Quantum Glass of Interacting Bosons with Off-Diagonal Disorder.

We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n-replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

Scaling near the quantum-critical point in the SO(5) theory of the high-T(c) superconductivity.

We study the quantum-critical point scenario within the unified theory of superconductivity and antiferromagnetism based on the SO(5) symmetry. Closed-form expression for the quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear sigma-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also presented.

Three-dimensional Josephson-junction arrays in the quantum regime.

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. We obtain a phase diagram as a function of temperature, Josephson coupling, and charging energy. We also analyze the corresponding fluctuation conductivity and its universal scaling form in the vicinity of the zero-temperature quantum critical point.