Abstract
Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg spin ladders. Two-leg ladders provide a rich and highly nontrivial extension of the single chain case on the way towards the relatively little explored two-dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and , we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, , strongly differ for even versus odd . For even and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of rungs. For odd and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd , albeit of a different nature for as compared to . For , we find a novel gapless intermediate phase with -dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For , there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear. Our results are based on (i) field theoretical techniques, (ii) qualitative symmetry considerations, and (iii) large-scale density matrix renormalization group (DMRG) simulations keeping beyond a million of states by fully exploiting and thus preserving the symmetry.
8 More- Received 24 March 2018
- Revised 30 May 2018
DOI:https://doi.org/10.1103/PhysRevB.98.085104
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