List of poster contributions

We study the localization properties (in a given configuration basis) of pure interacting many-body systems. We introduce two quantum Monte Carlo schemes that allow for the calculation of Shannon-Renyi entropies (related to generalized inverse participation ratios) for large quantum many-body systems (such as quantum spin models) in any dimension. We find that multifractality is a generic feature of many-body systems and that a more relevant information is located in sub-leading terms of these entropies. Using several examples in spin chains and 2d spin systems, our simulations reveal that these subleading corrections are universal and reveal the nature of physical phases (such as symmetry-broken phases) or quantum phase transitions.

Work done in collaboration with David Luitz and Nicolas Laflorencie.

We study the density of states(DoS) of graphene,(tight-binding model on the
bipartite honeycomb lattice) with vacancies using a krylov subspace method. In
particular, we focus on compensated disorder, where the are equal number of
vacancies in both sublattices. In this poster, we present the details of the
simulations and numerical subtleties. In particular, we find that krylov subspace
method works well in practice for disorder concentrations more than 5%.
Finally, we allude to the fact that using this method, one can show that the
vacancy-induced DoS may not follow the expected Gade-Wegner form.

Chia-Wei Huang1,2, Sam T. Carr3,4, Dmitri Gutman2, Efrat Shimshoni2, and Alexander  D. Mirlin4,5,6
	
		
1Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany 
2 Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
3School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
4Institut für Theorie der Kondensierten Materie and DFG Center for  Functional Nanostructures, Karlsruher Institut für Technologie, 76128 Karlsruhe, Germany

5Institut für Nanotechnologie, Karlsruher Institut für Technologie, 76021 Karlsruhe, Germany
6Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

     We study transport properties of the helical edge states of two-dimensional integer and fractional topological insulators via double constrictions. Such constrictions couple the upper and lower edges of the sample and can be made and tuned by adding side gates to the system. Using renormalization group and duality mapping, we analyze phase diagrams and transport properties in each of these cases. Most interesting is the case of two constrictions tuned to resonance, where we obtain Kondo behavior, with a tunable Kondo temperature. Moving away from resonance gives the possibility of a metal-insulator transition at some finite detuning. For integer topological insulators, this physics is predicted to occur for realistic interaction strengths and gives a conductance G with two temperature T scales where the sign of dG/dT changes, one being related to the Kondo temperature while the other is related to the detuning.

Daniel Jung
    School of Engineering and Science, Jacobs University Bremen, 28759 Bremen,
    Germany.

Keith Slevin
    Department of Physics, Graduate School of Science, Osaka University, 1-1
    Machikaneyama, Toyonaka, Osaka 560-0043, Japan.

Stefan Kettemann
    School of Engineering and Science, Jacobs University Bremen, 28759 Bremen,
    Germany;
    Division of Advanced Materials Science, Pohang University of Science and
    Technology (POSTECH), Pohang 790-784, South Korea.

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition numerically [1, 2].  In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude $W_{rm c}$, in the presence of Heisenberg impurities, $W_{rm c}$ is first enhanced with increasing exchange coupling strength $J$ due to time-reversal symmetry breaking.  The resulting scaling with $J$ is analyzed and compared to analytical predictions by Wegner [3].  The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [4], which is the geometric average of the local density of states. The latter can efficiently be calculated using the kernel polynomial method [5].  We extend previous approaches [6] by combining the KPM with a finite-size scaling analysis.  We also discuss the relevance of our findings for systems like phosphor-doped silicon, which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [7].

[1] D. Jung, and S. Kettemann, AIP conference proceedings, submitted.
[2] D. Jung, K. Slevin, and S. Kettemann, to be published.
[3] F. Wegner, Nucl. Phys. B 280, 210 (1987).
[4] D. Jung, G. Czycholl, and S. Kettemann, Int. J. Mod.  Phys. Conf. Ser. 11,
    108 (2012).
[5] A. Weiße, G. Wellein, A. Alvermann, and H. Fehske, Rev. Mod. Phys. 78, 275
    (2006).
[6] G. Schubert, and H. Fehske, in Quantum and Semi-classical Percolation and
    Breakdown in Disordered Solids, edited by Bikas K. Chakrabarti, Kamal K.
    Bardhan, and Asok K. Sen, Lecture Notes in Physics Vol. 762 (Springer,
    Berlin, Heidelberg, 2009).
[7] H. von Löhneysen, Adv. Solid State Phys. 40, 143 (2000).

We consider transport characteristics of the 2D topological insulator edge
states in the presence of disorder. Two general setups are studied: a
junction of the two quantum-Hall insulators and a relatively thick HgTe quantum
well. In the first setup, an imbalance between the number of left- and right
propagating modes (n_L and n_R) may occur at the interface if the filling factor
is different on both sides of the junction. In this case, |n_L - n_R| edge modes
are topologically protected while all other states get eventually localized by
disorder. If an edge of a thick HgTe quantum well carries an odd number of
modes, one of them is also topologically protected from localization while
others are localized at sufficiently long scales. For both systems, we compute
the distribution of transmission probabilities and mesoscopic conductance
fluctuations. Technically, this requires solving the one-dimensional non-linear
sigma model with a topological term. At relatively short scales, we use
quasiclassical approximation and perturbation theory while for longer setups the
transfer-matrix formalism is employed. For the quantum-Hall edge this yields a
modified Dorokhov distribution of transmission probabilities with a gap around
unit transparency. In the case of HgTe quantum well, the probability
distribution is also suppressed but does not exhibit a hard gap.

Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition, a finite size scaling analysis and the resulting extraction of critical parameters as well as the detection of a mobility edge has not been possible due to a large drift with system size in the studied quantities. In this work we provide such analysis, made possible by studying various properties of the entanglement in exact eigenstates in a disordered quantum Ising chain. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being separate from the many-body localization transition. We thereby give numerical support for a recently proposed phase diagram of many-body localization with localization protected order [Huse et al. Phys. Rev. B 88, 014206 (2013)].

The sake of the Dirac-like surface states of 3D topological insulators (TIs) under the influence of electron-electron interactions and/or a strong magnetic field is investigated.

First, a theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is presented. We focus on a slab geometry (characteristic for most experiments) and show that intersurface interaction between the two major surfaces is relevant in the renormalization group sense and the case of decoupled surfaces is therefore unstable. 
We predict a characteristic non-monotonic temperature dependence of the conductivity. In the infrared (low-temperature) limit, the systems flows into a metallic fixed point. At this point, even initially different surfaces have the same transport properties. 

Second, the unconventional (half-integer) quantum Hall effect for a single Dirac fermion is revisited. The following important questions, which were not or only partially answered to present date, are discussed:
(i) How can half-integer Hall conductance g_{xy} be measured experimentally?
(ii) Doesn’t Laughlin’s flux insertion argument forbid half-integer g_{xy}?
(iii) What is the field theory describing the localization physics of the single Dirac fermion quantum Hall effect?
Additionally, a semiclassical calculation of the anomalous quantum Hall conductance of gapped 2D Dirac fermions in the presence of magnetic field is presented.

While the observation of the Anderson transition in systems of ultracold atoms placed in optical speckle potentials has recently been reported [1,2], the impact of speckle statistics on the critical regime has up to now only scarcely been characterized [3,4]. In this contribution, we present numerical results for the mobility edge and critical scaling in correlated and uncorrelated speckle potentials on the lattice, with a special emphasis on the lower band edge, which emulates the continuum limit.

[1] S. S. Kondov et al., Science 334, 66 (2011)
[2] F. Jendrzejewski et al., Nature Physics 8, 392 (2012)
[3] A. Yedjour and B. Van Tiggelen, European Physical Journal D 59, 249 (2010)
[4] M. Piraud et al., New Journal of Physics 15, 075007 (2013)

We study the disorder-induced topological phase transition of one-dimensional fermions belonging to class AIII of the Altland-Zirnbauer classification. To characterize the topological state, we derive a covariant real-space representation of the integer invariant. Using this invariant, we show that the system remains topological even after all the single particle states of the system become localized and the energy spectrum becomes gapless. For a critical disorder strength which we compute analytically, there emerges a delocalized state at zero energy where the topological invariant changes value and the nontrivial ground state transforms into a trivial one. This type of topological phase transition is fundamentally different from the levitation and annihilation paradigm that is found in higher-dimensional systems e.g. the quantum Hall state. In order to understand this type of phase transition, we map the system to a spin-1/2 model which provides an insightful real-space picture of the underlying physics near the critical point.

In a recent experimental study, Siegrist et al. [Nature Materials 10, 202 (2011)] investigated the metal-insulator transition (MIT) of GeSb_2Te_4 and related phase-change materials on increasing annealing temperature. The authors conclude that these materials exhibit a discontinuous MIT with a finite minimum metallic conductivity, and that they violate the Mott criterion for the critical charge carrier concentration. The striking contrast to reports on other disordered substances motivates the present in-depth study of the influence of the MIT criterion used on the character of the MIT derived. First, we discuss in detail the inherent biases of the various available approaches to locating the MIT. Second, reanalyzing the GeSb_2Te_4 measurements, we show that this solid resembles other disordered materials to a large extent: According to a widely-used approach, these data may also be interpreted in terms of a continuous MIT. Carefully checking the justification of the respective fits, however, uncovers inconsistencies in the experimental data, which currently render an unambiguous interpretation impossible. Moreover, several arguments are
given, which attribute the violation of the Mott criterion, claimed by Siegrist et al., to an inappropriate relating to shallow impurity states instead of deep ones. Third, comparing with previous experimental studies of crystalline Si:As, Si:P, Si:B, Ge:Ga, disordered Gd, and nano-granular Pt-C, we show that such an
inconclusive behavior occurs frequently: The consideration of the logarithmic derivative of the conductivity highlights serious inconsistencies in the original interpretations in terms of a continuous MIT. In part, they are common to all these studies and seem to be generic, in part, they vary from experiment to experiment and may arise from measurement problems. Thus, the question of the character of the MIT of these materials has to be considered as yet
open, and the primary challenge lies in improving the measurement precision and accuracy rather than in extending the temperature range.

Analysis of localisation-delocalisation transitions in corner-sharing tetrahedral lattices

Martin Puschmann, Philipp Cain, and Michael Schreiber

Institute of Physics, Chemnitz University of Technology, Chemnitz

The corner-sharing tetrahedral (CST) lattice appears as a sublattice in different materials, e.g.spinels and pyrochlore. We consider the transport of non-interacting electrons and analyse the localisation-delocalisation (LD) transition induced by random on-site potentials. We use the multifractal analysis (MFA), the Green resolvent method (GRM) and the energy-level statistics (ELS) to obtain the singularity strength, the decay length of the wavefunctions, and the (integrated) energy-level distribution, respectively. These measurands are then used to compute the critical parameters by a finite-size scaling (FSS) ansatz using expansions with regular and irregular scaling exponents [1]. With particular emphasis we calculate the propagation of the statistical errors of the measured data in order to get a highly accurate error estimate. This is done by a Monte-Carlo method [2]: Based on the original dataset we use up to 10000 synthetic datasets. Every dataset is built by adding Gaussian distributed random noise to the original dataset. The noise simulates the errors of the data points. Distributions for the critical parameters are obtained by applying the FSS to each dataset. The resulting distributions are Gaussian and their standard deviations reflect the statistical errors. The accuracy is analysed in dependence on the expansion orders. 
The critical points in the energy-disorder diagram are comparable to a previous less accurate study of the LD transitions in CST lattices [3]. The values of the critical exponent show a very good agreement between the different methods. They are comparable to recent studies on lattices of the
orthogonal universality class. In addition, we investigated the influence of different representations of the CST lattice used for the GRM. This affects the computation time and the accuracy of the results.
[1] K. Slevin, P. Marko, and T. Ohtsuki, Phys. Rev. Lett. 82, 382–385 (1999)
[2] A. Rodriguez, L. J. Vasquez, K. Slevin, and R. A. Römer, Phys. Rev. B 84, 134209 (2011)
[2] F. Fazileh, X. Chen, R. J. Gooding, and K. Tabunshchyk, Phys. Rev. B 73, 035124 (2006)

In a one-dimensional spinless p-wave superconductor with coherence length
xi, disorder induces a phase
transition between a topologically nontrivial phase and a trivial
insulating phase at the critical mean free path
l = xi/2. Here, we show that a multichannel spinless p-wave
superconductor goes through an alternation of
topologically trivial and nontrivial phases upon increasing the disorder
strength, the number of phase transitions
being equal to the channel number N. The last phase transition, from a
nontrivial phase into the trivial phase,
takes place at a mean free path l = xi/(N + 1), parametrically smaller
than the critical mean free path in one
dimension. Our result is valid in the limit that the wire width W is much
smaller than the superconducting
coherence length xi.

We study quasiparticle dynamics in graphene exposed to a linearly polarized electromagnetic wave of very large intensity. We demonstrate that low-energy transport in such system can be described by an effective time-independent Hamiltonian, characterized by multiple Dirac points in the first Brillouin zone. Around each Dirac point the spectrum is anisotropic: the velocity along the polarization of the radiation significantly exceeds the velocity in the perpendicular direction. Moreover, in some of the points the transverse velocity oscillates as a function of the radiation intensity. We find that the conductance of a graphene p-n junction in the regime of strong irradiation depends on the polarization as G(θ)∝|sinθ|^3/2, where θ is the angle between the polarization and the p-n interface, and oscillates as a function of the radiation intensity.

Alberto Rodriguez (1), Arunava Chakrabarti (2), and Rudolf A. Römer (3)

(1) Physikalisches Institut, Albert-Ludwigs Universität Freiburg, Hermann-Herder Strasse 3, D-79104, Freiburg, Germany
(2) Department of Physics, University of Kalyani, Kalyani, West Bengal-741 235, India
(3) Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom

We describe how to engineer wavefunction delocalization in disordered systems modelled by tightbinding
Hamiltonians in d > 1 dimensions. We show analytically that a simple product structure
for the random onsite potential energies, together with suitably chosen hopping strengths, allows a
resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence
of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate
that these features persist in the thermodynamic limit for a continuous range of the system parameters.
Numerical results support these findings and highlight the robustness of the extended regime
with respect to deviations from the exact resonance condition for finite systems. The localization
and transport properties of the system can be engineered almost at will and independently in each
direction. This study gives rise to the possibility of designing disordered potentials that work as
switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.
[Phys. Rev. B 86, 085119-12 (2012)]

C. Gonzalez-Santander (1), F. Domnguez-Adame (1) M. Hilke (2) and R. A. Römer (3)

(1) GISC, Departamento de Fsica de Materiales, Universidad Complutense, E-28040 Madrid, Spain
(2) Department of Physics, McGill University, Montreal (Quebec) H3A 2T8, Canada
(3) Department of Physics and Centre for Scientic Computing, University of Warwick, Coventry, CV4 7AL, UK

We show that electron states in disordered graphene, with an onsite potential that induces intervalley
scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean
graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene
flakes of size  200x200 nm^2 or larger are needed. For smaller samples, due to the surprisingly large
extent of the electronic wave functions, a regime of apparently extended (or even critical) states is
identied. Our results complement earlier studies of macroscopically large samples and can explain
the divergence of results for finite-size graphene flakes.

Alberto Rodriguez (1, 2),  Louella J. Vasquez (3), Keith Slevin (4) and Rudolf A. Römer (1)

(1) Department of Physics and Centre for Scientic Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
(2) Departamento de Fsica Fundamental, Universidad de Salamanca, 37008 Salamanca, Spain
(3) Institute of Advanced Study, Complexity Science Centre and Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom
(4) Department of Physics, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

We describe a new multifractal finite size scaling (MFSS) procedure and its application to the
Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the
critical parameters and the multifractal exponents. Simulations of system sizes up to L^3 = 120^33
and involving nearly 10^6 independent wavefunctions have yielded unprecedented precision for the
critical disorder Wc = 16.530(16.524, 16.536) and the critical exponent = 1.590(1.579, 1.602). We
nd that the multifractal exponents q exhibit a previously predicted symmetry relation and we
confirm the non-parabolic nature of their spectrum. We explain in detail the MFSS procedure rst
introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)] and, in addition, we show how to take
account of correlations in the simulation data. The MFSS procedure is applicable to any continuous
phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.
[Phys. Rev. B 84, 134209-16 (2011), Phys. Rev. Lett. 105, 046403-4 (2010)]

We propose an approach to treat the effects of interactions in disordered electron systems on a numerical level. The idea is to solve the non-interacting disorder problem for a given disorder realization exactly. We then use the functional renormalization group method to introduce interactions on a perturbative level. In contrast to usual applications of the fRG, we formulate it in terms of the eigenfunctions of the disordered non-interacting Hamiltonian. Disorder averaging of physical quantities is performed as the final step. The main advantage of our approach is that we are able to treat disorder exactly from a numerical point of view. In fRG applications for clean systems the number of active degrees of freedom is reduced by projecting momenta near the Fermi surface to certain spots on this surface. Disordered systems do not lend themselves to such a treatment since momentum no longer is a good quantum number. Here, the challenge is to find another appropriate decimation technique. We devise, compare and discuss several candidates for such disorder-adapted decimation schemes.

In the limit of large Thouless energy quantum dot(QD) is described by the so-called universal Hamiltonian.   
In the framework of the universal Hamiltonian the only manifestation of disorder is single-particle level fluctuations.   Fluctuations of spectrum lead to fluctuations of spin of QD. Near the Stoner instability point fluctuations of spin become extremely strong. The main question is: Can the fluctuations affect the curve of transition from paramagnetic to ferromagnetic state?
To answer this question we studied the statistics of spin fluctuations.   This problem can be reduced to studying the statistics of extrema of a certain Gaussian process. 
We found the distribution function for longitudinal spin susceptibility and proved rigorously that Stoner instability point cannot be shifted due to fluctuations of single-particle spectrum of QD.  

We investigated the 3D quantum percolation model: A three dimensional nearest neighbor, noninteracting hopping model, where a special kind of disorder
has been introduced: every site is filled with probability p, and empty with probability 1 − p. 
We calculated wave functions at different system sizes up to linear size L=100. We use a multifractal quantities $D_q$ and $alpha_q$, to describe the scaling of the eigenstates with system size. Using one-parameter finite size scaling the localization–delocalization transition has observed. The critical exponent was found the same as the one for the 3D Anderson transition energy- and $q$-independently within 95% confidence level. The critical point was found energy-dependent, and the critical line on the p − E plane (mobility edge) has been obtained.
Our further goal is to investigate the interplay of the satial percolation-like disorder and an Anderson-like diagonal disorder.

Motivated by a possible description of the IQHE in terms of a series of critical lattice truncations, we consider a series of critical integrable vertex models with finite dimensional spaces of states on each edge, some of which related to well or no so well known physical problems : the O(n) model on the square lattice,dense and dilute 2 colours loop models, the latter being related to a truncation of the Chalker Coddington model for the IQHE. We show using Bethe ansatz that these models allow for a regime with non-compact continuum limit. The corresponding CFTs are identified, and some important consequences are exposed.

[several publications corresponding to this work should be submitted by march]