Kaleidoscope of exotic quantum phases in a frustrated XY model

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions

Chaotic quantum dots with strongly correlated electrons

Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix theory (RMT), the Renormalization Group (RG) and the 1/N expansion. Here the reader is introduced to these techniques and shown how they may be combined to answer a set of questions pertaining to quantum dotsComment: latex file 16 pages 8 figures, to appear in Reviews of Modern Physic

Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid

Recent experiments on the organic compound \kappa-(ET)_2Cu_2(CN)_3 have provided a promising example of a two dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular-momentum/spin-triplet channels. Implications to experiments are discussed.Comment: 4 pages, 1 figur

Screening of a hypercritical charge in graphene

Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened potential with distance is shown to follow the 3/2 power. It gradually changes to the Coulomb law outside of a hypercritical core whose radius is proportional to the external charge.Comment: (v1) 4 pages, 1 figure (v2) Much improved introduction; extended range of numeric

Hartree-Fock ground state of the two-dimensional electron gas with Rashba spin-orbit interaction

We search for the uniform Hartree-Fock ground state of the two-dimensional electron gas formed in semiconductor heterostructures including the Rashba spin-orbit interaction. We identify two competing quantum phases: a ferromagnetic one with partial spin polarization in the perpendicular direction and a paramagnetic one with in-plane spin. We present a phase diagram in terms of the relative strengths of the Rashba to the Coulomb interaction and the electron density. We compare our theoretical description with existing experimental results obtained in GaAs-AlGaAs heterostructures.Comment: 5 pages, 2 figure

Atomic Collapse and Quasi-Rydberg States in Graphene

Charge impurities in graphene can host an infinite family of Rydberg-like resonance states of massless Dirac particles. These states, appearing for supercritical charge, are described by Bohr-Sommerfeld quantization of collapsing classical trajectories that descend on point charge, in analogy to Rydberg states relation with planetary orbits. We argue that divalent and trivalent charge impurities in graphene is an ideal system for realization of this atomic collapse regime. Strong coupling of these states to the Dirac continuum via Klein tunneling leads to striking resonance effects with direct signatures in transport, local properties and enhancement of the Kondo effect.Comment: 5 pages, 4 figure

Vacuum Polarization and Screening of Supercritical Impurities in Graphene

Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below certain critical value no density perturbation is found away from the impurity, in agreement with the linear response theory result. For supercritical charge, however, the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances. The Dirac-Kepler scattering states give rise to standing wave oscillations in the local density of states which appear and become prominent in the supercritical regime.Comment: 5 pages, 2 figure

The structure of the QED-Vacuum and Electron-Positron Pair Production in Super-Intense, pulsed Laser Fields

We discuss electron-positron pair-production by super-intense, short laser pulses off the physical vacuum state locally deformed by (stripped) nuclei with large nuclear charges. Consequences of non-perturbative vacuum polarisation resulting from such a deformation are shortly broached. Production probabilities per pulse are calculated.Comment: 10 pages, 1 figure, submitted to Journal of Physics

Large Rapidity Gap Processes in Proton-Nucleus Collisions

The cross sections for a variety of channels of proton-nucleus interaction associated with large gaps in rapidity are calculated within the Glauber-Gribov theory. We found inelastic shadowing corrections to be dramatically enhanced for such events. We employ the light-cone dipole formalism which allows to calculate the inelastic corrections to all orders of the multiple interaction. Although Gribov corrections are known to make nuclear matter more transparent, we demonstrate that in some instances they lead to an opaqueness. Numerical calculations are performed for the energies of the HERA-B experiment, and the RHIC-LHC colliders.Comment: 19 page

Fermi liquid near Pomeranchuk quantum criticality

We analyze the behavior of an itinerant Fermi system near a charge nematic(n=2) Pomeranchuk instability in terms of the Landau Fermi liquid (FL) theory. The main object of our study is the fully renormalized vertex function $\Gamma\Omega$, related to the Landau interaction function. We derive $\Gamma^\Omega$ for a model case of the long-range interaction in the nematic channel. Already within the Random Phase Approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor $Z_\Gamma$, related to the single-particle residue $Z$ and effective mass renormalization $m^*/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of $\Gamma^\Omega$, to obtain and solve a set of coupled non-linear equations for $Z_\Gamma$, $Z$, and $m^*/m$. We show that near the transition the system enters a critical FL regime, where $Z_\Gamma \sim Z \propto (1 + g_{c,2})^{1/2}$ and $m^*/m \approx 1/Z$, where $g_{c,2}$ is the $n=2$ charge Landau component which approaches -1 at the instability. We construct the Landau function of the critical FL and show that all but $g_{c,2}$ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\Sigma (K) \propto \int dP G(P) D (K-P)$ is asymptotically exact if one identifies the effective interaction $D$ with the RPA form of $\Gamma^\Omega$.Comment: References added, discussion of the dynamic vertex is modifie