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Article Dans Une Revue Physical Review B Année : 2018

Unified phase diagram of antiferromagnetic SU($N$) spin ladders

Résumé

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 SU(N) 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 2≤N≤6, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, J⊥/J∥, strongly differ for even versus odd N. For even N=4 and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of N/2 rungs. For odd N=3 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 N 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 N, albeit of a different nature for N=3 as compared to N=5. For N=3, we find a novel gapless intermediate phase with J⊥-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For N=5, 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 SU(N) symmetry.

Dates et versions

hal-01867192 , version 1 (04-09-2018)

Identifiants

Citer

Andreas Weichselbaum, Sylvain Capponi, Philippe Lecheminant, Alexei M. Tsvelik, Andreas M. Läuchli. Unified phase diagram of antiferromagnetic SU($N$) spin ladders. Physical Review B, 2018, 98 (8), pp.085104. ⟨10.1103/PhysRevB.98.085104⟩. ⟨hal-01867192⟩
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