A one-dimensional quantum version of the frustrated XY (planar rotor) model is considered which can be physically realized as a ladder of Josephson junctions at half a flux quantum per plaquette. This system undergoes a superconductor to insulator transition at zero temperature as a function of charging energy. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. Depending on the ratio between the interchain and intrachain couplings the system can have single or double transitions which is consistent with the prediction that its critical behavior should be described by the two-dimensional classical XY-Ising model.
A generalization of the one-dimensional frustrated quantum
XY model is considered in which the interchain and intrachain coupling constants of the two infinite
XY (planar rotor) chains have different strengths. The model can describe the superconductor to insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical
XY-Ising model. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal interchain and intrachain coupling constants, the
XY and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behavior for the chirality order parameter and a superconductor-insulator transition in the universality class of the two-dimensional classical
XY model.
We study the zero-temperature phase diagram of a dissipationless and disorder-free Josephson junction chain. Namely, we determine the critical Josephson energy below which the chain becomes insulating as a function of the ratio of two capacitances: the capacitance of each Josephson junction and the capacitance between each superconducting island and the ground. We develop an imaginary-time path integral quantum Monte Carlo algorithm in the charge representation, which enables us to efficiently handle the electrostatic part of the chain Hamiltonian. We find that a large part of the phase diagram is determined by anharmonic corrections which are not captured by the standard Kosterlitz-Thouless renormalization group description of the transition.
We numerically study the superconductor-insulator phase transition in a model disordered two-dimensional (2D) superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the
(2+1)D XY model in the presence of both disorder and magnetic field. The
XY coupling is assumed to have the form $\ensuremath{-}J\text{ }\text{cos}({\ensuremath{\theta}}_{i}\ensuremath{-}{\ensuremath{\theta}}_{j}\ensuremath{-}{A}_{ij})$, where
Aij has a mean of zero and a standard deviation $\ensuremath{\Delta}{A}_{ij}$. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values $\ensuremath{\Delta}{A}_{ij}$ then correspond to an applied field such that the average number of flux quanta per plaquette has various integer values
N: larger
N corresponds to larger $\ensuremath{\Delta}{A}_{ij}$. For any value of $\ensuremath{\Delta}{A}_{ij}$, there appears to be a critical coupling constant ${K}_{c}(\ensuremath{\Delta}{A}_{ij})=\sqrt{{[J/(2U)]}_{c}}$, where
U is the charging energy, below which the system is a Mott insulator; there is also a corresponding critical conductivity ${\ensuremath{\sigma}}^{\ensuremath{\ast}}(\ensuremath{\Delta}{A}_{ij})$ at the transition. For $\ensuremath{\Delta}{A}_{ij}=\ensuremath{\infty}$, the order parameter of the transition is a renormalized coupling constant
g. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of $\ensuremath{\Delta}{A}_{ij}$ takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is $z\ensuremath{\sim}1.3$. By contrast,
z=1 for this model at $\ensuremath{\Delta}{A}_{ij}=0$. We suggest that the superconductor-to-insulator transition is actually of this I to BG class at all nonzero $\ensuremath{\Delta}{A}_{ij}$'s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion [A. B. Harris, J. Phys. C 7, 1671 (1974)].
Kc is found to be a monotonically increasing function of $\ensuremath{\Delta}{A}_{ij}$. For certain values of
K, a disordered Josephson array may undergo a transition from an ordered, Bose glass phase to an insulator with increasing $\ensuremath{\Delta}{A}_{ij}$.
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to
f flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of
f. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near
f=1/2 are consistent with the experimental observations. The same scaling behavior is observed near
f=1/3. For a honeycomb array, although similar results are obtained for
f=1/3, the transition is absent for
f=1/2, consistent with an incommensurate vortex phase.
We investigate the effect of a magnetic field on a bosonic ladder. We show that such a system leads to the one-dimensional equivalent of a vortex lattice in a superconductor. We investigate the physical properties of the vortex phase, such as vortex density and vortex correlation functions, and show that magnetization has plateaus for some commensurate values of the magnetic field. The lowest plateau corresponds to a true Meissner to vortex transition at a critical field
Hc1 that exists although the system has no long-range superconducting order. Implications for experimental realizations such as Josephson-junction arrays are discussed.