Matrix product operator representation of polynomial interactions. (1st May 2020)

• Record Type: Journal Article
• Authors: Wall, Michael L
• Is Part Of: Journal of physics. Volume 53:Number 21(2020)
• Publication Date: 2020-05-01
• Subjects: matrix product operators -- tensor network -- lattice models; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab8675
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We provide an exact construction of particular Hamitonians on a one-dimensional lattice as matrix product operators, a type of tensor network. Namely, we consider Hamiltonians describing interactions between degrees of freedom at lattice sites whose strength grows with the lattice site separation as a polynomial multiplied by an exponential. 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.