Morse Theory in Field Theory

We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in TQM can be expressed via intersection numbers of certain submanifolds of the target space with paths of steepest descent between critical points of a Morse function. In the end we conjecture another correspondence between quantum mechanics correlators and integrals of Massey products of certain cohomology classes.Comment: updated versio

Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions

Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP(2,2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."Comment: 15 pages, no figures, minor correction

Quantum K-theory of Quiver Varieties and Many-Body Systems

We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.Comment: v3: 33 pages, some clarifications and correction

Quantum Deformations of the One-Dimensional Hubbard Model

The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation U_q(psu(2|2)xR^3) and derive the fundamental R-matrix. From the latter we deduce an integrable spin chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model

Surface-electronic structure of La(0001) and Lu(0001)

Most spectroscopic methods for studying the electronic structure of metal surfaces have the disadvantage that either only occupied or only unoccupied states can be probed, and the signal is cut at the Fermi edge. This leads to significant uncertainties, when states are very close to the Fermi level. By performing low-temperature scanning tunneling spectroscopy and ab initio calculations, we study the surface-electronic structure of La(0001) and Lu(0001), and demonstrate that in this way detailed information on the surface-electronic structure very close to the Fermi energy can be derived with high accuracy.Comment: 6 pages, 4 figures, 1 table submitted to PR

Strong spin-orbit splitting on Bi surfaces

Using first-principles calculations and angle-resolved photoemission, we show that the spin-orbit interaction leads to a strong splitting of the surface state bands on low-index surfaces of Bi. The dispersion of the states and the corresponding Fermi surfaces are profoundly modified in the whole surface Brillouin zone. We discuss the implications of these findings with respect to a proposed surface charge density wave on Bi(111) as well as to the surface screening, surface spin-density waves, electron (hole) dynamics in surface states, and to possible applications to the spintronics.Comment: 4 pages 2 figure

The role of the spin in quasiparticle interference

Quasiparticle interference patterns measured by scanning tunneling microscopy (STM) can be used to study the local electronic structure of metal surfaces and high temperature superconductors. Here, we show that even in non-magnetic systems the spin of the quasiparticles can have a profound effect on the interference patterns. On Bi(110), where the surface state bands are not spin-degenerate, the patterns are not related to the dispersion of the electronic states in a simple way. In fact, the features which are expected for the spin-independent situation are absent and the observed interference patterns can only be interpreted by taking spin-conserving scattering events into account.Comment: 4 pages, 2 figure

Holographic Superconductor for a Lifshitz fixed point

We consider the gravity dual of strongly coupled system at a Lifshitz-fixed point and finite temperature, which was constructed in a recent work arXiv:0909.0263. We construct an Abelian Higgs model in that background and calculate condensation and conductivity using holographic techniques. We find that condensation happens and DC conductivity blows up when temperature turns below a critical value.Comment: 14 pages, 4 figures, v4: improved version, references adde

Acoustic Plasmons in Nickel and Its Modification upon Hydrogen Uptake

In this work, we study, in the framework of the ab initio linear-response time-dependent density functional theory, the low-energy collective electronic excitations with characteristic sound-like dispersion, called acoustic plasmons, in bulk ferromagnetic nickel. Since the respective spatial oscillations in slow and fast charge systems involve states with different spins, excitation of such plasmons in nickel should result in the spatial variations in the spin structure as well. We extend our study to NiHx with different hydrogen concentrations x. We vary the hydrogen concentration and trace variations in the acoustic plasmons properties. Finally, at x=1 the acoustic modes disappear in paramagnetic NiH. The explanation of such evolution is based on the changes in the population of different energy bands with hydrogen content variation.Y.M.K. acknowledges support from the Government research assignment for ISPMS SB RAS, project FWRW-2022-0001 (in the part of band structure calculations). I.V.S. acknowledges support from the Ministry of Education and Science of the Russian Federation within State Task No. FSWM-2020-0033 (in the part of electronic structure and dielectric function calculations). E.V.C. acknowledges support from Saint Petersburg State University (Project ID No. 90383050). V.M.S. acknowledges financial support by Grant No. PID2019-105488GB-I00 funded by MCIN/AEI/10.13039/501100011033/