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Title: Unified phase diagram of antiferromagnetic SU( N ) spin ladders

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 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 =more » 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.« less

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. 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
  2. Univ. de Toulouse (France). Lab. de Physique Théorique, IRSAMC
  3. Univ. de Cergy-Pontoise, Cergy-Pontoise (France). Site de Saint-Martin
  4. Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science
  5. Univ. Innsbruck (Austria). Inst. fur Theoretische Physik
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1466592
Alternate Identifier(s):
OSTI ID: 1462793
Report Number(s):
BNL-207997-2018-JAAM
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 8; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., and Läuchli, A. M. Unified phase diagram of antiferromagnetic SU(N) spin ladders. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.085104.
Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., & Läuchli, A. M. Unified phase diagram of antiferromagnetic SU(N) spin ladders. United States. doi:10.1103/PhysRevB.98.085104.
Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., and Läuchli, A. M. Fri . "Unified phase diagram of antiferromagnetic SU(N) spin ladders". United States. doi:10.1103/PhysRevB.98.085104. https://www.osti.gov/servlets/purl/1466592.
@article{osti_1466592,
title = {Unified phase diagram of antiferromagnetic SU(N) spin ladders},
author = {Weichselbaum, Andreas and Capponi, S. and Lecheminant, P. and Tsvelik, A. M. and Läuchli, A. M.},
abstractNote = {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.},
doi = {10.1103/PhysRevB.98.085104},
journal = {Physical Review B},
number = 8,
volume = 98,
place = {United States},
year = {2018},
month = {8}
}

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