Supersymmetric Model of a 2D Long-Range Bose Liquid

The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane, Kivelson, Lee and Zhang as the Hamiltonian which has Jastrow-type wavefunctions as the ground-state solution), is shown to possess nonrelativistic supersymmetry. For the special value of the coupling constant $\alpha=1/2$ the quantum mechanics described by this Hamiltonian is shown to be equivalent to the dynamics of (complex) eigenvalues of random Gaussian ensemble of normal complex matrices. For general $\alpha$, an exact relation between the equal-time current-current and density-density correlation functions is obtained, and used to derive an asymptotically exact (at low wavevectors q) spectrum of single-particle excitations beyond the superfluid ground-state (realized at low $\alpha$'s). The ground-state at very large $\alpha$ is shown to be of ``Quantum Hexatic" type, possessing long-range orientational order and quasi-long-range translational order but with zero shear modulus. Possible scenaria of the ground-state phase transitions as function of $\alpha$ are discussed.Comment: Revtex; 12 pages, 1 Postscript figur

Superconductor-insulator duality for the array of Josephson wires

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state corresponding to small $q < q_c$. The values of $q_c$ are calculated for magnetic frustrations $f= 0$ and $f= \frac12$. Temperature of superconductive transition $T_c(q)$ and $q < q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q} = q/\sqrt{N}$; we estimated critical value $\bar{q}_c$.Comment: 5 pages, 2 figure

Coulomb effects in a ballistic one-channel S-S-S device

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy $E_C \ll \Delta$. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to $\pi$, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge $Q_x=C V_g$ with period $2e$.Comment: 11 pages, REVTeX, 10 figures, uses eps

Quantum spin metal state on a decorated honeycomb lattice

We present a modification of exactly solvable spin-(1/2) Kitaev model on the decorated honeycomb lattice, with a ground state of "spin metal" type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi-circle those size depends on the ratio of exchange couplings. Low-temperature heat capacity C(T) and dynamic spin susceptibility \chi(\omega,T) are calculated in the case of small Fermi-circle. Whereas C(T)\sim T at low temperatures as it is expected for a Fermi-liquid, spin excitations are gapful and \chi(\omega,T) demonstrate unusual behaviour with a power-law peak near the resonance frequency. The corresponding exponent as well as the peak shape are calculated.Comment: 4 pages, 3 figure