245 research outputs found

### 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]

### 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

### Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals

When a d-dimensional quantum system is subjected to a periodic drive, it may
be treated as a (d+1)-dimensional system, where the extra dimension is a
synthetic one. In this work, we take these ideas to the next level by showing
that non-uniform potentials, and particularly edges, in the synthetic dimension
are created whenever the dynamics of system has a memory component. We
demonstrate that topological states appear on the edges of these synthetic
dimensions and can be used as a basis for a wave packet construction. Such
systems may act as an optical isolator which allows transmission of light in a
directional way. We supplement our ideas by an example of a physical system
that shows this type of physics.Comment: 7 Pages, 5 Figure

### Floquet second-order topological insulators from nonsymmorphic space-time symmetries

We propose a systematic way of constructing Floquet second-order topological
insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time
symmetry that is unique in Floquet systems. In particular, we are able to show
that the static enlarged Hamiltonian in the frequency domain acquires the
reflection symmetry, which is inherited from the time-glide symmetry of the
original system. As a consequence, one can construct a variety of time-glide
symmetric Floquet SOTIs using the knowledge of static SOTIs. Moreover, the
time-glide symmetry only needs to be implemented approximately in practice,
enhancing the prospects of experimental realizations. We consider two examples,
a 2D system in class AIII and a 3D system in class A, to illustrate our ideas,
and then present a general recipe for constructing Floquet SOTIs in all
symmetry classes.Comment: 5 pages + supplemental materia

### 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

### 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.

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