Xiao Yang and Paul Fendley 2004 J. Phys. A: Math. Gen. 37 8937 doi:10.1088/0305-4470/37/38/003
Xiao Yang and Paul Fendley
Show affiliationsWe show that several well-known one-dimensional quantum systems possess a hidden non-local 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 spacetime supersymmetry holds for the t–J model at its integrable ferromagnetic point, where the spacetime supersymmetry and the Hamiltonian it yields coexist with a global u(1|2) graded Lie algebra symmetry. Possible generalizations to other algebras are discussed.
81T60 Supersymmetric field theories
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Quantum information and quantum mechanics
Issue 38 (24 September 2004)
Received 24 June 2004, in final form 24 June 2004
Published 8 September 2004
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