of spatial coherence larger than 50% over distances 50 times the polariton De Broglie wavelength. The expansion of the condensate is shown to be governed by the repulsive potential induced by photo-generated excitons within the excitation area. The control of this local potential offers a new and versatile method to manipulate extended polariton condensates. As an illustration, we demonstrate synchronization of extended condensates via controlled tunnel coupling and localization of condensates in a trap with optically controlled dimensions.

Quarter-filled supersolid and solid phases in the extended Bose–Hubbard model

We numerically study the ground state phase diagram of thetwo-dimensional hard-core Bose–Hubbard model with nearest-(V1) andnext-nearest-neighbour (V2) repulsions. In particular, we focus on the quarter-filled phases where onesupersolid and two solid phases are observed. Using both canonical and grandcanonical quantum Monte Carlo (QMC) methods and a mean-field calculation, weprovide evidence for the existence of a commensurate supersolid. Despite thetwo possible diagonal long-range orderings for the solid phase, only one kind ofsupersolid phase is found to be energetically stable. The competition betweenthe two solid phases manifests itself as a first-order phase transition around2V2 ∼ V1. The change of order parameters as a function of the chemical potential is also presented.

A possible mechanism of concurring diagonal and off-diagonal long-range order for soft interactions

This paper is a contribution to the theory of coherent crystals. We present arguments claiming that negative minima in the Fourier transform of a soft pair interaction may give rise to the coexistence of diagonal and off-diagonal long-range orders at high densities, and that this coexistence may be detectable due to a periodicity seen on the off-diagonal part of the one-body reduced density matrix, without breaking translation invariance. As an illustration, we study the ground state of a homogenous system of bosons in continuous space, from the interaction retaining only the Fourier modes v(k) belonging to a single nonzero wave number |k|=q. The result is a mean-field model. We prove that for v(k)>0 the ground state is asymptotically fully Bose condensed, while for v(k)<0 at densities exceeding a multiple of ℏ2q2/2m|v(k)| it exhibits both Bose–Einstein condensation and diagonal long-range order, and the latter can be seen on both the one- and the two-body density matrix.

Iterative identification of temperature dynamics in single wafer rapid thermal processing

As the standard size of silicon wafers grows and performance specifications of integrated circuits become more demanding, a better control system to improve the processing time, uniformity and repeatability in rapid thermal processing (RTP) is needed. Identification and control are complicated because of nonlinearity, drift and the time-varying nature of the wafer dynamics. Various physical models for RTP are available. For control system design they can be approximated by diagonal nonlinear first order dynamics with multivariable static gains. However, these model structures of RTP have not been exploited for identification and control. Here, an identification method that iteratively updates the multivariable static gains is proposed. It simplifies the identification procedure and improves the accuracy of the identified model, especially the static gains, whose accurate identification is very important for better control.

Vacancy supersolid of hard-core bosons on the square lattice

The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}l0.25$. At filling $\ensuremath{\rho}g0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}g0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.

Modeling shock waves in orthotropic elastic materials

A constitutive relationship for modeling of shock wave propagation in orthotropic materials is proposed for nonlinear explicit transient large deformation computer codes (hydrocodes). A procedure for separation of material volumetric compression (compressibility effects equation of state) from deviatoric strain effects is formulated, which allows for the consistent calculation of stresses in the elastic regime as well as in the presence of shock waves. According to this procedure the pressure is defined as the state of stress that results in only volumetric deformation, and consequently is a diagonal second order tensor. As reported by Anderson et al. [Comput. Mech. 15, 201 (1994)], the shock response of an orthotropic material cannot be accurately predicted using the conventional decomposition of the stress tensor into isotropic and deviatoric parts. This paper presents two different stress decompositions based on the assumption that the stress tensor is split into two components: one component is due to volumetric strain and the other is due to deviatoric strain. Both decompositions are rigorously derived. In order to test their ability to describe shock propagation in orthotropic materials, both algorithms were implemented in a hydrocode and their predictions were compared to experimental plate impact data. The material considered was a carbon fiber reinforced epoxy material, which was tested in both the through-thickness and longitudinal directions. The ψ decomposition showed good agreement with the physical behavior of the considered material, while the ζ decomposition significantly overestimated the longitudinal stresses.

Numerical schemes for the Barenblatt model of non-equilibrium two-phase flow in porous media

We introduce some numerical approximations to a quasilinear problem proposed by G. I. Barenblatt to describe non-equilibrium two-phase fluid flows in permeable porous media, which apply to secondary oil recovery from natural reservoirs. Taking into account the theoretical results of global existence and uniqueness, we approximate the solutions by three numerical schemes, namely, the Diagonal First Order schemes (DFO and DF02) and the Diagonal Second Order scheme (DSO). For DFO schemes convergence is proved. The schemes' behaviour is analysed and discussed through some numerical experiments.