Onsager's Inequality, the Landau-Feynman Ansatz and Superfluidity

We revisit an inequality due to Onsager, which states that the (quantum) liquid structure factor has an upper bound of the form (const.) x |k|, for not too large modulus of the wave vector k. This inequality implies the validity of the Landau criterion in the theory of superfluidity with a definite, nonzero critical velocity. We prove an auxiliary proposition for general Bose systems, together with which we arrive at a rigorous proof of the inequality for one of the very few soluble examples of an interacting Bose fluid, Girardeau's model. The latter proof demonstrates the importance of the thermodynamic limit of the structure factor, which must be taken initially at k different from 0. It also substantiates very well the heuristic density functional arguments, which are also shown to hold exactly in the limit of large wave-lengths. We also briefly discuss which features of the proof may be present in higher dimensions, as well as some open problems related to superfluidity of trapped gases.Comment: 28 pages, 2 figure, uses revtex

Quantum state transformations and the Schubert calculus

Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular focus on applications to quantum information theory. After discussing the connection between Horn's Problem and Nielsen's Theorem, we move on to characterizing the eigenvalues of the partial trace of a matrix.Comment: 40 pages. Accepted for publication in Annals of Physic

Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f-interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization V_c, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value in the limit of vanishing hybridization.Comment: 7 pages, 6 figure

Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model

Artificial spin ice systems have been introduced as a possible mean to investigate frustration effects in a well-controlled manner by fabricating lithographically-patterned two-dimensional arrangements of interacting magnetic nanostructures. This approach offers the opportunity to visualize unconventional states of matter, directly in real space, and triggered a wealth of studies at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite the strong efforts made these last ten years to provide an artificial realization of the celebrated square ice model, no simple geometry based on arrays of nanomagnets succeeded to capture the macroscopically degenerate ground state manifold of the corresponding model. Instead, in all works reported so far, square lattices of nanomagnets are characterized by a magnetically ordered ground state consisting of local flux-closure configurations with alternating chirality. Here, we show experimentally and theoretically, that all the characteristics of the square ice model can be observed if the artificial square lattice is properly designed. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of an algebraic spin liquid state characterized by the presence of pinch points in the associated magnetic structure factor. Local excitations, i.e. classical analogues of magnetic monopoles, are found to be free to evolve in a massively degenerated, divergence-free vacuum. We thus provide the first lab-on-chip platform allowing the investigation of collective phenomena, including Coulomb phases and ice-like physics.Comment: 26 pages, 10 figure

Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations

We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.Comment: 24 pages, 3 figure

Dynamical Properties of one dimensional Mott Insulators

At low energies the charge sector of one dimensional Mott insulators can be described in terms of a quantum Sine-Gordon model. Using exact results derived from integrability it is possible to determine dynamical properties like the frequency dependent optical conductivity. We compare the exact results to perturbation theory and renormalisation group calculations. We also discuss the application of our results to experiments on quasi-1D organic conductors.Comment: 17 pages, 5 figures, to appear in the proceedings of the NATO ASI/EC summer school "New Theoretical Approaches to Strongly Correlated Systems" Newton Institute for Mathematical Sciences, Cambridge UK, April 200

Ground State and Excitations of Spin Chain with Orbital Degeneracy

The one dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric viewpoint by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.Comment: Revtex, 9 pages, 3 figures; typos correcte

Charge-transfer metal-insulator transitions in the spin-one-half Falicov-Kimball model

The spin-one-half Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.Comment: 22 pages including 4 figures(eps), RevTe

Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases

We review our recent result on the rigorous derivation of the renormalized Gibbs measure from the many-body Gibbs state in 1D and 2D. The many-body renormalization is accomplished by simply tuning the chemical potential in the grand-canonical ensemble, which is analogous to the Wick ordering in the classical field theory.Comment: Contribution to Proceedings of the International Congress of Mathematical Physics, Montreal, Canada, July 23-28, 201

Excitons in quasi-one dimensional organics: Strong correlation approximation

An exciton theory for quasi-one dimensional organic materials is developed in the framework of the Su-Schrieffer-Heeger Hamiltonian augmented by short range extended Hubbard interactions. Within a strong electron-electron correlation approximation, the exciton properties are extensively studied. Using scattering theory, we analytically obtain the exciton energy and wavefunction and derive a criterion for the existence of a $B_u$ exciton. We also systematically investigate the effect of impurities on the coherent motion of an exciton. The coherence is measured by a suitably defined electron-hole correlation function. It is shown that, for impurities with an on-site potential, a crossover behavior will occur if the impurity strength is comparable to the bandwidth of the exciton, corresponding to exciton localization. For a charged impurity with a spatially extended potential, in addition to localization the exciton will dissociate into an uncorrelated electron-hole pair when the impurity is sufficiently strong to overcome the Coulomb interaction which binds the electron-hole pair. Interchain coupling effects are also discussed by considering two polymer chains coupled through nearest-neighbor interchain hopping $t_{\perp}$ and interchain Coulomb interaction $V_{\perp}$. Within the $t$ matrix scattering formalism, for every center-of-mass momentum, we find two poles determined only by $V_{\perp}$, which correspond to the interchain excitons. Finally, the exciton state is used to study the charge transfer from a polymer chain to an adjacent dopant molecule.Comment: 24 pages, 23 eps figures, pdf file of the paper availabl