Non-local space-time supersymmetry on the lattice

Abstract

We show that several well-known one-dimensional quantum systems possess a hidden nonlocal supersymmetry. The simplest example is the open XXZ spin chain with Δ=-1/2. We use the supersymmetry to place lower bounds on the ground state energy with various boundary conditions. For an odd number of sites in the periodic chain, and with a particular boundary magnetic field in the open chain, we can derive the ground state energy exactly. The supersymmetry thus explains why it is possible to solve the Bethe equations for the ground state in these cases. We also show that a similar space-time supersymmetry holds for the t-J model at its integrable ferromagnetic point, where the space-time supersymmetry and the Hamiltonian it yields coexist with a global u(1|2) graded Lie algebra symmetry. Possible generalizations to other algebras are discussed.

arXiv comment12 pages

References in corpus (9)

• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Lattice Models with N=2 Supersymmetry
• Zero Temperature Phase Transition in Spin-ladders: Phase Diagram and Dynamical studies of Cu(Hp)Cl
• The Importance of being Odd
• Lattice fermion models with supersymmetry
• Spin chains and combinatorics: twisted boundary conditions
• Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta =1/2$
• Quantum Affine Symmetry as Generalized Supersymmetry

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