Corrected confidence intervals for secondary parameters following sequential tests

Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a pivotal quantity, and then using very weak expansions to determine the correction terms. The asymptotic sampling distribution of the renormalised pivotal quantity is established in both the case where the covariance matrix is known and when it is unknown. The resulting approximations have a simple form and the results of a simulation study of two well-known sequential tests show that they are very accurate. The practical usefulness of the approach is illustrated by a real example of bivariate data. Detailed proofs of the main results are provided.Comment: Published at http://dx.doi.org/10.1214/074921706000000617 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Pairing versus phase coherence of doped holes in distinct quantum spin backgrounds

We examine the pairing structure of holes injected into two \emph{distinct} spin backgrounds: a short-range antiferromagnetic phase versus a symmetry protected topological phase. Based on density matrix renormalization group (DMRG) simulation, we find that although there is a strong binding between two holes in both phases, \emph{phase fluctuations} can significantly influence the pair-pair correlation depending on the spin-spin correlation in the background. Here the phase fluctuation is identified as an intrinsic string operator nonlocally controlled by the spins. We show that while the pairing amplitude is generally large, the coherent Cooper pairing can be substantially weakened by the phase fluctuation in the symmetry-protected topological phase, in contrast to the short-range antiferromagnetic phase. It provides an example of a non-BCS mechanism for pairing, in which the paring phase coherence is determined by the underlying spin state self-consistently, bearing an interesting resemblance to the pseudogap physics in the cuprate.Comment: 9 pages, 6 figure

Intrinsic translational symmetry breaking in a doped Mott insulator

A central issue of Mott physics, with symmetries being fully retained in the spin background, concerns the charge excitation. In a two-leg spin ladder with spin gap, an injected hole can exhibit either a Bloch wave or a density wave by tuning the ladder anisotropy through a `quantum critical point' (QCP). The nature of such a QCP has been a subject of recent studies by density matrix renormalization group (DMRG). In this paper, we reexamine the ground state of the one doped hole, and show that a two-component structure is present in the density wave regime in contrast to the single component in the Bloch wave regime. In the former, the density wave itself is still contributed by a standing-wave-like component characterized by a quasiparticle spectral weight $Z$ in a finite-size system. But there is an additional charge incoherent component emerging, which intrinsically breaks the translational symmetry associated with the density wave. The partial momentum is carried away by neutral spin excitations. Such an incoherent part does not manifest in the single-particle spectral function, directly probed by the angle-resolved photoemission spectroscopy (ARPES) measurement, however it is demonstrated in the momentum distribution function. The Landau's one-to-one correspondence hypothesis for a Fermi liquid breaks down here. The microscopic origin of this density wave state as an intrinsic manifestation of the doped Mott physics will be also discussed.Comment: 11 pages, 6 figures, an extended version of arXiv:1601.0065