Certain Quantum Many-body states defined on lattices can be efficiently described in terms of tensor networks. Those include Matrix Product States (MPS), Projected Entangled-Pair States (PEPS), or the Multi-scale Entanglement Renormalization Ansatz. They play an important role in quantum computing, error correction, or the description of topological order in condensed matter physics, and are...
In the last years, the suitability of tensor network states for the study of one-dimensional gauge theories has been established: it is possible to conduct numerical studies of lattice gauge theories (LGT) using TNS that enable precise continuum extrapolations in very different setups, including finite density scenarios, where traditional Monte Carlo approaches fail. A similar systematic study...
Computationally intractable tasks are ubiquitous in physics and optimization . Whereas variational approaches count amongst the most direct tools to find an optimal solution, they suffer from two main drawbacks: (i) non-convexity of the cost function and/or the feasible set and (ii) they provide only an inner bound to the optimal solution. On the other hand, relaxation techniques, which allow...
The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a non-relativistic quantum field theory in the vacuum limit, and we show that the latter has vanishing entanglement. In the opposite limit of a region that is large compared to the...
