2004/04/30 by Xiao Yang, Paul Fendley · 44 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary value problem #Ground state #Hamiltonian (control theory) #Integrable system #Quantum #Quantum Mechanics and Non-Hermitian Physics #Supersymmetry #Supersymmetry algebra #Supersymmetry breaking #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1088/0305-4470/37/38/003
published in Journal of Physics A Mathematical and General 37(38), 8937-8948 (Institute of Physics) · 12 pages
arxiv created 2004/06/24 · openalex publication_date 2004/09/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We 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.