Commensurate incommensurate phase transitions

there are two types of Commensurate-Incommensurate Phase Transitions : t_I between the basic structure and the incommensurate phasis and t_L between the inc. phasis and the lock in phasis. They both have connected structures. So that, they must verify the relation between crystallographic groups in accordance with Landau's Theory. But we have to consider the three phases in the superspace - as we do at an ordered-disordered magnetic transition-because the inc. phasis ins't a crystal in the physical space; e.g., in order to cancel the “middle range order” of the inc. phasis at t_I, we are led to assume the grey (point) group to the basic structure in the superspace. Now both inc. phase and basic structure verify the connection between point-groups in the superspace in the same way as both para and ferro phases do at a ferroic transition in the physical space. We also show that the same type of relation is possible at t_L and we give the order parameter at both t_I and t_L.     

Commensurate and incommensurate modulated structures of Rb2ZnCl4

The commensurate and incommensurate structures of Rb₂ZnCl₄ have been refined using the four-dimensional formalism for modulated structures. They are characterized by a rigid body modulated rotation of the ZnCl₄ tetrahedra and by a translation motion of the Rb atoms.     

Exotic spectra, wavefunctions and transport in incommensurate lattices

We present numerical results on a range of related issues for a number of incommensurate TMB’s, each of which shows a metal-insulator type transition as a binding-to-hopping ratio is made to increase through some limiting value. These supplement a series of similar results on a couple of 1D lattices in a number of recent works (see below). A brief review pertaining to spectral properties and wavefunctions in incommensurate lattices is followed by results on the above TBM’s relating to an interesting correlation between the gross features of wavefunctions and the energies arranged in a particular sequence termed thelattice-ordered sequence, and also between the lattice-ordered energies and the on-site potentials. We present a qualitative explanation of these correlations on the basis of perturbation theory. Basic results on dynamics of wavepackets in relation to spectral characteristics of incommensurate TBM’s are also reviewed. Features of lattice-ordered energies and wavefunctions for the TBM’s under study are used in the framework of the so-called Maryland construction, leading to a qualitative prediction of criteria for recurrent and non-recurrent wavepacket dynamics in these lattices, and these predictions are checked against numerical iterations of the relevant ‘quantum maps’. Closely related to the dynamics of wavepackets are the transport properties of these lattices. Results are available to indicate that the unusual spectral characteristics of pseudorandom lattices lead to novel features in transport properties of these systems. In this context, low temperature a.c conductivity in these lattices is a good probe for the spectral characteristics and wavefunctions. However, not much is known about the a.c conductivity, excepting a set of early results pertaining to the low frequency regime, principally because of the fact that the a.c conductivity depends on global characteristics of the spectrum and the entire set of wavefunctions. We present a simple model whereby the gross structure of variation of the a.c conductivity with frequency can be obtained from a knowledge of the spectrum alone for the set of TMB’s under consideration. Numerical computations show that despite its simplicity, the model leads to results in good agreement with those from the Kubo-Greenwood formula for a.c conductivity.     

Ground states of Fermions on lattices

We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).     

Inhomogeneous states of a thin-film incommensurate ferroelectric

Nonuniform distributions of the order parameter in a film of an incommensurate ferroelectric whose free energy expansion does not contain Lifshitz invariants are considered. An equation describing the order parameter distribution over the film thickness is derived in the approximation of slowly varying amplitudes. The effect of film thickness and surface properties on the temperature of transition to the incommensurate phase is analyzed.     

Vortex-Peierls states in optical lattices

We show that vortices, induced in cold atom superfluids in optical lattices, may order in a novel vortex-Peierls ground state. In such a state vortices do not form a simple lattice but arrange themselves in clusters, within which the vortices are partially delocalized, tunneling between classically degenerate configurations. We demonstrate that this exotic quantum many-body state is selected by an order-from-disorder mechanism for a special combination of the vortex filling and lattice geometry that has a macroscopic number of classically degenerate ground states.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials.     

Quantum processing photonic states in optical lattices

The mapping of photonic states to collective excitations of atomic ensembles is a powerful tool which finds a useful application in the realization of quantum memories and quantum repeaters. In this work we show that cold atoms in optical lattices can be used to perform an entangling unitary operation on the transferred atomic excitations. After the release of the quantum atomic state, our protocol results in a deterministic two qubit gate for photons. The proposed scheme is feasible with current experimental techniques and robust against the dominant sources of noise.     

Defect-free surface states in modulated photonic lattices

We predict that interfaces of periodically curved waveguide arrays can support a novel type of surface states which exist in a certain region of modulation parameters associated with the band flattening. Such linear surface states appear in truncated but otherwise perfect (defect-free) lattices as a direct consequence of the periodic modulation of the lattice potential. We show that the existence of these modes in different band gaps can be flexibly controlled by selecting the modulation profile, with no restrictions on Bloch-wave symmetries characteristic of Shockley states.     

Chimera states in Gaussian coupled map lattices

We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.