Level statistics of XXZ spin chains with a random magnetic field

The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude of the random magnetic field h. In the energy spectrum, quantum integrability competes with nonintegrability derived from the randomness, where the XXZ interaction is modified by the parameter $\Delta$. When $\Delta \ne 0$, the level-spacing distribution mostly shows Wigner-like behavior, while when $\Delta$=0, Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\Delta \ne 0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.Comment: 4 pages, 3 figures, to be published in Phys. Rev.

Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains

The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearest-neighbor coupled XXZ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.Comment: 4 pages, 4 figures, to be published in Physical Review

Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and the XXZ anisotropy, which should reflect competition among quantum chaos, integrability and finite-size effects. Here discrete symmetries play a central role in our analysis. Evaluating the level-spacing distribution, the spectral rigidity and the number variance, we confirm the correspondence between non-integrability and Wigner behavior in the spectrum. We also show that non-Wigner behavior appears due to mixed symmetries and finite-size effects in some nonintegrable cases.Comment: 19 pages, 6 figure

Semiclassical theory for many-body Fermionic systems

We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response function the classical time correlation function of the observable followed by the Weyl-Wigner series, on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it makes no assumption of the integrability of classical dynamics underlying the one-body quantal system. Applications of the framework are also discussed.Comment: 18 pages, Te

Arable weed seeds as indicators of regional cereal provenance: a case study from Iron Age and Roman central-southern Britain

The ability to provenance crop remains from archaeological sites remains an outstanding research question in archaeology. Archaeobotanists have previously identified the movement of cereals on the basis of regional variations in the presence of cereal grain, chaff and weed seeds (the consumer–producer debate), and weed seeds indicative of certain soil types, principally at Danebury hillfort. Whilst the former approach has been heavily criticised over the last decade, the qualitative methods of the latter have not been evaluated. The first interregional trade in cereals in Britain is currently dated to the Iron Age hillfort societies of the mid 1st millennium bc. Several centuries later, the development of urban settlements in the Late Iron Age and Roman period resulted in populations reliant on food which was produced elsewhere. Using the case study of central-southern Britain, centred on the oppidum (large fortified settlement) and civitas capital of Silchester, this paper presents the first regional quantitative analysis of arable weed seeds in order to identify the origin of the cereals consumed there. Analysis of the weed seeds which were present with the fine sieve by-products of the glume wheat Triticum spelta (spelt) shows that the weed floras of samples from diverse geological areas can be separated on the basis of the soil requirements of individual taxa. A preliminary finding is that, rather than being supplied with cereals from the wider landscape of the chalk region of the Hampshire Downs, the crops were grown close to Late Iron Age Silchester. The method presented here requires further high quality samples to evaluate this conclusion and other instances of cereal movement in the past