Figure 4
From: Thermal bosons in 3d optical lattices via tensor networks
(Color online) (a) Superfluid density \(\rho _s\), and particle density \(\rho _0\), for the 3d BH model on the cubic lattice for \(t/U=0.01\), \(T/t=0\) and \(T/t=0.07\). While the SF phase is characterized by non-zero \(\rho _s\), both MI and NG (which exists for \(T>0\)) phases have zero \(\rho _s\). However, the MI phase has integer \(\rho _0\) whereas NG phases (shaded grey regions) have non-integer \(\rho _0\). (b) \(\rho _s\) and (c) \(\rho _0\) for the hard-core (\(n_{oc} = 1\)) BH model on the pyrochlore lattice for \(t=1, U=0\). Both plots show how \(\rho _s\) and \(\rho _0\) evolve when increasing the temperature, eventually having a conventional gas phase at large T. The shaded grey regions are the NG phases emerging at \(T=1\) (we use T instead of T/t since \(t =1\) in this case).
