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We describe a solvable model of a quantum transition in a single band modelinvolving a change in the size of the electron Fermi surface without anysymmetry breaking. In a model with electron density $1-p$, we find a 'large'Fermi surface state with the conventional Luttinger volume $1-p$ of electronsfor $p>p_c$, and a first order transition to a 'small' Fermi surface state witha non-Luttinger volume $p$ of holes for $p<p_c$. As required by extendedLuttinger theorems, the small Fermi surface state also has fractionalizedspinon excitations. The model has electrons with strong local interactions in asingle band; after a canonical transformation, the interactions are transferredto a coupling to two layers of ancilla qubits, as proposed by Zhang and Sachdev(Phys. Rev. Research ${\bf 2}$, 023172 (2020)). Solvability is achieved byemploying random exchange interactions within the ancilla layers, and takingthe large $M$ limit with SU($M$) spin symmetry, as in the Sachdev-Ye-Kitaevmodels. The local electron spectral function of the small Fermi surface phasedisplays a particle-hole asymmetric pseudogap, and maps onto the spectralfunction of a lightly doped Kondo insulator of a Kondo-Heisenberg latticemodel. We discuss connections to the physics of the hole-doped cuprates: theasymmetric pseudogap observed in STM, and the sudden change from incoherent tocoherent anti-nodal spectra observed recently in photoemission. A holographicanalogy to wormhole transitions between multiple black holes is briefly noted.

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