3,264 research outputs found
Shannon-R\'enyi entropies and participation spectra across 3d criticality
Universal features in the scalings of Shannon-R\'enyi entropies of many-body
groundstates are studied for interacting spin- systems across
(2+1) dimensional critical points, using quantum Monte Carlo simulations
on dimerized and plaquettized Heisenberg models on the square lattice.
Considering both full systems and line shaped subsystems, symmetry
breaking on the N\'eel ordered side of the transition is characterized by the
presence of a logarithmic term in the scaling of Shannon-R\'enyi entropies,
which is absent in the disordered gapped phase. Such a difference in the
scalings allows to capture the quantum critical point using Shannon-R\'enyi
entropies for line shaped subsystems of length embedded in
tori, as the smaller subsystem entropies are numerically accessible to much
higher precision than for the full system. Most interestingly, at the quantum
phase transition an additive subleading constant
emerges in the critical scaling of the line Shannon-R\'enyi entropy
. This number appears to be universal for 3d
criticality, as confirmed for the finite-temperature transition in the 3d
antiferromagnetic spin- Heisenberg model. Additionally, the phases
and phase transition can be detected in several features of the participation
spectrum, consisting of the diagonal elements of the reduced density matrix of
the line subsystem. In particular the N\'eel ordering transition can be simply
understood in the basis by a confinement mechanism of ferromagnetic
domain walls.Comment: 16 pages, 19 figure
Many-body localization edge in the random-field Heisenberg chain
We present a large scale exact diagonalization study of the one dimensional
spin Heisenberg model in a random magnetic field. In order to access
properties at varying energy densities across the entire spectrum for system
sizes up to spins, we use a spectral transformation which can be applied
in a massively parallel fashion. Our results allow for an energy-resolved
interpretation of the many body localization transition including the existence
of an extensive many-body mobility edge. The ergodic phase is well
characterized by Gaussian orthogonal ensemble statistics, volume-law
entanglement, and a full delocalization in the Hilbert space. Conversely, the
localized regime displays Poisson statistics, area-law entanglement and non
ergodicity in the Hilbert space where a true localization never occurs. We
perform finite size scaling to extract the critical edge and exponent of the
localization length divergence.Comment: 4+3 pages, 5+3 figure
IS THE THINLY-TRADED BUTTER FUTURES CONTRACT PRICED EFFICIENTLY?
After over eight years of trading, the Chicago Mercantile Exchange butter futures contract remains thinly traded, possibly impeding price discovery. Pricing efficiency was assessed using cointegration techniques and error correction models. Results suggest that market efficiency could not be rejected up to a two-month forecast horizon. Illiquid markets reduce hedging performance, which in turn discourage liquidity growth.Marketing,
Entanglement entropies of the Heisenberg antiferromagnet on the square lattice
Using a modified spin-wave theory which artificially restores zero sublattice
magnetization on finite lattices, we investigate the entanglement properties of
the N\'eel ordered Heisenberg antiferromagnet on the square
lattice. Different kinds of subsystem geometries are studied, either
corner-free (line, strip) or with sharp corners (square). Contributions from
the Nambu-Goldstone modes give additive logarithmic corrections with a
prefactor independent of the R\'enyi index. On the other hand,
corners lead to additional (negative) logarithmic corrections with a prefactor
which does depend on both and the R\'enyi index , in good
agreement with scalar field theory predictions. By varying the second neighbor
coupling we also explore universality across the N\'eel ordered side of
the phase diagram of the antiferromagnet, from the frustrated side
where the area law term is maximal, to the strongly
ferromagnetic regime with a purely logarithmic growth
, thus recovering the mean-field limit for a subsystem
of sites. Finally, a universal subleading constant term is extracted in the case of strip subsystems, and a direct relation is
found (in the large-S limit) with the same constant extracted from free lattice
systems. The singular limit of vanishing aspect ratios is also explored, where
we identify for a regular part and a singular component,
explaining the discrepancy of the linear scaling term for fixed width {\it{vs}}
fixed aspect ratio subsystems.Comment: 14 pages, 18 figure
Deflection of a Viscoelastic Cantilever under a Uniform Surface Stress: Applications to Static-mode Microcantilever Sensors Undergoing Adsorption
The equation governing the curvature of a viscoelastic microcantilever beam loaded with a uniform surface stress is derived. The present model is applicable to static-mode microcantilever sensors made with a rigid polymer, such as SU-8. An analytical solution to the differential equation governing the curvature is given for a specific surface stress representing adsorption of analyte onto the viscoelastic beamâs surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoneyâs equation to analyze stress-induced deflection of viscoelastic microcantilevers (in the present case due to surface analyte adsorption) can lead to poor predictions of the beamâs response. It is shown that using a viscoelastic substrate can greatly increase sensitivity (due to a lower modulus), but at the cost of a longer response time due to viscoelasticcreep in the microcantilever. In addition, the effects of a coating on the cantilever are considered. By defining effective moduli for the coated-beam case, the analytical solution for the uncoated case can still be used. It is found that, unlike the case of a silicon microcantilever, the stress in the coating due to bending of a polymer cantilever can be significant, especially for metalcoatings. The theoretical results presented here can also be used to extract time-domain viscoelasticproperties of the polymermaterial from beam response data
Doping quantum dimer models on the square lattice
A family of models is proposed to describe the motion of holes in a
fluctuating quantum dimer background on the square lattice. Following
Castelnovo et al. [Ann. Phys. (NY) 318, 316 (2005)], a generalized
Rokhsar-Kivelson Hamiltonian at **finite doping** which can be mapped on a
**doped** interacting classical dimer model is constructed. A simple physical
extension of this model is also considered. Using numerical computations and
simple considerations based on the above exact mapping, we determine the phase
diagram of the model showing a number of quantum phases typical of a doped Mott
insulator. The two-hole correlation function generically exhibits short-range
or long-range algebraic correlations in the solid (columnar) and liquid
(critical) phases of the model, respectively. Evidence for an extended region
of a doped VBS phase exhibiting holon pairing but **no** phase separation is
given. In contrast, we show that hole deconfinement occurs in the staggered
dimer phase.Comment: 5 page
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Generation Adequacy and Investment Incentives in Britain: from the Pool to NETA
Three years after the controversial change of the British market design from compulsory Pool with capacity payments to decentralised energy-only New Electricity Trading Arrangements (NETA) market framework, we compare the two designs in terms of investment incentives. We review the biases of the Pool capacity payments design, the drought of investment following the introduction of NETA, and the reaction of the market during the first âstress-testâ of NETA during the winter 2003. In an energy-only market such as NETA, it is essential that price signals are right and the system operator has a crucial role in contracting ahead for reserve. We recommend that NETA adopt a single marginal imbalance price as dual imbalance pricing distorts price signals in times of scarcity. The lack of long-term contracting that causes hedging and financing difficulties for power projects can becompensated by vertical and horizontal reintegration at a cost of increased market power
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