TY  - JOUR
A1  - Barthel, Thomas
A1  - Pineda, Carlos
A1  - Eisert, Jens
T1  - Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
N2  - 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 ansaumltze (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.
Y1  - 2009
UR  - http://pra.aps.org/
U6  - https://doi.org/10.1103/Physreva.80.042333
SN  - 1050-2947
ER  - 
TY  - JOUR
A1  - Barthel, Thomas
A1  - Schollwock, Ulrich
A1  - White, Steven R.
T1  - Spectral functions in one-dimensional quantum systems at finite temperature using the density matrix renormalization group
N2  - We present time-dependent density matrix renormalization group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution, and for the XXX model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data.
Y1  - 2009
UR  - http://prb.aps.org/
U6  - https://doi.org/10.1103/Physrevb.79.245101
SN  - 1098-0121
ER  -