Disorder-driven Phase Transition Research Articles

Disorder-driven phase transitions in bosonic fractional quantum Hall liquids

We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At $f=1$, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the $f=5/2$ fermionic cousin.

Disorder-driven phase transition in the second-order non-Hermitian skin effect

The non-Hermitian skin effect exhibits a collapse of extended bulk modes into an extensive number of localized boundary states in the open boundary condition. Here, we demonstrate a disorder-driven phase transition of a trivial non-Hermitian system to the higher-order non-Hermitian skin effect phase. In contrast to clean systems, the disorder-induced boundary modes form an arc in the complex energy plane, which is a manifestation of the disorder-driven energy-dependent phase transition. At the phase transition, localized corner modes and bulk modes characterized by trivial Hamiltonians coexist within a single band, while they remain separated in the complex energy plane. This behavior is analogous to the mobility edge phenomena in disordered Hermitian systems. Using effective medium theory and numerical diagonalizations, we provide a systematic characterization of the disorder-driven phase transition.

Disorder-enhanced superconductivity in a quasi-one-dimensional strongly correlated system

We perform an analytical and numerical study of a superconducting instability in quasi-one-dimensional (quasi-1D) disordered systems. Modeling them as an array of Luttinger liquids with Josephson-type interchain coupling, we employed renormalization-group analysis with an extensive search for parameters that support superconductivity enhancement. We have found that this phenomenon is possible in the parameters range that support a latent disorder-driven phase transition between charge- and spin-density-wave phases. Our results may explain the experimental observation of disorder-enhanced superconductivity.

Disorder driven phase transitions in weak AIII topological insulators

The tenfold classification of topological phases enumerates all strong topological phases for both clean and disordered systems. These strong topological phases are connected to the existence of robust edge states. However, in addition to the strong topological phases in the tenfold classification, there exist weak topological phases whose properties under disorder are less well understood. It is unknown if the weak topological indices can be generalized for arbitrary disorder, and the physical signatures of these indices is not known. In this paper, we study disordered models of the two dimensional weak AIII insulator. We demonstrate that the weak invariants can be defined at arbitrary disorder, and that these invariants are connected to the presence or absence of bound charge at dislocation sites.

Unveiling the vortex glass phase in the surface and volume of a type-II superconductor

Order-disorder transitions between glassy phases are common in nature and yet a comprehensive survey on the entailed structural changes is challenging since the constituents are in the micro-scale. Vortex matter in type-II superconductors is a model system where some of these experimental challenges can be tackled. Samples with point disorder present a glassy transition on increasing the density of vortices. A glassy yet quasi-crystalline phase, the Bragg glass, nucleates at low densities. The vortex glass stable at high densities is expected to be disordered, however its detailed structural properties remained experimentally elusive. Here we show that the vortex glass has large crystallites with in-plane positional displacements growing algebraically and short-range orientational order. Furthermore, the vortex glass has a finite and almost constant correlation length along the direction of vortices, in sharp contrast with strong entanglement. These results are important for the understanding of disorder-driven phase transitions in glassy condensed matter.

Evolution of quantum entanglement with disorder in fractional quantum Hall liquids

We present a detailed study of the ground-state entanglement in disordered fractional quantum Hall liquids. We consider electrons at various filling fractions $f$ in the lowest Landau level, with Coulomb interactions. At $f=1/3,1/5$ and $2/5$ where an incompressible ground-state manifold exists at zero disorder, we observe a pronounced minimum in the derivative of entanglement entropy with respect to disorder. At each filling, the position of this minimum is stable against increasing system size, but its magnitude grows monotonically and appears to diverge in the thermodynamic limit. We consider this behaviour of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to a trivial insulating phase. On the contrary, at $f=1/2$ where a compressible composite fermion sea is present at zero disorder, the entropy derivative exhibits much greater, almost chaotic, finite-size effects, without a clear phase transition signal for system sizes within our exact diagonalization limit. However, the dependence of entanglement entropy with system size changes with increasing disorder, consistent with the expectation of a phase transition from a composite fermion sea to an insulator. Finally, we consider $f=1/7$ where compressible Wigner crystals are quite competitive at zero disorder, and analyze the level statistics of entanglement spectrum at $f=1/3$.

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids.

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.

Can 3D light localization be reached in ‘white paint’?

When waves scatter multiple times in 3D random media, a disorder driven phase transition from diffusion to localization may occur (Anderson 1958 Phys. Rev. 109 1492–505; Abrahams et al 1979 Phys. Rev. Lett. 42 673–6). In ‘The question of classical localization: a theory of white paint?’ Anderson suggested the possibility to observe light localization in TiO2 samples (Anderson 1985 Phil. Mag. B 52 505–9). We recently claimed the observation of localization effects measuring photon time of flight (ToF) distributions (Störzer et al 2006 Phys. Rev. Lett. 96 063904) and evaluating transmission profiles (TPs) (Sperling et al 2013 Nat. Photonics 7 48–52) in such TiO2 samples. Here we present a careful study of the long time tail of ToF distributions and the long time behavior of the TP width for very thin samples and different turbidities that questions the localization interpretation. We further show new data that allow an alternative consistent explanation of these previous data by a fluorescence process. An adapted diffusion model including an appropriate exponential fluorescence decay accounts for the shape of the ToF distributions and the TP width. These observations question whether the strong localization regime can be reached with visible light scattering in polydisperse TiO2 samples, since the disorder parameter can hardly be increased any further in such a ‘white paint’ material.

Disorder-driven phase transition in La0.37D0.30Ca0.33MnO3 (D = Bi, Sm) manganites

In the present work we report the structural, electron spin resonance (ESR) and magnetic properties of La0.37D0.30Ca0.33MnO3 (D = Bi, Sm) manganites synthesized by sol-gel method. The critical behavior at the critical point, where the system undergoes phase transition from paramagnetic (PM) to ferromagnetic (FM) state, is investigated by using modified-Arrott plots, Kouvel-Fisher method and critical isotherm analysis. Both the samples show second-order phase transition near the critical point. The decrease in magnetization (M), Curie temperature (TC), evolution of spin or cluster glass behavior and the nature of second-order phase transition compared to the first-order transition reported in the literature for La0.67Ca0.33MnO3 are ascribed to disorder caused by the size mismatch of the A-site cations with Bi and Sm doping at La-site.

Critical behavior of the random-field Ising model at and beyond the upper critical dimension

The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d=6,7 which are larger or equal to the assumed upper critical dimension, d_u=6, mean-field behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.

Effects of dilute columnar defects on the vortex matter in Bi 2Sr 2CaCu 2O 8+δ near the disorder-driven phase transition

Magneto-optical measurements are employed to characterize the disorder-driven vortex phase transition and the metastable disordered vortex state in heavy-ion irradiated and pristine regions of the same Bi 2Sr 2CaCu 2O 8+δ crystal. We find that dilute columnar defects, while hardly affect the disorder-driven phase transition line, significantly increase the lifetime of the metastable state created in the vicinity of this line. Study of flux injection from the pristine region into the irradiated region suggests that in presence of columnar defects a metastable disordered state may be created in the bulk, in addition to being injected from the edges.

Disorder-driven phase transition in a spring-block type magnetization model

The critical behavior of a one-dimensional Burridge–Knopoff type spring-block model, aimed to describe magnetization phenomena, is studied by Monte Carlo type computer simulations. Disorder is introduced through randomly distributed pinning centers and the magnetization process is modeled through a relaxation dynamics. The distribution of avalanche sizes (jumps in magnetization) is studied for different disorder values. The results indicate that the model exhibits a disorder-driven phase transition. Estimates for some critical exponents and scaling laws are given.

Angular dependence of the order-disorder transition in proton irradiated single crystalMgB2

We present magnetization results on a proton irradiated $\mathrm{Mg}{\mathrm{B}}_{2}$ single crystal that displays a peak in magnetization for the field applied parallel to the $c$ axis. Magnetic history effects are observed, which are ascribed to the occurrence of a disorder driven phase transition close to an inflection point in the magnetization-field curve. We demonstrate that the angular and temperature dependence of this feature is significantly different to that of the lower and upper critical fields.

Disorder-tuned transition between a quantum Hall liquid and Hall insulator.

We report measurements of the disorder-driven phase transition from a quantum Hall liquid to Hall insulator at \ensuremath{\nu}=1/3 and \ensuremath{\nu}=2 observed in a two-dimensional electron gas. The data show good scaling behavior over a wide range of densities and temperatures with an exponent 1/zx\ensuremath{\sim}0.43 for both \ensuremath{\nu}=1/3 and 2, where z is the dynamical exponent and x is the correlation length exponent. The critical conductance at the transition is found to be ${\mathrm{\ensuremath{\sigma}}}_{\mathit{xx}}$=0.09\ifmmode\pm\else\textpm\fi{}0.01${\mathit{e}}^{2}$/h for the \ensuremath{\nu}=1/3 transition and ${\mathrm{\ensuremath{\sigma}}}_{\mathit{xx}}$=0.9\ifmmode\pm\else\textpm\fi{}0.15${\mathit{e}}^{2}$/h for the \ensuremath{\nu}=2 case.