Figure 1
From: Thermal bosons in 3d optical lattices via tensor networks
(Color online) (a) Pyrochlore lattice of corner-sharing tetrahedrons. (b) PEPO for the cubic lattice. In this tensor network diagram, shapes are tensors, lines are indices, and connected lines are contracted common indices. Red and blue indices at every tensor correspond to the local bra and ket degrees of freedom, respectively. (c) Action of the Suzuki–Trotter gate g on both ket and bra indices of two nearest-neighbouring sites, for the PEPO tensors of the cubic lattice. Small red tensors \(\lambda \) correspond to the matrices of singular values obtained from the simple update76. (d) Thermal expectation value of a local two-body operator O in the cubic lattice, with a mean-field approximation of the environment (see main text for more details).
