Small to large Fermi surface transition in a single-band model using randomly coupled ancillas

We describe a solvable model of a quantum transition in a single band model involving a change in the size of the electron Fermi surface without any symmetry breaking. In a model with electron density $1\ensuremath{-}p$, we find a ``large'' Fermi surface state with the conventional Luttinger volume $1\ensuremath{-}p$ of electrons for $p>{p}<sub>c</sub>$, and a first-order transition to a ``small'' Fermi surface state with a non-Luttinger volume $p$ of holes for $p<{p}_c$. As required by extended Luttinger theorems, the small Fermi surface state also has fractionalized spinon excitations. The model has electrons with strong local interactions in a single band; after a canonical transformation, the interactions are transferred to a coupling to two layers of ancilla qubits, as proposed by Zhang and Sachdev [Phys. Rev. Research 2, 023172 (2020)]. Solvability is achieved by employing random exchange interactions within the ancilla layers, and taking the large $M$ limit with $\mathrm{SU}(M)$ spin symmetry, as in the Sachdev-Ye-Kitaev models. The local electron spectral function of the small Fermi surface phase displays a particle-hole asymmetric pseudogap, and maps onto the spectral function of a lightly doped Kondo insulator of a Kondo-Heisenberg lattice model. We discuss connections to the physics of the hole-doped cuprates: the asymmetric pseudogap observed in STM, and the sudden change from incoherent to coherent antinodal spectra observed recently in photoemission. A holographic analogy to wormhole transitions between multiple black holes is briefly noted.