Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
- Institute for Physics and Astronomy, Potsdam University, 14476 Potsdam (Germany)
- Instituto de Fisica, Universidad Nacional Autonoma de Mexico, 01000 Mexico D.F. (Mexico)
A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated d-dimensional systems: the multiscale entanglement renormalization ansaetze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of d-dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case.
- OSTI ID:
- 21316386
- Journal Information:
- Physical Review. A, Vol. 80, Issue 4; Other Information: DOI: 10.1103/PhysRevA.80.042333; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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