Continuous Matrix Product States for Quantum Field Theories with Broken Translational Invariance*

Continuous Matrix Product States (cMPS) are powerful variational ansatz states for continuous
quantum field theories in (1+1) dimension. In this talk I will introduce a novel parametrization of
the cMPS wavefunction based on basis-spline functions and show how it can be used to optimize
the cMPS to approximate ground states of Quantum Field Theories with periodic symmetry.
Comparison with regular lattice Density Matrix Renormalization Group calculations confirms that
this approach is essentially free of any discretization artifacts. The method provides the first working implementation of a cMPS optimization for non-translational invariant systems. I will explain how manipulation techniques for regular lattice Matrix Product States (MPS), like for example regauging, are extended the case of spline-based MPS.