Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a ${\mathbb{Z}}_2$ spin liquid of the Yao-Lee type, with a Majorana Fermi surface. The associated ${\mathbb{Z}}_2$ gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.

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• Pseudogap
• Quantum spin liquid
• Cuprates
• High-temperature superconductors
• Strongly correlated systems
• Kitaev model
• Kondo lattice model