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Continuous Tensor Network States
Teresa Karanikolaou MPQ Garching
18.02.2020
The physical understanding of quantum many-body systems is hindered by the fact that the number of parameters describing the physical state grows exponentially with the number of degrees of freedom. Consequently, it is notoriously hard to solve strongly coupled Quantum field theories as they have infinitely many degrees of freedom. A new variational class of states aimed at dealing with strongly coupled QFT was recently put forward in [Physical Review X 9 (2), 021040]. This class is obtained as the continuum limit of Tensor Network States, which have been extremely successful on the lattice, both theoretically and numerically. However, the success of this continuum ansatz has so far not been demonstrated. In my Master Thesis, a subclass of continuous Tensor Network States, the gaussian continuous Tensor Network states, are tested on a simple quasifree bosonic Hamiltonian, in one and two spacial dimensions. The variational algorithm performs succesfully in both cases. Particularly, in the two dimensional case the implementation is not trivial, due to the appearance of infinities in the energy density.
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