First- and second-order quantum phase transitions of a q-state Potts model in fractal lattices.

Quantum phase transitions of a q-state Potts model in fractal lattices are studied using a continuous-time quantum Monte Carlo simulation technique. For small values of q, the transition is found to be second order and critical exponents of the quantum critical point are calculated. The dynamic critical exponent z is found to be greater than one for all fractals studied, which is in contrast to integer-dimensional regular lattices. When q is greater than a certain value q_{c}, the phase transition becomes first order, where q_{c} depends on the lattice. Further analysis shows that the characteristics of phase transitions are more sensitive to the average number of nearest neighbors than the Hausdorff dimension or the order of ramification.

Quantum critical behavior of the quantum Ising model on fractal lattices.

I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpinski carpet, Sierpinski gasket, and Sierpinski tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpinski tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.

Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.

I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.

Critical behavior of the quantum Ising model on a fractal structure.

We study the critical behavior of the transverse-field quantum Ising model on a fractal structure, namely the Sierpinski carpet. When a magnetic field Δ is applied perpendicular to the Ising spin direction, quantum fluctuations affect the transition between the ferromagnetic and the paramagnetic phases. Employing the continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, we investigate the interplay between the quantum fluctuations and the exotic dimensionality of the fractal structure and its effect on the critical behavior. As the transverse magnetic field increases, the critical temperature monotonically decreases until it apparently vanishes at a critical field Δ(c), beyond which the system becomes paramagnetic at all temperatures. However, the critical exponents are independent of Δ and remain the same as in the purely classical(Δ=0) case.

Quantum effects on criticality of an Ising model in scale-free networks: Beyond mean-field universality class.

We study the effect of quantum fluctuations on the critical behavior of the Ising ferromagnetic phase transitions that do not belong to the mean-field universality class. A model system is considered, in which Ising spins are placed on the nodes of a scale-free network. Our Monte Carlo analysis shows that the critical exponents differ from those of mean-field phase transitions when degree exponent gamma is in the range 3

Quantum depinning transition of quantum Hall stripes.

We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor Deltanu(c). For DeltanuDeltanu(c). For Deltanu> or =Deltanu(c), we find a partial RSB solution in which there is free sliding only along the stripe direction. The transition is analogous to the Kosterlitz-Thouless phase transition.

Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction.

Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature or voltage dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.

Effect of quantum fluctuations in an Ising system on small-world networks.

We study quantum Ising spins placed on small-world networks. A simple model is considered in which the coupling between any given pair of spins is a nonzero constant if they are linked in the small-world network, and zero otherwise. By applying a transverse magnetic field, we have investigated the effect of quantum fluctuations. Our numerical analysis shows that the quantum fluctuations do not alter the universality class at the ferromagnetic phase transition, which is of the mean-field type. The transition temperature is reduced by the quantum fluctuations and eventually vanishes at the critical transverse field Delta(c). With increasing rewiring probability, Delta(c) is shown to be enhanced.

Coulomb blockade and kondo effect in a quantum Hall antidot.

We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, h/(2e) Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.