Matrix product operator representation of polynomial interactions
- URL: http://arxiv.org/abs/2001.04617v1
- Date: Tue, 14 Jan 2020 04:15:32 GMT
- Title: Matrix product operator representation of polynomial interactions
- Authors: Michael L. Wall
- Abstract summary: We provide an exact construction of interaction Hamiltonians on a one-dimensional lattice which grow as an exponential with the lattice site separation as a matrix product operator (MPO)
Our results provide new insight into the correlation structure of many-body quantum operators, and may also be practical in simulations of many-body systems whose interactions are exponentially screened at large.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We provide an exact construction of interaction Hamiltonians on a
one-dimensional lattice which grow as a polynomial multiplied by an exponential
with the lattice site separation as a matrix product operator (MPO), a type of
one-dimensional tensor network. We show that the bond dimension is $(k+3)$ for
a polynomial of order $k$, independent of the system size and the number of
particles. Our construction is manifestly translationally invariant, and so may
be used in finite- or infinite-size variational matrix product state
algorithms. Our results provide new insight into the correlation structure of
many-body quantum operators, and may also be practical in simulations of
many-body systems whose interactions are exponentially screened at large
distances, but may have complex short-distance structure.
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