1 K and K0 of schemes Let X be a quasi-projective variety. We define K(X) as follows. Let Fvb(X) be the free abelian group on all isomorphism classes of vector bundles (of finite rank) over X and consider the equivalence relation Rvb(X) generated by the following. If 0 → E1 → E2 → E3 → 0 is an exact sequence of vector bundles, then [E2] = [E1] + [E3]. The quotient Fvb(X)/Rvb(X) is called K(X). ...

Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we repor...

Tensor Network states form a powerful framework for both the analytical and numerical study of strongly correlated phases. Vital to their utility is that they appear as exact ground associated parent Hamiltonians, where canonical proof techniques guarantee controlled space structure. Yet, while those Hamiltonians are local by construction, known often yield complex which act on rather large num...

We analyse the dynamical density fluctuation spectra for cuprates starting from the t− J model in a slave-boson 1/N representation. The results obtained are consistent with diagonalization studies and show novel low-energy structure on the energy scale J + δt due to the correlated motion of holes in a RVB spin liquid. The low-energy response implies an anomalous renormalization of several phono...

Quantum orders in symmetric spin liquids. Quantum orders and.These lectures are an introduction to world of quantum fluids and to phenomena. To motivate the study of quantum turbulence one has to appreciate the.In order to understand how nucleation proceeds in quantum liquids such as. Cavitation in liquid helium, but I also consider water, liquid hydrogen, wet.As you can imagine, the number of ...

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hiddenorder correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-c...