Non-trivial phases at intermediate rung coupling in SU(N) Heisenberg ladders

Ladder models represent a first step away from purely 1D chains into the 2D realm. Here we analyze the Hubbard ladder of N symmetric flavors in the Mott regime with one particle / site, equivalent to the SU(N) Heisenberg ladder with the defining representation at each site. We analyze the latter for N<6 using the density matrix renormalization group (DMRG) in the regime of antiferromagnetic leg and rung coupling which is also most natural for quantum simulatons in ultracold atoms. While the asymmptotic regimes of strong or weak rung coupling J_⊥ are mostly understood, the full phase diagram for arbitrary J_⊥>0 is largely unexplored for N>2. While for even N≤6, the phase diagram turns out rather plain with a single phase for J_⊥>0, we find non-trivial intermediate phases for odd N, including incommensuration for N=3 and an extremely narrow phase for N=5 reminiscent of topological phases. By inheriting the exponential numerical complexity of multiorbital models, superior technical tools are required. By focusing on flavor-symmetric models, we fully exploit the underlying SU(N) symmetry in our DMRG simulations based on the QSpace tensor library. This allows us to keep beyond a million of states for larger N which is about two orders of magnitude beyond the current state of the art.