Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS(3), mixed-flux relativistic AdS(3) and massless AdS(2). We also attack the class of models akin to AdS(5) with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

Automated summary

This paper investigates the new models of integrable nearest-neighbour Hamiltonians introduced recently, and demonstrates their satisfaction of the free fermion condition. By recasting the transfer matrix in free fermion form, known results are greatly simplified and reinterpreted, providing a suggestive reformulation of the spectral problem in various situations.