Path integrals for dimerized quantum spin systems

Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a N\'eel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin $S=1/2$ dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both a SO(4) formulation and bond-operators.Comment: 20 pages, no figure

Optimizing gravitational-wave searches for a population of coalescing binaries: Intrinsic parameters

We revisit the problem of searching for gravitational waves from inspiralling compact binaries in Gaussian coloured noise. For binaries with quasicircular orbits and non-precessing component spins, considering dominant mode emission only, if the intrinsic parameters of the binary are known then the optimal statistic for a single detector is the well-known two-phase matched filter. However, the matched filter signal-to-noise ratio is /not/ in general an optimal statistic for an astrophysical population of signals, since their distribution over the intrinsic parameters will almost certainly not mirror that of noise events, which is determined by the (Fisher) information metric. Instead, the optimal statistic for a given astrophysical distribution will be the Bayes factor, which we approximate using the output of a standard template matched filter search. We then quantify the possible improvement in number of signals detected for various populations of non-spinning binaries: for a distribution of signals uniformly distributed in volume and with component masses distributed uniformly over the range $1\leq m_{1,2}/M_\odot\leq 24$, $(m_1+m_2) /M_\odot\leq 25$ at fixed expected SNR, we find $\gtrsim 20\%$ more signals at a false alarm threshold of $10^{-6}\,$Hz in a single detector. The method may easily be generalized to binaries with non-precessing spins.Comment: Version accepted by Phys. Rev.