Fig. 1: A geometrical presentation of two partition functions within different space-time manifolds. | Nature Communications

Fig. 1: A geometrical presentation of two partition functions within different space-time manifolds.

From: Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative

Fig. 1

a \({Z}_{A}^{(2)}={{\rm{Tr}}}{[{{{\rm{Tr}}}}_{B}{e}^{-\beta H}]}^{2}\) and b \({Z}^{2}={[{{\rm{Tr}}}({e}^{-\beta H})]}^{2}\), where H is the Hamiltonian of the system. a The entangling regions A of two replicas are glued together along the imaginary time direction and the environment regions B of replicas are not connected each other. While the glued region is zero, it becomes back to Z2 as shown in (b). c Reweighting a distribution: the sampled distribution (black, before reweighting) is used to reweight another distribution (blue, after reweighting), which is reasonable if these two distributions are close to each other, as the importance sampling can be approximately kept.

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