Triaxial compression tests on a crushable sand in dry and wet conditions

A calcareous sand from the Persian Gulf is subjected to a series of dry and fully drained saturated triaxial shear tests. The samples are prepared at relative densities of 65% and either left dry or saturated. They are consolidated to confining pressures ranging from 50 to 750 kPa, and sheared until shear strains of 20%. It is shown that the stress-strain and strength characteristics of crushable sand are significantly affected by the presence of water. During shearing of wet samples, there is less dilation, the peak is postponed and a lower shear strength is reached compared to dry samples. Crushability is assessed by comparing the granulometry before and after the triaxial tests. While both dry and wet samples show breakage, the wet sand is consistently more crushable. It is stated that the higher crushability of the wet sand suppresses its dilation during shearing

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model and a non-integrable extended Hubbard model, and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.Comment: 13 pages, 4 pages appendix, 8 figure

Thermal States as Convex Combinations of Matrix Product States

We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.Comment: v3: 10 pages, 2 figures, final published versio

Deconstructing the Subject Condition in terms of cumulative constraint violation

Chomsky (1973) attributes the island status of nominal subjects to the Subject Condition, a constraint specific to subjects. English and Spanish are interesting languages for the comparative study of extraction from subjects, because subjects in English are predominantly preverbal, whereas in Spanish they can be either preverbal or postverbal. In this paper we argue that the islandhood of subject DPs in both English and Spanish is not categorical. The degradation associated with extraction from subjects must be attributed to the interplay of a range of more general constraints which are not specific to subjects. We argue that the interaction of these constraints has a cumulative effect whereby the more constraints that are violated, the higher the degree of degradation that results. We also argue that some speakers have a greater tolerance for constraint violations than others, which would account for widespread inter-speaker judgment variability

Variational optimization algorithms for uniform matrix product states

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation

Faster methods for contracting infinite two-dimensional tensor networks

We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods