Session Z16: Disordered and other Strongly Correlated Systems

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. We study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also investigate the influence of spatial disorder correlations on smeared phase transitions. We compare our results to computer simulations of a toy model, and we discuss experiments.   

Understanding zero-bias anomalies in disordered strongly-correlated electron systems: An atomic-limit perspective

Many interesting phenomena arise in strongly-correlated electron systems which are disordered, either intrinsically or due to doping. In trying to understand these phenomena, the single-particle density of states provides a useful bridge between theory and experiment. Progress has recently been made in understanding the origins of the zero-bias anomaly that appears in these systems, and how this zero-bias anomaly differs from that studied by Altshuler and Aronov in weakly-correlated systems . Because both interactions and disorder reduce the importance of kinetic energy, the atomic limit provides a useful perspective. The case of long-range 1/r interactions in the atomic limit was addressed by Efros and Shklovskii, who showed the density of states is suppressed to zero at the Fermi level. However, the argument they used does not address screened interactions or the effect of double occupancy. This talk presents classical Monte Carlo results for the density of states in the atomic limit of the extended Anderson-Hubbard model. The origin of the zero-bias anomaly in this system is explained, and the results are compared both with those obtained when hopping is allowed and with those of Efros and Shklovskii.   

Novel critical point in the random quantum Ashkin-Teller model

The first order phase transition of the quantum Ashkin-Teller model has been intensely studied over many decades. In this work, we study the effect of disorder on this quantum phase transition using a strong-disorder renormalization group approach. Specifically, we develop an implementation of the strong-disorder renormalization group that works for both weak and strong four-spin couplings. For large four-spin coupling, we find a novel type of infinite-randomness fixed point. We investigate the critical properties of this fixed point, and we discuss broader implications for the fate of the first-order quantum phase transitions in disordered systems.   

Spectral function of two-dimensional disordered Hubbard model

We show that moderate disorder introduces extended states in the Mott gap which upon further increase of disorder strength become localized states [1]. We propose that the inverse of the Lorentzian broadening of the spectral function A({\bf k}, $\omega$=0) as a function of {\bf k} can be used as an order parameter for describing the both the transition from a Mott insulator to an unusual metallic state and the transition from the metal to a localized insulator of spin singlets. We further track the evolution of A({\bf k},$\omega$) as a function of disorder and interaction strength. We also obtain the screening length of an external Coulomb potential from the density-density correlation function and find that the screening length is shortest at intermediate disorder in the metallic region. Our calculations are performed within an exact eigenstate formalism that treats the disorder exactly. The single particle Green's function is calculated within self-consistent mean field theory. In real space the bubble diagrams for this on-site interaction are an exact representation of density-density correlation function. \\[4pt] [1] D. Heidarian and N. Trivedi, Phys. Rev. Lett. {\bf 93}, 126401 (2004)   

Variational Monte Carlo Study of Anderson Localization in the Hubbard Model

We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short range correlations near the Mott transition. A persistent current is induced with an Aharonov-Bohm flux, and the Anderson localization length is extracted from the scaling of the current with system size. We find that, at half filling, the localization length grows monotonically with interaction strength, even though the current itself is suppressed by strong correlations. This supports earlier dynamical mean field theory predictions that the elastic scattering rate is reduced near the Mott transition.   

Spin fluctuations near a spin-density-wave instability in periodic Anderson model studied by two-particle approach in dynamical mean field theory

We study the magnetic properties of periodic Anderson model when the system approaches to the vicinity of a spin-density-wave(SDW) instability from paramagnetic phase. Static and dynamical $Q$-dependent susceptibility are calculated using a two-particle approach in dynamical mean field theory. The SDW instability at a critical value of hybridyztion $V_c$ is identified by the divergence of static susceptibility at low temperature and at a wavevector $Q_c$ which connects the ``hot zones'' of the conduction band. Away from $V_c$, spin fluctuations at $Q_c$ is suppressed at low energy and at low temperature in the heavy Fermi liquid regime, while near $V_c$, spin fluctuations at $Q_c$ are significantly enhanced as temperature decreases. This indicates that the SDW instability is due to the competition between RKKY interaction and Kondo coupling in the crossover regime.   

Large Disorder Renormalization Group Study of Singularities in the Insulating Phase of the Anderson Model of Localization

A recent study\footnote{S. Johri, R.N. Bhatt, arXiv:1106.1131v2 } of Anderson's 1958 model of localization\footnote{P. W. Anderson, Physical Review \textbf{109}, 1492 (1958).} reveals singular behavior of electronic eigenstates, as displayed by the density of states and inverse participation ratio, as a function of energy. This behavior occurs inside the insulating phase and separates typical Anderson localized from rare configuration, resonant Lifshitz states. Here, we use the large disorder renormalization group (LDRG) approach to study this problem. In particular, we study, using the LDRG approach, how the singular behavior evolves as a function of system size, starting from a toy model with two-sites which can be solved analytically. We assess the accuracy of the LDRG approach in obtaining the singular behavior in the thermodynamic limit for different disorder strengths, by comparing with results obtained by exact numerical diagonalization.   

Long-range spatial correlations in one-dimensional Anderson models

The study of metal-insulator transitions (MIT) in one-dimensional (1d) Anderson disordered systems remains an active topic of research. Analytic and numerical results have confirmed the scaling prediction on the absence of MIT for short-range correlated disorder potentials. Solutions for long-range correlated potential models (i.e. the dimer model and those with power-law spectral densities) have shown MITs in 1d. However, long-range correlations remain poorly understood. In order to gain some insight, we study a 1d Anderson model with disorder potential correlations described by a power-law model with $\langle \epsilon_r \epsilon_{0} \rangle = 1/(1 + r/a)^\alpha$. Here $\epsilon_i$, $r$, $a$, and $\alpha$ are the on-site energy, position, lattice constant, and strength of the correlation respectively. We obtained results with various methods (wave packet diffusion, participatio ratio, transfer matrix and Green's function) that support the absence of a MIT in these models in. We further show that an analysis of the beta function provides evidence for the validity of the same one-parameter scaling law valid for short-range correlated potentials.   

Dispersive Impurities in one-dimensional Fermi Gases: From one to two Channel Kondo Polarons

We consider the problem of a dispersive magnetic impurity interacting antiferromagnetically with a one dimensional fermionic gas. By combining general considerations and extensive numerical simulations we show that the problem displays a quantum phase transition between two-channel and one-channel Kondo behaviour upon increasing the Kondo coupling and construct a phase diagramme. We also discuss possible experimental realisations.   

Charge fractionalization on quantum Hall edges

Interactions between edges of quantum Hall bars give rise to Luttinger Liquid behavior with a nontrivial interaction parameter g. This leads to fractionalization of localized charges that propagate along the edges. We focus on fractionalization in systems with variable g and the separation of a charge into a sharply defined front pulse and a broader tail. The possibility of detecting the front pulse through noise measurement is discussed and illustrated by numerical simulations of a simplified Hall bar model.   

Study of spontaneous anomalous Hall effect in 2-D electron fluid by bosonization

We explore spontaneous time-reversal symmetry breaking in two-dimensional electron fluids using the method of higher dimensional bosonization. We focus on a fluid phase in which time-reversal symmetry and chiral symmetry are broken, but the space inversion and the combination of chiral and time-reversal symmetries are intact. This phase exhibits non-quantized anomalous Hall effect in the absence of external magnetic fields which corresponds to the Berry curvature on the Fermi surface. Furthermore we investigate the Berry phase connection and its representation in terms of bosonized fields.   

Non-chiral Bosonization of Fermions in One Dimension

An alternative to the conventional approach to bosonization in one dimension that invokes the Dirac equation in 1+1 dimension with chiral ``right-movers'' and ``left-movers'' is proposed that works directly with the bounded parabolic energy bands relevant to Condensed Matter problems. This technique allows us to use a basis different from the plane wave basis that makes this non-chiral approach ideally suited to study Luttinger liquids that have boundary or impurities that break translational symmetry. We provide a simple solution to the electron Green function for the problem of Luttinger liquid (LL) with a boundary and also for a LL with a single impurity. The present method is significantly easier than the g-ology based standard bosonization and other methods that require a combination of RG along with bosonization/refermionization techniques. Our results are broadly consistent with these more established approaches.   

A Partially-ordered-set Based Approach to the Dirac Equation in 3+1 space-time

Recent work by Knuth and co-workers has shown how insights into Einstein's Theory of Special Relativity may be obtained by careful reasoning about consistent quantification of a poset. The Feynman Chessboard problem in 1+1 spacetime can be treated from this perspective, for example. Alternative methods of solution based on techniques borrowed from statistical mechanics have also been developed over the years to solve the Feynman Chessboard model in 1+1 spacetime. One particularly intriguing solution is based on a master-equation approach developed by McKeon and Ord for 1+1 spacetime. We will show how this model may be extended to 3+1 spacetime using techniques developed by Bialynicki-Birula, thus providing an alternative derivation of the Dirac equation. An external electromagnetic field can be accommodated very naturally in the formalism from which a pleasing pictorial representation of electromagnetic interactions in the lattice picture emerges.