Quantum critical phenomena of long-range interacting bosons in a time-dependent random potential

We study the superfluid-insulator transition of a particle-hole symmetric system of long-range interacting bosons in a time-dependent random potential in two dimensions, using the momentum-shell renormalization-group method. We find a new stable fixed point with non-zero values of the parameters representing the shortand long-range interactions and disorder when the interaction is asymptotically logarithmic. This is contrasted to the non-random case with a logarithmic interaction, where the transition is argued to be firstorder, and to the 1/r Coulomb interaction case, where either a first-order transition or an XY-like transition is possible depending on the parameters. We propose that our model may be relevant in studying the vortex liquidvortex glass transition of interacting vortex lines in point-disordered type-II superconductors. PACS Numbers: 05.30.Jp, 64.60.Ak, 74.40.+k, 74.60.Ge Typeset using REVTEX 1 In recent years, there has been great interest in quantum critical phenomena occurring in systems of interacting bosons [1–8]. This has largely been motivated by several beautiful experiments on the superconductor to insulator transition in thin metallic films at very low temperature [9–14]. In many models, the superconductor (or charged superfluid) to insulator (or Bose glass) transition in disordered films is considered as a localization transition of bosonic Cooper pairs in an external random potential [1,4–7]. In non-random systems, the superfluid to (Mott) insulator transition can be triggered by changing the density of bosons through critical values commensurate with the underlying periodic lattice [1,2]. Since Cooper pairs are charged, one needs to consider the influence of long-range interactions on the nature of the critical phenomena. In the absence of disorder, the superconductor-Mott insulator transition of charged bosons in two dimensions interacting by the 1/r Coulomb potential has been studied by Fisher and Grinstein via renormalization-group methods [1]. They showed that when the (bare) Coulomb interaction is sufficiently weak, the transition belongs to the three-dimensional XY-model universality class, whereas when the Coulomb interaction is sufficiently strong, it is first-order. In this paper, we generalize Fisher and Grinstein’s model to the cases with the 1/r or logarithmic interaction in a time-dependent random potential. Time dependence of the potential in classical static critical phenomena is unimportant [8]. In quantum critical phenomena, however, it can lead to new universality classes as will be shown in the present work. As well as being relevant in studying novel quantum critical phenomena, our model may be also a useful representation of a system of long-range interacting vortex lines in point-disordered type-II superconductors in an external magnetic field. According to the mapping originally due to Nelson, vortex lines in three spatial dimensions are considered as the world lines of bosons residing in two spatial dimensions perpendicular to the magnetic field [15–17]. The dimension parallel to the magnetic field is mapped to the imaginary time dimension of a bosonic system. Therefore the static random potential provided by isotropically distributed impurities in superconductors can be regarded as a time-dependent potential that is random in both space and time. The quantum superconductor-insulator transition of interacting bosons is analogous to the clas2 sical vortex liquid-vortex glass transition of interacting vortex lines. We caution that in our model, the long-range interaction between vortex lines is confined to the plane perpendicular to the magnetic field. Applying the standard momentum-shell renormalization-group method to the logarithmically interacting case, we discover a new stable fixed point in two dimensions with non-zero values in the shortand long-range interactions and disorder when there exists a time-dependent random potential, whereas we find a first-order transition in the non-random case. Since the interaction between vortex lines is logarithmic in a wide range of length scales when the magnetic field is close to the upper critical field [18], we propose a possibility that our new random fixed point may describe the real vortex liquidvortex glass transition in point-disordered type-II superconductors. On the other hand, when the interaction is the 1/r Coulomb interaction, we find a behavior analogous to Fisher and Grinstein’s results in a non-random system. We consider the (d+ 1)-dimensional classical action for the m-component classical complex Bose field ψi(~x, τ) coupled to the scalar gauge field A(~x, τ) mediating the long-range interaction between charge e bosons in d spatial and one temporal dimensions: S = ∫