QUROPE Quantum Information Processing and Communication in Europe

We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature.

We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large and strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation.

We present a mapping of quantum many body states with a global symmetry to states with local gauge symmetry. The prescription implements the principle of minimal coupling at the level of individual quantum states as opposed to Hamiltonians or Lagrangians. Using the formalism of projected entangled-pair states (PEPS), we construct an associated gauging map for Hamiltonians and show how this results in a frustration free gauge theory Hamiltonian.

We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with Projected Entangled Pair States (PEPS) as a function of the bond dimension (D), temperature (&#946;&#8722;1), and system size (N). First, we introduce a compression method in which the bond dimension scales as D=eO(log2(N/&#1013;)) if &#946;<O(log(N)).

We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially decaying correlations and can be interpreted as a (special) subset of the resonating Affleck-Kennedy-Lieb-Tasaki (AKLT) loop states.

We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension D=3 which are exactly hole-doped resonating valence bond (RVB) wavefunctions with short-range singlet bonds. Under doping the insulating RVB spin liquid evolves immediately into a superconductor with mixed d+is pairing symmetry whose pair amplitude grows as the square-root of the doping.

We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian and show that the Frobenius norm bounds the time scale of relaxation of the operator.

We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.

It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states - a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one dimension.

We analyze the strongly correlated regime of a two-component trapped ultracold fermionic gas in a synthetic non-Abelian U(2) gauge potential, that consists of both a magnetic field and a homogeneous spin-orbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spin-orbit coupling.