Thed-p model of ‘highT c’ superconductivity is the Anderson lattice

We show that thed-p model of HighT _c superconductivity can be mapped ontoa spin half Anderson latticewith vanishing conduction electron band width. Using the non-orthogonal basis of Zhang and Rice [1], we show that the orthogonalised combinations are very short range and make up a conduction band for the resulting Anderson Lattice. The only motion is restricted to that with achange of orbital character.     

A perturbative approach to the quantum elliptic Calogero–Sutherland model

We solve perturbatively the quantum elliptic Calogero–Sutherland model in the regime in which the quotient between the real and imaginary semiperiods of the Weierstrass $\text{P}$ function is small.     

Global phase diagram of a spin–orbit-coupled Kondo lattice model on the honeycomb lattice

Motivated by the growing interest in the novel quantum phases in materials with strong electron correlations and spin–orbit coupling, we study the interplay among the spin–orbit coupling, Kondo interaction, and magnetic frustration of a Kondo lattice model on a two-dimensional honeycomb lattice.We calculate the renormalized electronic structure and correlation functions at the saddle point based on a fermionic representation of the spin operators.We find a global phase diagram of the model at half-filling, which contains a variety of phases due to the competing interactions.In addition to a Kondo insulator, there is a topological insulator with valence bond solid correlations in the spin sector, and two antiferromagnetic phases.Due to the competition between the spin–orbit coupling and Kondo interaction, the direction of the magnetic moments in the antiferromagnetic phases can be either within or perpendicular to the lattice plane.The latter antiferromagnetic state is topologically nontrivial for moderate and strong spin–orbit couplings.     

Topological quantum phase transitions and topological flat bands on the kagomé lattice

We investigate the topological properties of the tight-binding electrons on the two-dimensional kagomé lattice with two kinds of short-range hopping integral and two kinds of staggered magnetic flux. Considering the nearest-neighbor hopping (t(1)) with the staggered flux parameter φ(1) and the next nearest-neighbor hopping (t(2)) with the staggered flux parameter φ(2), we demonstrate a series of topological quantum phase transitions and find some topological bands with high Chern numbers, when tuning one parameter (t(2) or φ(2)) while the others are fixed. We have also found that, in some parameter regions, the system exhibits interesting topological flat bands with Chern number C =± 1 and a large gap above them, and the flatness ratio can reach a high value of about 170.     

Simulation of quantum wells with ‘spikes’ and ‘dips’

The use of thin high-bandgap ‘spikes’ or thin low-bandgap ‘dips’ inside conventional rectangular quantum wells (QWs) gives supplementary flexibility in engineering intra- and inter-band energy level separation. The paper presents simulation and experimental studies on the effects of ‘spikes’ and ‘dips’ on the fundamental quantum well properties.     

Response to ‘On the orthogonality of the phase velocity and its feasibility for plane waves’

A recent theoretical study of plane waves with orthogonal phase velocity is premised on incorrect assumptions. The conclusion reached therein – namely, that “a plane wave with orthogonal phase velocity cannot possess linear momentum” and therefore “cannot propagate at all” – is incorrect in general.     

Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions

Wavenumber–frequency spectra of the streamwise velocity component obtained from large-eddy simulations (LES) are presented. Following recent work we show that the main features, a Doppler shift and a Doppler broadening of frequencies, are captured by an advection model based on the Tennekes–Kraichnan random-sweeping hypothesis with additional mean flow. In this paper, we focus on the height-dependence of the spectra within the logarithmic layer of the flow. We furthermore benchmark an analytical model spectrum that takes the predictions of the random-sweeping model as a starting point and find good agreement with the LES data. We also quantify the influence of the LES grid resolution on the wavenumber–frequency spectra.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

‘Percolative’ dynamics in the hexagonal lattice

We study a percolative dynamic model for the hexagonal lattice. Random trajectories are generated and their critical behaviour is studied. The critical behaviour corresponds to that of simple percolatio in some of the parameter space, but elsewhere the exponents reveal new universality classes. We calculate the fractal dimension of extended trajectories for different critical points.     

On the relation of Manin’s quantum plane and quantum Clifford algebras

In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined and interpreted in Clifford algebraic terms. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Quantum phase transition of the Jaynes-Cummings model

Herein, we propose an experimentally feasible scheme to show the quantum phase transition of the Jaynes-Cummings(JC) model by modulating the transition frequency of a two-level system in a quantum Rabi model with strong coupling. By tuning the modulation frequency and amplitude, the ratio of the effective coupling strength of the rotating terms to the effective cavity(atomic transition) frequency can enter the deep-strong coupling regime, while the counter-rotating terms can be neglected. Thus, ...     

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO₂-substrate. By tuning the laser excitation energy across the E ₃₃ excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the D mode and the G mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E ₃₃ excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G band and D band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E ₃₃ resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.     

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Atomic emission and cavity field spectra of the Jaynes－Cummings model

Atomic emission and cavity field spectra of the Jaynes－Cummings model are analytically compared. We show that the two spectra are in general different, except for the special case where the interaction is resonant, the cavity is initially empty and the retarded time of one-photon emission is considered in calculations of the spectra. In this case, the two spectra are the same. We also show that this result comes from the fact that the two-time autocorrelation function of the cavity field is not directly proportional to that of the atom.     

Darboux–Bäcklund transformation and explicit solutions to a hybrid lattice of the relativistic Toda lattice and the modified Toda lattice

The relativistic Toda lattice and the modified Toda lattice are two important discrete integrable equations. In this paper, we investigate a hybrid lattice equation of the two lattice equations. Darboux–Bäcklund transformation and explicit solutions to the hybrid lattice equation are constructed.     

‘Measurement of quantum mechanical operators’ revisited

The Wigner-Araki-Yanase (WAY) theorem states a remarkable limitation to quantum mechanical measurements in the presence of additive conserved quantities. Discovered by Wigner in 1952, this limitation is known to induce constraints on the control of individual quantum systems in the context of information processing. It is therefore important to understand the precise conditions and scope of the WAY theorem. Here we elucidate its crucial assumptions, briefly review some generalizations, and show how a particular extension can be obtained by a simple modification of the original proofs. We also describe the evolution of the WAY theorem from a strict no-go verdict for certain, highly idealized, precise measurements into a quantitative constraint on the accuracy and approximate repeatability of imprecise measurements.     

Response to ‘Comment on a recent conjectured solution of the three-dimensional Ising model’

This is a Response to a recent Comment [F.Y. Wu, B.M. McCoy, M.E. Fisher et al., Phil. Mag. 88 (2008)] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87 5309 (2007)]. Several points are made: (1) Conjecture 1, regarding the additional rotation, is understood as performing a transformation for smoothing all the crossings of the knots. (2) The weight factors in Conjecture 2 are interpreted as a novel topologic phase. (3) The conjectured solution and its low- and high-temperature expansions are supported by the mathematical theorems for the analytical behavior of the Ising model. The physics behind the extra dimension is also discussed briefly.     

New Baxter phase in the Ashkin–Teller model on a cubic lattice

The mean field theory results are obtained from the Bogoliubov inequality for the spin-1/2 Ashkin–Teller model on a cubic lattice for different cluster sizes. The phase diagram, magnetization and free energy are obtained. From those expressions we observed a new phase in the model. Denoted in the course of this work by Baxter⁽²⁾ this new phase presents $〈S〉\ne 〈\sigma 〉\ne 0$. The phase transitions between the Baxter⁽²⁾ and the others well known phases for the model are studied and classified.