The universal behavior of a disordered system

The Landau theory of phase transitions and the concept of symmetry breaking provide a unifying description of even such seemingly different many-body systems as a paramagnet cooled to the verge of ferromagnetic order or a metal approaching the superconducting transition. What happens, however, when these systems can lose energy to their environment? For example, in rare-earth compounds called “heavy-fermion” materials, the f-shell magnetic moments interact with a sea of mobile electrons [1]. Similarly, near the metalsuperconductor transition in ultrathin wires, the electrons pair up in a connected network of small, superconducting puddles that are surrounded by a bath of unpaired metallic electrons [2]. The surrounding metal gives rise to a parallel resistive channel and hence dissipation. Introducing dissipation into a many-body quantum mechanical problem presented a theoretical challenge that was only resolved in the last quarter of the 20th century [3–5]

Ground-state degeneracy of correlated insulators with edges

Using the topological flux insertion procedure, the ground-state degeneracy of an insulator on a periodic lattice with filling factor nu=p/q was found to be at least q-fold. Applying the same argument in a lattice with edges, we show that the degeneracy is modified by the additional edge density nuE associated with the open boundaries. To carry out this generalization we demonstrate how to distinguish between bulk and edge states, and follow how an edge modifies the thermodynamic limit of Oshikawa's original argument. In particular, we also demonstrate that these edge corrections may even make an insulator with integer bulk filling degenerate

Energy Correlations In Random Transverse Field Ising Spin Chains

The end-to-end energy - energy correlations of random transverse-field quantum Ising spin chains are computed using a generalization of an asymptotically exact real-space renormalization group introduced previously. Away from the critical point, the average energy - energy correlations decay exponentially with a correlation length that is the same as that of the spin - spin correlations. The typical correlations, however, decay exponentially with a characteristic length proportional to the square root of the primary correlation length. At the quantum critical point, the average correlations decay sub-exponentially as $\bar{C_{L}}\sim e^{-const\cdot L^{1/3}}$, whereas the typical correlations decay faster, as $\sim e^{-K\sqrt{L}}$, with $K$ a random variable with a universal distribution. The critical energy-energy correlations behave very similarly to the smallest gap, computed previously; this is explained in terms of the RG flow and the excitation structure of the chain. In order to obtain the energy correlations, an extension of the previously used methods was needed; here this was carried out via RG transformations that involve a sequence of unitary transformations.Comment: Submitted to Phys. Rev.

Criticality and entanglement in random quantum systems

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ("pure") quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.Comment: Review article for the special issue "Entanglement entropy in extended systems" in J. Phys.

Time-quasiperiodic topological superconductors with Majorana Multiplexing

Time-quasiperiodic Majoranas are generalizations of Floquet Majoranas in time-quasiperiodic superconducting systems. We show that in a system driven at $d$ mutually irrational frequencies, there are up to $2^d$ types of such Majoranas, coexisting despite spatial overlap and lack of time-translational invariance. Although the quasienergy spectrum is dense in such systems, the time-quasiperiodic Majoranas can be stable and robust against resonances due to localization in the periodic-drives induced synthetic dimensions. This is demonstrated in a time-quasiperiodic Kitaev chain driven at two frequencies. We further relate the existence of multiple Majoranas in a time-quasiperiodic system to the time quasicrystal phase introduced recently. These time-quasiperiodic Majoranas open a new possibility for braiding which will be pursued in the future

Strong disorder renormalization group primer and the superfluid-insulator transition

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well understood weak disorder theory for this problem allows to illustrate what aspects of the physics change at strong disorder. In particular the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed

Theoretical analysis of drag resistance in amorphous thin films exhibiting superconductor-insulator transitions

The magnetical field tuned superconductor-insulator transition in amorphous thin films, e.g., Ta and InO, exhibits a range of yet unexplained curious phenomena, such as a putative low-resistance metallic phase intervening the superconducting and the insulating phase, and a huge peak in the magnetoresistance at large magnetic field. Qualitatively, the phenomena can be explained equally well within several significantly different pictures, particularly the condensation of quantum vortex liquid, and the percolation of superconducting islands embedded in normal region. Recently, we proposed and analyzed a distinct measurement in Y. Zou, G. Refael, and J. Yoon, Phys. Rev. B 80, 180503 (2009) that should be able to decisively point to the correct picture: a drag resistance measurement in an amorphous thin-film bilayer setup. Neglecting interlayer tunneling, we found that the drag resistance within the vortex paradigm has opposite sign and is orders of magnitude larger than that in competing paradigms. For example, two identical films as in G. Sambandamurthy, L. W. Engel, A. Johansson, and D. Shahar, Phys. Rev. Lett. 92, 107005 _2004_ with 25 nm layer separation at 0.07 K would produce a drag resistance ~10^(−4) Ω according the vortex theory but only ~10^(−12) Ω for the percolation theory. We provide details of our theoretical analysis of the drag resistance within both paradigms and report some results as well

Orbital Floquet Engineering of Exchange Interactions in Magnetic Materials

We present a new scheme to control the spin exchange interactions between two magnetic ions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, we modify the properties of the ligand orbitals which mediate magnetic interactions between two transition metal ions. While in the other case, we mix the d orbitals on each magnetic ion. In contrast to previous works on Floquet engineering of magnetic properties, the present scheme makes use of the AC Stark shift of the states involved in the exchange process

Variational-Correlations Approach to Quantum Many-body Problems

We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed

Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations

The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.Comment: 13 pages, 4 figures, Comments welcom