47 research outputs found
Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes
Majorana fermions with random all-to-all four-body interactions. We consider
the SYK model in the framework of a many-body Altland-Zirnbauer classification
that sees the system as belonging to one of eight (real) symmetry classes
depending on the value of . We show that, depending on the symmetry
class, the system may support exact many-body zero modes with the symmetries
also dictating whether these may have a nonzero contribution to Majorana
fermions, i.e., single-particle weight. These zero modes appear in all but two
of the symmetry classes. When present, they leave clear signatures in physical
observables that go beyond the threefold (Wigner-Dyson) possibilities for level
spacing statistics studied earlier. Signatures we discover include a
zero-energy peak or hole in the single-particle spectral function, depending on
whether symmetries allow or forbid zero modes to have single-particle weight.
The zero modes are also shown to influence the many-body dynamics, where
signatures include a nonzero long-time limit for the out-of-time-order
correlation function. Furthermore, we show that the extension of the four-body
SYK model by quadratic terms can be interpreted as realizing the remaining two
complex symmetry classes; we thus demonstrate how the entire tenfold
Altland-Zirnbauer classification may emerge in the SYK model
Transport in topological insulator nanowires
In this chapter we review our work on the theory of quantum transport in
topological insulator nanowires. We discuss both normal state properties and
superconducting proximity effects, including the effects of magnetic fields and
disorder. Throughout we assume that the bulk is insulating and inert, and work
with a surface-only theory. The essential transport properties are understood
in terms of three special modes: in the normal state, half a flux quantum along
the length of the wire induces a perfectly transmitted mode protected by an
effective time reversal symmetry; a transverse magnetic field induces chiral
modes at the sides of the wire, with different chiralities residing on
different sides protecting them from backscattering; and, finally, Majorana
zero modes are obtained at the ends of a wire in a proximity to a
superconductor, when combined with a flux along the wire. Some parts of our
discussion have a small overlap with the discussion in the review [Bardarson
and Moore, Rep. Prog. Phys., 76, 056501, (2013)]. We do not aim to give a
complete review of the published literature, instead the focus is mainly on our
own and directly related work.Comment: 22 pages, 8 figures; Chapter in "Topological Matter. Springer Series
in Solid-State Sciences, vol 190. Springer
Many-body localization in a quantum simulator with programmable random disorder
When a system thermalizes it loses all local memory of its initial
conditions. This is a general feature of open systems and is well described by
equilibrium statistical mechanics. Even within a closed (or reversible) quantum
system, where unitary time evolution retains all information about its initial
state, subsystems can still thermalize using the rest of the system as an
effective heat bath. Exceptions to quantum thermalization have been predicted
and observed, but typically require inherent symmetries or noninteracting
particles in the presence of static disorder. The prediction of many-body
localization (MBL), in which disordered quantum systems can fail to thermalize
in spite of strong interactions and high excitation energy, was therefore
surprising and has attracted considerable theoretical attention. Here we
experimentally generate MBL states by applying an Ising Hamiltonian with
long-range interactions and programmably random disorder to ten spins
initialized far from equilibrium. We observe the essential signatures of MBL:
memory retention of the initial state, a Poissonian distribution of energy
level spacings, and entanglement growth in the system at long times. Our
platform can be scaled to higher numbers of spins, where detailed modeling of
MBL becomes impossible due to the complexity of representing such entangled
quantum states. Moreover, the high degree of control in our experiment may
guide the use of MBL states as potential quantum memories in naturally
disordered quantum systems.Comment: 9 pages, 9 figure
Holographic Conductivity in Disordered Systems
The main purpose of this paper is to holographically study the behavior of
conductivity in 2+1 dimensional disordered systems. We analyze probe D-brane
systems in AdS/CFT with random closed string and open string background fields.
We give a prescription of calculating the DC conductivity holographically in
disordered systems. In particular, we find an analytical formula of the
conductivity in the presence of codimension one randomness. We also
systematically study the AC conductivity in various probe brane setups without
disorder and find analogues of Mott insulators.Comment: 43 pages, 28 figures, latex, references added, minor correction
Properties of Graphene: A Theoretical Perspective
In this review, we provide an in-depth description of the physics of
monolayer and bilayer graphene from a theorist's perspective. We discuss the
physical properties of graphene in an external magnetic field, reflecting the
chiral nature of the quasiparticles near the Dirac point with a Landau level at
zero energy. We address the unique integer quantum Hall effects, the role of
electron correlations, and the recent observation of the fractional quantum
Hall effect in the monolayer graphene. The quantum Hall effect in bilayer
graphene is fundamentally different from that of a monolayer, reflecting the
unique band structure of this system. The theory of transport in the absence of
an external magnetic field is discussed in detail, along with the role of
disorder studied in various theoretical models. We highlight the differences
and similarities between monolayer and bilayer graphene, and focus on
thermodynamic properties such as the compressibility, the plasmon spectra, the
weak localization correction, quantum Hall effect, and optical properties.
Confinement of electrons in graphene is nontrivial due to Klein tunneling. We
review various theoretical and experimental studies of quantum confined
structures made from graphene. The band structure of graphene nanoribbons and
the role of the sublattice symmetry, edge geometry and the size of the
nanoribbon on the electronic and magnetic properties are very active areas of
research, and a detailed review of these topics is presented. Also, the effects
of substrate interactions, adsorbed atoms, lattice defects and doping on the
band structure of finite-sized graphene systems are discussed. We also include
a brief description of graphane -- gapped material obtained from graphene by
attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic
Efficient spin filter using multi-terminal quantum dot with spin-orbit interaction
We propose a multi-terminal spin filter using a quantum dot with spin-orbit interaction. First, we formulate the spin Hall effect (SHE) in a quantum dot connected to three leads. We show that the SHE is significantly enhanced by the resonant tunneling if the level spacing in the quantum dot is smaller than the level broadening. We stress that the SHE is tunable by changing the tunnel coupling to the third lead. Next, we perform a numerical simulation for a multi-terminal spin filter using a quantum dot fabricated on semiconductor heterostructures. The spin filter shows an efficiency of more than 50% when the conditions for the enhanced SHE are satisfied
Finding purifications with minimal entanglement
Purification is a tool that allows to represent mixed quantum states as pure states on enlarged Hilbert spaces. A purification of a given state is not unique and its entanglement strongly depends on the particular choice made. Moreover, in one-dimensional systems, the amount of entanglement is linked to how efficiently the purified state can be represented using matrix-product states (MPS). We introduce an MPS based method that allows to find the minimally entangled representation by iteratively minimizing the second Rényi entropy. First, we consider the thermofield double purification and show that its entanglement can be strongly reduced especially at low temperatures. Second, we show that a slowdown of the entanglement growth following a quench of an infinite temperature state is possible