The low-temperature phase diagram of one-dimensional weakly disordered quantum systems such as charge or spin density waves and Luttinger liquids is studied by a full finite temperature renormalization-group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an exact solution in the case of strong disorder and by a mapping onto the Burgers equation with noise in the case of weak disorder, respectively. At zero temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wavelength of the phason excitations. The existence of a zero-temperature transition is reflected in a rich crossover phase diagram of the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.
The low-temperature phase diagram of one-dimensional weakly disordered quantum systems such as charge or spin density waves and Luttinger liquids is studied by a full finite temperature renormalization-group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an exact solution in the case of strong disorder and by a mapping onto the Burgers equation with noise in the case of weak disorder, respectively. At zero temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wavelength of the phason excitations. The existence of a zero-temperature transition is reflected in a rich crossover phase diagram of the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.
The low temperature phase diagram of 1D disordered quantum systems such as charge or spin density waves, superfluids, and related systems is considered by a full finite- T renormalization group approach for the first time. At zero temperature the consideration of quantum phase slips leads to a new scenario for the unpinning (delocalization) transition. In the strong pinning limit the model is solved exactly. At finite T a rich crossover diagram with various scaling regions is found which reflects the zero temperature quantum critical behavior.
Disordered elastic systems are studied in the quantum, classical, and dynamic regime in the present thesis. The thesis consists of two main parts: In the first part we study the low temperature phase diagram of one-dimensional weakly disordered quantum systems like charge or spin density waves and Luttinger liquids by a full finite temperature renormalization group (RG) calculation. In the classical region, for vanishing quantum fluctuations those results are supplemented by an exact solution of the model in the case of strong disorder, described by the ground state and the correlation function. Furthermore, by a mapping of the problem onto a Burgers equation with noise, in the case of weak disorder, we can derive an expression for the correlation length. At zero temperature we reproduce the (quantum) phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram determined by the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential, and for the case of density waves we discuss the influence of quantum phase-slips, which might lead to a new scenario for the unpinning (delocalization) transition at zero temperature. Additionally, we analyze the current noise in a classical one-dimensional charge density wave system in the weak pinning regime by solving the overdamped equation of motion numerically. At low temperatures and just above the zero temperature depinning threshold, the power spectrum of the current noise reveals the existence of 1/f or flicker noise. Our results are in agreement with experimental measurements in quasi-one-dimensional charge density wave systems. In part two, we examine the viscous motion of an interface driven by a periodically oscillating external field in a random medium. The velocity exhibits a smeared depinning transition showing a pronounced hysteresis, which is absent in the adiabatic case. Its width is determined by a new length scale, introduced by the frequency of the external drive and - in the low frequency regime - by the critical exponents of the zero frequency depinning transition. Scaling arguments and an approximate renormalization group treatment predict a power law behavior of the velocity as a function of frequency and field amplitude at the dc depinning threshold, which is confirmed numerically. Thermal fluctuations lead to an additional smearing of the transition. If the amplitude of the external driving force is smaller than the depinning field, the motion of the interface by avalanches has to be taken into account in order to describe the velocity hysteresis. To check the validity of our model with respect to experimental results, we calculate the complex susceptibilities using an adiabatic and non-adiabatic approach numerically for finite systems and compare it to measurements of a superferromagnetic granular multilayer system and find that the model of an ac driven interface in a disordered environment can describe the main features of the experimental results. Additionally, the influence of a strong surface potential on the critical depinning of an elastic system, driven in a random medium is considered. If the surface potential prevents depinning completely, the curvature of the displacement profile at zero temperature exhibits a pronounced rhombic hysteresis curve with width of two times the (bulk) depinning field. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depinns by the applied force or thermal creep, the curvature is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices, and charge-density waves. As addendum we examine low dimensional interacting, but clean Bose systems at low temperatures. The interaction leads to scattering events of the over-condensate particles for which we calculate the scattering times using Fermi's golden rule. With that we derive the thermal conductivity and the related weak localization corrections. This is done for short and long-range interactions.
The low temperature phase diagram of 1D disordered quantum systems like charge or spin density waves, superfluids, and related systems is considered by a full finite T renormalization group approach for the first time. At zero temperature the consideration of quantum phase slips leads to a new scenario for the unpinning (delocalization) transition. In the strong pinning limit the model is solved exactly. At finite T a rich crossover diagram with various scaling regions is found which reflects the zero temperature quantum critical behavior.
In this dissertation, we study the superfluid-insulator quantum phase transition in disordered boson systems. Recently, there has been considerable controversy over the validity of the scaling relations of the superfluid--Bose-glass quantum phase transition in three dimensions. Results from experimental and numerical studies on disordered quantum magnets contradict the scaling relations and the associated conventional scaling hypothesis for the singular part of the free energy. We determine various critical exponents of the superfluid--Bose-glass quantum phase transition in three-dimensional disordered Bose-Hubbard model through extensive Monte Carlo simulations. Our numerical study shows the previous studies on disordered quantum magnets were performed outside the quantum critical region, and our results for the critical exponents are in perfect agreement with previous theoretical predictions. We next move to study theoretically and numerically the superfluid-insulator quantum phase transition in one-dimensional disordered boson systems. While the superfluid-insulator transition in the weak disorder limit is well understood through the perturbative renormalization group study by Giamarchi and Schulz, transitions in the strong disorder regime are beyond the reach of this method. This problem was recently attacked by Altman et al. with the real space renormalization group method. They reached the conclusion that the superfluid-insulator transition in the strong disorder regime can be explained by the Coulomb blockade physics of weak links. However, their method is actually uncontrolled. Taking account of the crucial role of the hydrodynamic renormalization of weak links, finally, Pollet et al. put forward an asymptotically exact renormalization group theory of the superfluid-insulator transition. Based on this theory, we are able to provide an accurate description of the interplay between the well-known Giamarchi-Schulz criticality and the new weak-link criticality. A significant part of the ground-state phase diagram of one-dimensional disordered Bose-Hubbard model at unit filling is also determined numerically. In particular, we established the position of the multicritical point beyond which the new weak-link criticality takes over of the Giamarchi–Schulz criticality.
We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values.
We analyze the finite-temperature effects on the phase diagram describing the insulating properties of interacting one-dimensional bosons in a quasiperiodic lattice. We examine thermal effects by comparing experimental results to exact diagonalization for small-sized systems and to density-matrix renormalization group (DMRG) computations. At weak interactions, we find short thermal correlation lengths, indicating a substantial impact of temperature on the system coherence. Conversely, at strong interactions, the obtained thermal correlation lengths are significantly larger than the localization length, and the quantum nature of the T=0 Bose-glass phase is preserved up to a crossover temperature that depends on the disorder strength. Furthermore, in the absence of disorder, we show how quasiexact finite-T DMRG computations, compared to experimental results, can be employed to estimate the temperature, which is not directly accessible in the experiment.