Uncovering the mechanism of the impurity-selective Mott transition in paramagnetic V2_{2}O3_{3}

While the phase diagrams of the one- and multi-orbital Hubbard model have been well studied, the physics of real Mott insulators is often much richer, material dependent, and poorly understood. In the prototype Mott insulator V$_{2}$O$_{3}$, chemical pressure was initially believed to explain why the paramagnetic-metal to antiferromagnetic-insulator transition temperature is lowered by Ti doping while Cr doping strengthens correlations, eventually rendering the high-temperature phase paramagnetic insulating. However, this scenario has been recently shown both experimentally and theoretically to be untenable. Based on full structural optimization, we demonstrate via the charge self-consistent combination of density functional theory and dynamical mean-field theory that changes in the V$_{2}$O$_{3}$ phase diagram are driven by defect-induced local symmetry breakings resulting from dramatically different couplings of Cr and Ti dopants to the host system. This finding emphasizes the high sensitivity of the Mott metal-insulator transition to the local environment and the importance of accurately accounting for the one-electron Hamiltonian, since correlations crucially respond to it.Comment: 5 pages, 5 figures, supplementary informatio

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This first paper explains the mathematical tools that underlie the method.Comment: This version contains minor updates of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4312--4328, July 201

Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods

In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable communication channels including the nonlinear Schr\"odinger channel, modeling pulse propagation in optical fibers. These methods are subsequently tested and their ability to estimate the spectrum are compared against each other. These methods are used to compute the spectrum of various signals commonly used in the optical fiber communications. It is found that the layer-peeling and the spectral methods are suitable schemes to estimate the nonlinear spectra with good accuracy. To illustrate the structure of the spectrum, the locus of the eigenvalues is determined under amplitude and phase modulation in a number of examples. It is observed that in some cases, as signal parameters vary, eigenvalues collide and change their course of motion. The real axis is typically the place from which new eigenvalues originate or are absorbed into after traveling a trajectory in the complex plane.Comment: Minor updates to IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4329--4345, July 201

Dimensional tuning of electronic states under strong and frustrated interactions

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.Comment: 4pages 4figures included. to appear in Phys. Rev. Lett. vol. 10