Efficient simulation of slightly entangled, forced, synthetic quantum matter.

Tensor networks are classes of ansätze that offer an efficient parameterization of the wave functions of many-body quantum systems with local Hamiltonians.

Famous examples of these classes are matrix product states (MPS) [Fannes92, White92]. Applications of tensor networks range from emerging phenomena in statistical mechanics and quantum matter, to ideas in quantum gravity neural networks.

Tensor networks have been very successful in characterizing the ground state and excitations of partially entangled systems in the discrete (lattice). Adapting its success to the efficient description of the ground state of continuous quantum systems is an intriguing avenue of research. Continuous tensor networks are non-perturbative tools for the analysis of quantum field theories.

In fact, continuum MPS (cMPS) was recently proposed to study the ground state of quantum field theories in 1 + 1 dimensions[Verstraete10]. Using cMPS, together with international collaborators, we build a bosonic model in the continuum that presents a transition super-fluid/quasi-crystal quantum phase [Rincón15].

This is compared to the famous Lieb-Liniger model (the most basic correlated model in the continuum) where only superfluidity is present.

Our model shows a quantum phase transition in the simplest continuum configuration.

From the point of view of conformal field theory, our model has a unitary central charge with a compactification radius in (0, ¥), which contrasts with Lieb-Liniger, where said radius is in [1, ¥).