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.

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

Supercurrent survival under Rosen-Zener quench of hard core bosons

We study the survival of super-currents in a system of impenetrable bosons subject to a quantum quench from its critical superfluid phase to an insulating phase. We show that the evolution of the current when the quench follows a Rosen-Zener profile is exactly solvable. This allows us to analyze a quench of arbitrary rate, from a sudden destruction of the superfluid to a slow opening of a gap. The decay and oscillations of the current are analytically derived, and studied numerically along with the momentum distribution after the quench. In the case of small supercurrent boosts $\nu$, we find that the current surviving at long times is proportional to $\nu^3$

Finding the Elusive Sliding Phase in the Superfluid-Normal Phase Transition Smeared by c-Axis Disorder

We consider a stack of weakly Josephson coupled superfluid layers with c-axis disorder in the form of random superfluid stiffnesses and vortex fugacities in each layer as well as random interlayer coupling strengths. In the absence of disorder this system has a 3D XY type superfluid-normal phase transition as a function of temperature. We develop a functional renormalization group to treat the effects of disorder, and demonstrate that the disorder results in the smearing of the superfluid-normal phase transition via the formation of a Griffiths phase. Remarkably, in the Griffiths phase, the emergent power-law distribution of the interlayer couplings gives rise to a sliding Griffiths superfluid, with a finite stiffness in the a-b direction along the layers, and a vanishing stiffness perpendicular to it

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