Q-operators for the open Heisenberg spin chain. (English) Zbl 1332.82014
Summary: We construct Q-operators for the open spin-\(\frac{1}{2}\) XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter’s TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 16T25 | Yang-Baxter equations |
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