Rajesh Narayanan

We investigate the behavior of the frustrated J1-J2 Ising model on a square lattice under the influence of random dilution and spatial anisotropies. Spinless impurities generate a random-field type disorder for the spin-density wave (stripe) order parameter. These random fields destroy the long-range stripe order in the case of spatially isotropic interactions. Combining symmetry arguments, percolation theory, and large-scale Monte Carlo simulations, we demonstrate that arbitrarily weak spatial interaction anisotropies restore the stripe phase. More specifically, the transition temperature Tc into the stripe phase depends on the interaction anisotropy ΔJ via Tc∼1/|ln(ΔJ)| for small ΔJ. This logarithmic dependence implies that very weak anisotropies are sufficient to restore the transition temperature to values comparable to that of the undiluted system. We analyze the critical behavior of the emerging transition and find it to belong to the disordered two-dimensional Ising universality class, which features the clean Ising critical exponents and universal logarithmic corrections. We also discuss the generality of our results and their consequences for experiments.

The N-color quantum Ashkin-Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin-Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers N, and the critical behavior for all . In the case of two colors, N = 2, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all , i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman-Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time. © Published under licence by IOP Publishing Ltd.

We study the ground-state phase diagram of the Ashkin-Teller random quantum spin chain by means of a generalization of the strong-disorder renormalization group. In addition to the conventional paramagnetic and ferromagnetic (Baxter) phases, we find a partially ordered phase characterized by strong randomness and infinite coupling between the colors. This unusual phase acts, at the same time, as a Griffiths phase for two distinct quantum phase transitions, both of which are of infinite-randomness type. We also investigate the quantum multicritical point that separates the two-phase and three-phase regions, and we discuss generalizations of our results to higher dimensions and other systems. © 2014 American Physical Society.

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary. © 2007 The American Physical Society.

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane. © 2012 American Physical Society.

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments. © 2010 The American Physical Society.

We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power law in the Griffiths phase. © 2010 The American Physical Society.

The Mott metal to insulator transition Mott!transition is a remarkable phenomenon observed in strongly correlated materials, where the localization of electronic waves is driven by on-site electron-electron repulsion (see [7] for a review). Although the appearance of a Mott gap Mott!gap is clearly a charge-related effect, magnetism is expected to play a key role in elucidating the true nature of this phase transition. Indeed, since the Mott insulating state is purely paramagnetic, local moments Local moments are well-defined objects between their formation at high temperature (about the local Coulomb interaction Coulomb interaction ) and their ultimate ordering at the Neel temperature. This offers a window for the Mott transition to occur, in which the behavior of these local spin excitations is yet to be clearly understood. The simplest situation lies in case where the low-temperature magnetic ordering is first order, as in Cr-doped . Accordingly magnetic fluctuations should be expected to be weak, so that many predictions can be made from a single-site approach such as the Dynamical Mean Field Theory (DMFT) Dynamical Mean Field Theory (DMFT) [4]. In particular, the fact that a low-temperature metallic state leads upon heating to an insulating phase can be understood as a Pomeranchuk effectPomeranchuk effect , where the entropy gain benefits the state with magnetic degeneracy. © 2010 Springer-Verlag Berlin Heidelberg.

The breached-pair state wherein superconductivity coexists with magnetic polarization is known to exist as a ground state of an imbalanced Fermi system only under very fine-tuned conditions. Here, we show that an s-wave superconductor that is well described by a spin-selectively disordered attractive Hubbard model away from half filling has the breached-pair state as a ground-state without the need for such fine-tuning. The existence of this breached-pair phase is established by laying recourse to a Monte Carlo technique called static path approximation (SPA). Further, by using the SPA, we map out the entire phase diagram of the spin-selectively disordered attractive Hubbard model and show that apart from the breached-pair phase, the many-body system hosts the putative s-wave superconducting state and a polarized Fermi-liquid state.