Shannon-R\'enyi entropies and participation spectra across 3d O(3)O(3) criticality

Universal features in the scalings of Shannon-R\'enyi entropies of many-body groundstates are studied for interacting spin-$\frac{1}{2}$ systems across (2+1) dimensional $O(3)$ 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, $SU(2)$ 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 $L$ embedded in $L\times L$ 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 $b_\infty^{*\rm line}=0.41(1)$ emerges in the critical scaling of the line Shannon-R\'enyi entropy $S_\infty^\text{line}$. This number appears to be universal for 3d $O(3)$ criticality, as confirmed for the finite-temperature transition in the 3d antiferromagnetic spin-$\frac{1}{2}$ 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 $\{S^z\}$ 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 $1/2$ 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 $L=22$ 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 J1−J2J_1 - J_2 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 $J_1 - J_2$ 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 $n_G=2$ Nambu-Goldstone modes give additive logarithmic corrections with a prefactor ${n_G}/{2}$ independent of the R\'enyi index. On the other hand, corners lead to additional (negative) logarithmic corrections with a prefactor $l^{c}_q$ which does depend on both $n_G$ and the R\'enyi index $q$, in good agreement with scalar field theory predictions. By varying the second neighbor coupling $J_2$ we also explore universality across the N\'eel ordered side of the phase diagram of the $J_1 - J_2$ antiferromagnet, from the frustrated side $0<J_2/J_1<1/2$ where the area law term is maximal, to the strongly ferromagnetic regime $-J_2/J_1\gg1$ with a purely logarithmic growth $S_q=\frac{n_G}{2}\ln N$, thus recovering the mean-field limit for a subsystem of $N$ sites. Finally, a universal subleading constant term $\gamma_q^{\rm ord}$ 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 $\gamma_q^\text{ord}$ 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 beam’s surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoney’s 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 beam’s 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

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 “stress-test” 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