640 research outputs found
Many body localization with long range interactions
Many body localization (MBL) has emerged as a powerful paradigm for
understanding non-equilibrium quantum dynamics. Folklore based on perturbative
arguments holds that MBL only arises in systems with short range interactions.
Here we advance non-perturbative arguments indicating that MBL can arise in
systems with long range (Coulomb) interactions. In particular, we show using
bosonization that MBL can arise in one dimensional systems with ~ r
interactions, a problem that exhibits charge confinement. We also argue that
(through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems
with log r interactions, and speculate that our arguments may even extend to
three dimensional systems with 1/r interactions. Our arguments are `asymptotic'
(i.e. valid up to rare region corrections), yet they open the door to
investigation of MBL physics in a wide array of long range interacting systems
where such physics was previously believed not to arise.Comment: Expanded discussion of higher dimensions, updated reference
AKLT Models with Quantum Spin Glass Ground States
We study AKLT models on locally tree-like lattices of fixed connectivity and
find that they exhibit a variety of ground states depending upon the spin,
coordination and global (graph) topology. We find a) quantum paramagnetic or
valence bond solid ground states, b) critical and ordered N\'eel states on
bipartite infinite Cayley trees and c) critical and ordered quantum vector spin
glass states on random graphs of fixed connectivity. We argue, in consonance
with a previous analysis, that all phases are characterized by gaps to local
excitations. The spin glass states we report arise from random long ranged
loops which frustrate N\'eel ordering despite the lack of randomness in the
coupling strengths.Comment: 10 pages, 1 figur
On the magnetization of two-dimensional superconductors
We calculate the magnetization of a two-dimensional superconductor in a
perpendicular magnetic field near its Kosterlitz-Thouless transition and at
lower temperatures. We find that the critical behavior is more complex than
assumed in the literature and that, in particular, the critical magnetization
is {\it not} field independent as naive scaling predicts. In the low
temperature phase we find a substantial fluctuation renormalization of the
mean-field result. We compare our analysis with the data on the cuprates.Comment: 8 pages, 3 figure
On product, generic and random generic quantum satisfiability
We report a cluster of results on k-QSAT, the problem of quantum
satisfiability for k-qubit projectors which generalizes classical
satisfiability with k-bit clauses to the quantum setting. First we define the
NP-complete problem of product satisfiability and give a geometrical criterion
for deciding when a QSAT interaction graph is product satisfiable with positive
probability. We show that the same criterion suffices to establish quantum
satisfiability for all projectors. Second, we apply these results to the random
graph ensemble with generic projectors and obtain improved lower bounds on the
location of the SAT--unSAT transition. Third, we present numerical results on
random, generic satisfiability which provide estimates for the location of the
transition for k=3 and k=4 and mild evidence for the existence of a phase which
is satisfiable by entangled states alone.Comment: 9 pages, 5 figures, 1 table. Updated to more closely match published
version. New proof in appendi
The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
The Pfaffian phase of electrons in the proximity of a half-filled Landau
level is understood to be a p+ip superconductor of composite fermions. We
consider the properties of this paired quantum Hall phase when the pairing
scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence
length is much larger than the charge screening length. We find that, as in a
Type I superconductor, the vortices attract so that, upon varying the magnetic
field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated
phase separation. We propose that the weakly and strongly coupled Pfaffian
states exemplify a general dichotomy between Type I and Type II quantum Hall
fluids.Comment: 4 pages, 1 figur
Current fluctuations near to the 2D superconductor-insulator quantum critical point
Systems near to quantum critical points show universal scaling in their
response functions. We consider whether this scaling is reflected in their
fluctuations; namely in current-noise. Naive scaling predicts low-temperature
Johnson noise crossing over to noise power at strong
electric fields. We study this crossover in the metallic state at the 2d z=1
superconductor/insulator quantum critical point. Using a Boltzmann-Langevin
approach within a 1/N-expansion, we show that the current noise obeys a scaling
form with . We recover
Johnson noise in thermal equilibrium and at strong
electric fields. The suppression from free carrier shot noise is due to strong
correlations at the critical point. We discuss its interpretation in terms of a
diverging carrier charge or as out-of-equilibrium Johnson
noise with effective temperature .Comment: 5 page
Floquet Prethermalization in a Bose-Hubbard System
Periodic driving has emerged as a powerful tool in the quest to engineer new
and exotic quantum phases. While driven many-body systems are generically
expected to absorb energy indefinitely and reach an infinite-temperature state,
the rate of heating can be exponentially suppressed when the drive frequency is
large compared to the local energy scales of the system -- leading to
long-lived 'prethermal' regimes. In this work, we experimentally study a
bosonic cloud of ultracold atoms in a driven optical lattice and identify such
a prethermal regime in the Bose-Hubbard model. By measuring the energy
absorption of the cloud as the driving frequency is increased, we observe an
exponential-in-frequency reduction of the heating rate persisting over more
than 2 orders of magnitude. The tunability of the lattice potentials allows us
to explore one- and two-dimensional systems in a range of different interacting
regimes. Alongside the exponential decrease, the dependence of the heating rate
on the frequency displays features characteristic of the phase diagram of the
Bose-Hubbard model, whose understanding is additionally supported by numerical
simulations in one dimension. Our results show experimental evidence of the
phenomenon of Floquet prethermalization, and provide insight into the
characterization of heating for driven bosonic systems
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