A Curious Mapping Between Supersymmetric Quantum Chains

  • Gyorgy Z. Feher
  • Alexandr GarbaliEmail author
  • Jan de Gier
  • Kareljan Schoutens
Part of the MATRIX Book Series book series (MXBS, volume 2)


We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first (Fendley and Schoutens, J Stat Mech, P02017, 2007) describes semionic particles on a 1D ladder, with supersymmetry moving particles between the two legs. The second (de Gier et al., J Stat Mech, 023104, 2016) is a fermionic model with particle-hole symmetry and with supersymmetry creating or annihilating pairs of domain walls. The mapping we display features non-trivial phase factors that generalise the sign factors occurring in the Jordan-Wigner transformation.


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We thank the hospitality of the international mathematical research institute MATRIX where a large part of this work was performed. JdG and AG gratefully thank financial support of the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). GZF was supported by the BME-Nanotechnology FIKP grant of EMMI (BME FIKP-NAT) and by the National Research Development and Innovation Office (NKFIH) (KH-17 grant no. 125567).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Gyorgy Z. Feher
    • 1
  • Alexandr Garbali
    • 2
    Email author
  • Jan de Gier
    • 3
  • Kareljan Schoutens
    • 4
  1. 1.BME “Momentum” Statistical Field Theory Research GroupBudapestHungary
  2. 2.Australian Research Council Centre of Excellence (ACEMS), School of Mathematics and StatisticsThe University of MelbourneVICAustralia
  3. 3.Australian Research Council Centre of Excellence (ACEMS)The University of MelbourneVICAustralia
  4. 4.Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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