Rajesh Narayanan

Bio: Rajesh Narayanan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Quantum phase transition & Phase transition. The author has an hindex of 15, co-authored 47 publications receiving 549 citations. Previous affiliations of Rajesh Narayanan include Asia Pacific Center for Theoretical Physics & University of Hong Kong.

Signatures of many-body localization and metastability by weak perturbation

Abstract: Nonequilibrium dynamics in isolated quantum many-body systems displays a number of intriguing features, such as many-body localization (MBL) and prethermalization. Here we investigate a simple ladder system with disorder, in which various distinct dynamical features coexist and interplay. By exact diagonalization, we demonstrate that the system exhibits the signatures of an MBL-ergodic-MBL reentrant transition, metastability, and disorder-free MBL. We give an account of these properties by introducing a quasiparticle picture and interpreting the quasivacuum energy fluctuation as an effective disorder on the quasi-particle dynamics. It is speculated that the weak perturbation behavior is a finite-size effect, but its relaxation timescale increases with the system size.

Order parameter symmetry and mode coupling effects at dirty superconducting quantum phase transitions

Abstract: We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-$s$-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the $p$-wave case, logarithmic corrections to scaling in all dimensions.

Emergent infinite-randomness fixed points from the extensive random bipartitions of the spin-1 Affleck-Kennedy-Lieb-Tasaki topological state

Abstract: Quantum entanglement under an extensive bipartition can reveal the critical boundary theory of a topological phase in a parameter space. In this study we demonstrate that the infinite-randomness fixed point for spin-$\frac{1}{2}$ degrees of freedom can emerge from an extensive random bipartition of the spin-1 Affleck-Kennedy-Lieb-Tasaki chain. The nested entanglement entropy of the ground state of the reduced density matrix exhibits a logarithmic scaling with an effective central charge $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}=0.72\ifmmode\pm\else\textpm\fi{}0.02\ensuremath{\approx}ln2$. We further discuss, in the language of bulk quantum entanglement, how to understand all phase boundaries and the surrounding Griffiths phases for the antiferromagnetic Heisenberg spin-1 chain with quenched disorder and dimerization.

Transport Anomalies and Marginal Fermi-Liquid Effects at a Quantum Critical Point

Abstract: The behaviour of the conductivity and the density of states, as well as the phase relaxation time, of disordered itinerant electrons across a quantum ferromagnetic transition is discussed. It is shown that critical fluctuations lead to anomalies in the temperature and energy dependence of the conductivity and the tunnelling density of states, respectively, that are stronger than the usual weak-localisation anomalies in a disordered Fermi liquid. This can be used as an experimental probe of the quantum critical behaviour. The energy dependence of the phase relaxation time at criticality is shown to be that of a marginal Fermi liquid.

Spin-selective metal insulator transition in two dimensions

Abstract: The phenomenon of Anderson localization wherein non-interacting electrons are localized by quenched impurities is a subject matter that has been extremely well studied. However, localization transition under the combined influence of interaction and quenched disorder is less well understood. In this context we study the localization transition in a two-dimensional Hubbard model under the influence of a spin-selective disorder i.e, disorder which is operational on just one of the spin-species. The model is analyzed by laying recourse to a Quantum Monte Carlo based scheme. Using this approach we show the possibility of a metal-insulator transition. However, we will show that this metal-insulator transition is extremely sensitive to the filling-fraction inherent in the system.

Anderson Transitions

Abstract: The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians Analytical approaches are complemented by advanced numerical simulations

Fermi-liquid instabilities at magnetic quantum phase transitions

Abstract: This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Superconducting phases of f -electron compounds

Abstract: Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.

Quantum phase transitions

Abstract: In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.