Unified phase diagram of antiferromagnetic SU(N) spin ladders

Weichselbaum, Andreas; Capponi, S.; Lecheminant, P.; Tsvelik, A. M.; Läuchli, A. M.

doi:10.1103/PhysRevB.98.085104

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

Journal Article · Fri Aug 03 00:00:00 EDT 2018 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.98.085104· OSTI ID:1466592

Weichselbaum, Andreas ^[1]; Capponi, S. ^[2]; Lecheminant, P. ^[3]; Tsvelik, A. M. ^[4]; Läuchli, A. M. ^[5]

Ludwig-Maximilians-Univ., Munich (Germany). Physics Dept., Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience; Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science
Univ. de Toulouse (France). Lab. de Physique Théorique, IRSAMC
Univ. de Cergy-Pontoise, Cergy-Pontoise (France). Site de Saint-Martin
Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science
Univ. Innsbruck (Austria). Inst. fur Theoretische Physik

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. Lastly, 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.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0012704

OSTI ID:: 1466592

Alternate ID(s):: OSTI ID: 1462793

Report Number(s):: BNL--207997-2018-JAAM

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 8 Vol. 98; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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A lattice of double wells for manipulating pairs of cold atoms Sebby-Strabley, J.; Anderlini, M.; Jessen, P. S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0602103	text	January 2006
Condensation of magnons and spinons in a frustrated ladder Fouet, J. -B.; Mila, F.; Clarke, D. arXiv https://doi.org/10.48550/arxiv.cond-mat/0603609	text	January 2006
Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains Shelton, D. G.; Nersesyan, A. A.; Tsvelik, A. M. arXiv https://doi.org/10.48550/arxiv.cond-mat/9508047	text	January 1995
Entanglement in Many-Body Systems Amico, Luigi; Fazio, Rosario; Osterloh, Andreas arXiv https://doi.org/10.48550/arxiv.quant-ph/0703044	text	January 2007
Spin ladders and quantum simulators for Tomonaga–Luttinger liquids Ward, Simon; Bouillot, Pierre; Ryll, Hanjo Institute of Physics Publishing IOP https://doi.org/10.7892/boris.39103	text	January 2013

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SU(3) fermions on the honeycomb lattice at 1 3 filling Chung, Sangwoo S.; Corboz, Philippe Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/physrevb.100.035134	journal	July 2019
Dimerization and effective decoupling in two spin-1 generalizations of the spin- 1 2 Majumdar-Ghosh chain Chepiga, Natalia; Mila, Frédéric Physical Review B, Vol. 100, Issue 10 https://doi.org/10.1103/physrevb.100.104426	journal	September 2019
Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders Robinson, Neil J.; Altland, Alexander; Egger, Reinhold Physical Review Letters, Vol. 122, Issue 2 https://doi.org/10.1103/physrevlett.122.027201	journal	January 2019
Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders Robinson, Neil J.; Altland, Alexander; Egger, Reinhold arXiv https://doi.org/10.48550/arxiv.1806.01925	text	January 2018

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Unified phase diagram of antiferromagnetic SU( N ) spin ladders

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