Quantum Critical Transport Near the Mott Transition

We perform a systematic study of incoherent transport in the high temperature crossover region of the half-filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form $\rho(\delta U,T)=\rho_{c}(T)f(T/T_{o}(\delta U))$, with $T_{o}(\delta U)\sim\delta U^{z\nu}$, and $\rho_{c}(T)\sim T$. The corresponding $\beta$-function displays a "strong coupling" form $\beta\sim\ln(\rho_{c}/\rho)$, reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.Comment: Published version; 4+epsilon pages, 4 figure

Symmetries and classical quantization

A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge) and discrete symmetries of the corresponding systems, but there are some special discrete values of them which give rise to the maximal global symmetries at the classical level. Exactly the same values of the parameters are separated at the quantum level, where, in particular, they are singled out by the requirement of conservation of the discrete symmetries. The phenomenon is observed for the familiar pseudoclassical model of 3D P,T-invariant massive fermion system and for a new pseudoclassical model of 3D P,T-invariant system of topologically massive U(1) gauge fields.Comment: 10 pages, LaTe

Hidden Kondo Effect in a Correlated Electron Chain

We develop a general Bethe Ansatz formalism for diagonalizing an integrable model of a magnetic impurity of arbitrary spin coupled ferro- or antiferromagnetically to a chain of interacting electrons. The method is applied to an open chain, with the exact solution revealing a ``hidden'' Kondo effect driven by forward electron scattering off the impurity. We argue that the so-called ``operator reflection matrices'' proposed in recent Bethe Ansatz studies of related models emulate only forward electron-impurity scattering which may explain the absence of complete Kondo screening for certain values of the impurity-electron coupling in these models.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N+1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.Comment: Latex, 12 page

Hidden nonlinear supersymmetries in pure parabosonic systems

The existence of intimate relation between generalized statistics and supersymmetry is established by observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear superalgebra. The nonlinear supersymmetry of parabosonic systems may be realized, in turn, by modifying appropriately the usual supersymmetric quantum mechanics. The relation of nonlinear parabosonic supersymmetry to the Calogero-like models with exchange interaction and to the spin chain models with inverse-square interaction is pointed out.Comment: 20 pages, one reference corrected, to appear in Int. J. Mod. Phys.

Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z_2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.Comment: 8 pages, 5 figures, 4 tables; Figure 2 and Table II update

Gauge non-invariance as tests of emergent gauge symmetry

We motivate the concept of emergent gauge symmetry and discuss ways that this concept can be tested. The key idea is that if a symmetry is emergent, one should look for small violations of this symmetry because the underlying fundamental theory does not contain the symmetry. We describe our recent work implementing this idea in the gravity sector. We also describe the reasons why violations of gauge symmetry may well be linked to violations of Lorentz invariance.Comment: 5 pages, Invited talk presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Classification of engineered topological superconductors

I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1d systems with Rashba spin-orbit coupling and time-reversal violating superconductivity, as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional "hidden" symmetries emerge, with a significant impact on the topological properties of the system. The latter, generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.Comment: To appear in New Journal of Physics for the Focus on Majorana Fermions in Condensed Matter; Final version 19 pages, 6 figures: a new section was added concerning the appearance of MFs in two coupled Rasba semiconducting wires with proximity induced superconductivity and a finite supercurrent flow, without the application of a magnetic field. Generally improved discussion and references adde