Drainage Walling as Excavation Support

In practice there are different processes which are used to support excavations and to maintain the groundwater level in excavations which go down to this level. In urban areas the diaphragm wall is frequently used to protect the excavation and as underground water packing against groundwater flowing in from the side. In addition, the lowering of groundwater is necessary using a well point within the excavation. A new foundation trench sheeting has been developed by the author of this paper. This new method is an improvement on the diaphragm wall by which not only is the earth shored up, but the lowering of the groundwater within the excavation can also be carried out. In accordance with the function of this method, we refer to the new type of foundation trench sheeting as drainage walling. This drainage walling is manufactured in a similar way to the diaphragm wall. We have observed drainage walling on building sites which differ greatly from each other. The results of our observations are intended to demonstrate the advantages and also the problems involved in this new process to the planning and project engineers

Topological States of Matter in Frustrated Quantum Magnetism

Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented. The stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase. We discuss the special case of the Heisenberg $J_1$-$J_2$ model and present a scenario where the critical point of phase transition from the 120-degree N\'eel to a putative $\mathbf{Z}_2$ spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and multi-column representations. We establish the phase boundary between the N\'eel ordered phase and the disordered phases. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.Comment: Ph.D. thesis, 161 page

Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields

We show that, in the presence of a $\pi/2$ artificial gauge field per plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N)_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux $\pi/N$ per triangular plaquette. Experimental implications are briefly discussed.Comment: 5+2 pages, 4 figures, 2 table

Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory

The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an intertwined manner, where the superconducting order parameter is coupled to the electronic density. Employing density matrix renormalization group simulations, we investigate the nature of such an intertwined state of matter stabilized in the phase diagram of the elementary $t$-$t^\prime$-$U$ Hubbard model in the strong coupling regime. Remarkably, the condensate of Cooper pairs is shown to be fragmented in the presence of a charge density wave where more than one pairing wave function is macroscopically occupied. Moreover, we provide conclusive evidence that the macroscopic wave functions of the superconducting fragments are well-described by soliton solutions of a Ginzburg-Landau equation in a periodic potential constituted by the charge density wave. In the presence of an orbital magnetic field, the order parameters are gauge invariant, and superconducting vortices are pinned between the stripes. This intertwined Ginzburg-Landau theory is proposed as an effective low-energy description of the stripe fragmented superconductor.Comment: 12 pages, 9 figure

Quantum spin liquid in the easy-axis Heisenberg model on frustrated lattices

So far quantum spin liquids have been mostly considered within the isotropic (or close to isotropic) Heisenberg models on frustrated lattices. Recently, such a state has been found experimentally in highly anisotropic easy-axis effective-spin-1/2 compound NdTa$_7$O$_{19}$ featuring a perfect triangular lattice. Performing a numerical calculation of thermodynamic quantities on systems with up to 36 sites in the corresponding spin model, we confirm the transition from an ordered magnetic state in the isotropic case, into the quantum spin-liquid state in the easy-axis regime, whereby the clearest signature is the vanishing generalized Wilson ratio. On the other hand, the same model on the kagome lattice reveals spin-liquid properties in the whole anisotropy regime.Comment: 10 page

Tunable Stripe Order and Weak Superconductivity in the Moir\'e Hubbard Model

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we study the superconducting correlation function and point out the possibility of weak superconductivity.Comment: 9 pages, 9 figure