Definitions of entanglement entropy of spin systems in the valence-bond basis

The valence-bond structure of spin-1/2 Heisenberg antiferromagnets is closely related to quantum entanglement. We investigate measures of entanglement entropy based on transition graphs, which characterize state overlaps in the overcomplete valence-bond basis. The transition graphs can be generated using projector Monte Carlo simulations of ground states of specific hamiltonians or using importance-sampling of valence-bond configurations of amplitude-product states. We consider definitions of entanglement entropy based on the bonds or loops shared by two subsystems (bipartite entanglement). Results for the bond-based definition agrees with a previously studied definition using valence-bond wave functions (instead of the transition graphs, which involve two states). For the one dimensional Heisenberg chain, with uniform or random coupling constants, the prefactor of the logarithmic divergence with the size of the smaller subsystem agrees with exact results. For the ground state of the two-dimensional Heisenberg model (and also Neel-ordered amplitude-product states), there is a similar multiplicative violation of the area law. In contrast, the loop-based entropy obeys the area law in two dimensions, while still violating it in one dimension - both behaviors in accord with expectations for proper measures of entanglement entropy.Comment: 9 pages, 8 figures. v2: significantly expande

Improved real-time imaging spectrometer

An improved AOTF-based imaging spectrometer that offers several advantages over prior art AOTF imaging spectrometers is presented. The ability to electronically set the bandpass wavelength provides observational flexibility. Various improvements in optical architecture provide simplified magnification variability, improved image resolution and light throughput efficiency and reduced sensitivity to ambient light. Two embodiments of the invention are: (1) operation in the visible/near-infrared domain of wavelength range 0.48 to 0.76 microns; and (2) infrared configuration which operates in the wavelength range of 1.2 to 2.5 microns

Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets

We study effects of disorder (randomness) in a 2D square-lattice $S=1/2$ quantum spin system, the $J$-$Q$ model with a 6-spin interaction $Q$ supplementing the Heisenberg exchange $J$. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks $Z_4$ symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent $z$ in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that $z$ varies, from $z=2$ at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr$_2$CuTe$_{1-x}$W$_x$O$_6$.Comment: 31 pages, 29 figures; substantial additions in v2; additional analysis in v

Random-singlet phase in disordered two-dimensional quantum magnets

We study effects of disorder (randomness) in a 2D square-lattice S=1/2 quantum spin system, the J-Q model with a 6-spin interaction Q supplementing the Heisenberg exchange J. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks Z4 symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent z in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that z varies, from z=2 at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr2CuTe1−xWxO6.Accepted manuscrip

On the constrained KP hierarchy

An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to the KdV hierarchies, the existence of additional symmetries allows to reduce KP to the constrained KP.Comment: 7pp, LaTe

Impact of the Casimir-Polder Potential and Johnson Noise on Bose-Einstein Condensate Stability near Surfaces

We investigate the stability of magnetically trapped atomic Bose-Einstein condensates and thermal clouds near the transition temperature at small distances 0.5 microns < d < 10 microns from a microfabricated silicon chip. For a 2 microns thick copper film the trap lifetime is limited by Johnson-noise induced currents and falls below 1 s at a distance of 4 microns. A dielectric surface does not adversely affect the sample until the attractive Casimir-Polder potential significantly reduces the trap depth.Comment: 4 pages, 5 figures, and submitted to Physical Review Letter

Modelling the multi-wavelength emissions from PSR B1259-63/LS 2883: the effects of the stellar disc on shock radiations

PSR B1259-63/LS 2883 is an elliptical pulsar/Be star binary and emits broadband emissions from radio to TeV $\gamma$-rays. The massive star possesses an equatorial disc, which is inclined with the orbital plane of the pulsar. The non-thermal emission from the system is believed to be produced by the pulsar wind shock and the double-peak profiles in the X-ray and TeV $\gamma$-ray light curves are related to the phases of the pulsar passing through the disc region of the star. In this paper, we investigate the interactions between the pulsar wind and stellar outflows, especially with the presence of the disc, and present a multi-wavelength modelling of the emission from this system. We show that the double-peak profiles of X-ray and TeV $\gamma$-ray light curves are caused by the enhancements of the magnetic field and the soft photons at the shock during the disc passages. As the pulsar is passing through the equatorial disc, the additional pressure of the disc pushes the shock surface closer to the pulsar, which causes the enhancement of magnetic field in the shock, and thus increases the synchrotron luminosity. The TeV $\gamma$-rays due to the inverse-Compton (IC) scattering of shocked electrons with seed photons from the star is expected to peak around periastron which is inconsistent with observations. However, the shock heating of the stellar disc could provide additional seed photons for IC scattering during the disc passages, and thus produces the double-peak profiles as observed in the TeV $\gamma$-ray light curve. Our model can possibly be examined and applied to other similar gamma-ray binaries, such as PSR J2032+4127/MT91 213, HESS J0632+057, and LS I+61$^{\circ}$303.Comment: 14 pages, 6 figure