110 research outputs found
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
Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
We analyze transitions between quantum Hall ground states at prominent
filling factors in the spherical geometry by tuning the width parameter
of the Zhang-Das Sarma interaction potential. We find that incompressible
ground states evolve adiabatically under this tuning, whereas the compressible
ones are driven through a first order phase transition. Overlap calculations
show that the resulting phase is increasingly well described by appropriate
analytic model wavefunctions (Laughlin, Moore-Read, Read-Rezayi). This scenario
is shared by both odd () and even
denominator states (). In particular, the Fermi
liquid-like state at gives way, at large enough value of the width
parameter, to an incompressible state identified as the Moore-Read Pfaffian on
the basis of its entanglement spectrum.Comment: 4 pages, 5 figures; modified version as appears in PR
Tunable Electron Interactions and Fractional Quantum Hall States in Graphene
The recent discovery of fractional quantum Hall states in graphene raises the
question of whether the physics of graphene and its bilayer offers any
advantages over GaAs-based materials in exploring strongly-correlated states of
two-dimensional electrons. Here we propose a method to continuously tune the
effective electron interactions in graphene and its bilayer by the dielectric
environment of the sample. Using this method, the charge gaps of prominent FQH
states, including \nu=1/3 or \nu=5/2 states, can be increased several times, or
reduced all the way to zero. The tunability of the interactions can be used to
realize and stabilize various strongly correlated phases in the FQH regime, and
to explore the transitions between them.Comment: 4.2 pages, 5 figure
Atypical Fractional Quantum Hall Effect in Graphene at Filling Factor 1/3
We study the recently observed graphene fractional quantum Hall state at a
filling factor using a four-component trial wave function and exact
diagonalization calculations. Although it is adiabatically connected to a 1/3
Laughlin state in the upper spin branch, with SU(2) valley-isospin
ferromagnetic ordering and a completely filled lower spin branch, it reveals
physical properties beyond such a state that is the natural ground state for a
large Zeeman effect. Most saliently, it possesses at experimentally relevant
values of the Zeeman gap low-energy spin-flip excitations that may be unveiled
in inelastic light-scattering experiments.Comment: 4 pages, 3 figures; slightly modified published versio
-Wave Pairing in Quantum Hall Bilayers
We show that the wave functions that describe the ground states of putative -wave-paired phases
in quantum Hall bilayers, like the Pfaffian at =1/2 or the paired phase at =1, are more
likely to describe the excited states of Fermi liquids at these filling factors. We point out to the
close competition between Fermi liquid and paired phases, which leads to the conclusion that in the
experiments only direct transitions from the correlated 111 and 331 states into Fermi liquid(s) are
likely to be observed
Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
The fractional quantum Hall plateau observed in GaAs wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that---in the absence of Landau level mixing---fillings and are in the Read-Rezayi phase. The lowest energy charged excitation is a non-Abelian Fibonacci anyon which can be trapped by a one-body potential. We point out extremely close energetic competition between the Read-Rezayi phase and a charge-density ordered phase, which suggests that even small particle-hole symmetry breaking perturbations can explain the experimentally observed asymmetry between and . Reducing the thickness of the quantum well drives a transition from the homogeneous Read-Rezayi phase to the charge-density ordered phase, providing a plausible explanation for the absence of a plateau in narrow GaAs wells
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