Uniform matrix product states from an algebraic geometer's point of view

Algebraic Geometry of Matrix Product States

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state’s amplitudes which hold if and only if the state is a translation invariant matrix product state or a limit of such states. For systems with few qubits, we give these equations explicitly, considering both periodic and open boundary condition...

Incidence geometry from an algebraic graph theory point of view

Geopolitical Divergence in the League of Arab States from a Neorealist Point of View

The League of Arab States (also known as the Arab League) is well past its sixth decade of establishment. However, it has a long way to go to achieve the objectives enumerated in its charter. In a sense, there is much stronger propensity towards disintegration than integration in the League. This article seeks to study the reasons that account for the failure of such integration in the Arab Lea...

S matrix from matrix product states.

We use the matrix product state formalism to construct stationary scattering states of elementary excitations in generic one-dimensional quantum lattice systems. Our method is applied to the spin-1 Heisenberg antiferromagnet, for which we calculate the full magnon-magnon S matrix for arbitrary momenta and spin, the two-particle contribution to the spectral function, and higher order corrections...

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 infini...