93 research outputs found
New Dirac points and multiple Landau level crossings in biased trilayer graphene
Recently a new high-mobility Dirac material, trilayer graphene, was realized
experimentally. The band structure of ABA-stacked trilayer graphene consists of
a monolayer-like and a bilayer-like pairs of bands. Here we study electronic
properties of ABA-stacked trilayer graphene biased by a perpendicular electric
field. We find that the combination of the bias and trigonal warping gives rise
to a set of new Dirac points: in each valley, seven species of Dirac fermions
with small masses of order of a few meV emerge. The positions and masses of the
emergent Dirac fermions are tunable by bias, and one group of Dirac fermions
becomes massless at a certain bias value. Therefore, in contrast to bilayer
graphene, the conductivity at the neutrality point is expected to show
non-monotonic behavior, becoming of the order of a few e^2/h when some Dirac
masses vanish. Further, we analyze the evolution of Landau level spectrum as a
function of bias. Emergence of new Dirac points in the band structure
translates into new three-fold-degenerate groups of Landau levels. This leads
to an anomalous quantum Hall effect, in which some quantum Hall steps have a
height of 3e^2/h. At an intermediate bias, the degeneracies of all Landau
levels get lifted, and in this regime all quantum Hall plateaus are spaced by
e^2/h. Finally, we show that the pattern of Landau level crossings is very
sensitive to certain band structure parameters, and can therefore provide a
useful tool for determining their precise values.Comment: 11 pages, 6 figures; v2: expanded introduction, new references added,
a few typos correcte
Quantum quenches in the many-body localized phase
Many-body localized (MBL) systems are characterized by the absence of
transport and thermalization, and therefore cannot be described by conventional
statistical mechanics. In this paper, using analytic arguments and numerical
simulations, we study the behaviour of local observables in an isolated MBL
system following a quantum quench. For the case of a global quench, we find
that the local observables reach stationary, highly non-thermal values at long
times as a result of slow dephasing characteristic of the MBL phase. These
stationary values retain the local memory of the initial state due to the
existence of local integrals of motion in the MBL phase. The temporal
fluctuations around stationary values exhibit universal power-law decay in
time, with an exponent set by the localization length and the diagonal entropy
of the initial state. Such a power-law decay holds for any local observable and
is related to the logarithmic in time growth of entanglement in the MBL phase.
This behaviour distinguishes the MBL phase from both the Anderson insulator
(where no stationary state is reached), and from the ergodic phase (where
relaxation is expected to be exponential). For the case of a local quench, we
also find a power-law approach of local observables to their stationary values
when the system is prepared in a mixed state. Quench protocols considered in
this paper can be naturally implemented in systems of ultra cold atoms in
disordered optical lattices, and the behaviour of local observables provides a
direct experimental signature of many-body localization.Comment: 11 pages, 4 figure
A bound on approximating non-Markovian dynamics by tensor networks in the time domain
Spin-boson (SB) model plays a central role in studies of dissipative quantum
dynamics, both due its conceptual importance and relevance to a number of
physical systems. Here we provide rigorous bounds of the computational
complexity of the SB model for the physically relevant case of a zero
temperature Ohmic bath. We start with the description of the bosonic bath via
its Feynman-Vernon influence functional (IF), which is a tensor on the space of
spin's trajectories. By expanding the kernel of the IF functional via a sum of
decaying exponentials, we obtain an analytical approximation of the continuous
bath by a finite number of damped bosonic modes. We bound the error induced by
restricting bosonic Hilbert spaces to a finite-dimensional subspace with small
boson numbers, which yields an analytical form of a matrix-product state (MPS)
representation of the IF. We show that the MPS bond dimension scales
polynomially in the error on physical observables , as well as in the
evolution time , . This bound indicates that the
spin-boson model can be efficiently simulated using polynomial in time
computational resources.Comment: 10 pages, 0 figure
Slow Nonthermalizing Dynamics in a Quantum Spin Glass
Spin glasses and many-body localization (MBL) are prime examples of
ergodicity breaking, yet their physical origin is quite different: the former
phase arises due to rugged classical energy landscape, while the latter is a
quantum-interference effect. Here we study quantum dynamics of an isolated 1d
spin-glass under application of a transverse field. At high energy densities,
the system is ergodic, relaxing via resonance avalanche mechanism, that is also
responsible for the destruction of MBL in non-glassy systems with power-law
interactions. At low energy densities, the interaction-induced fields obtain a
power-law soft gap, making the resonance avalanche mechanism inefficient. This
leads to the persistence of the spin-glass order, as demonstrated by resonance
analysis and by numerical studies. A small fraction of resonant spins forms a
thermalizing system with long-range entanglement, making this regime distinct
from the conventional MBL. The model considered can be realized in systems of
trapped ions, opening the door to investigating slow quantum dynamics induced
by glassiness.Comment: 6 pages, 3 figure
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