*Quantum Monte-Carlo phase diagram for a model cuprate*

#### Konev V.V.,Vasinovich E.V.

We introduce a minimal model for CT (charge transfer) unstable 2D cuprates with the on-site
Hilbert space reduced to only three effective valence centers and make use of
the S=1 pseudospin formalism.Focusing on the unconventional bosonic-like physics of the model
cuprate we neglect the one-particle transport.
Despite its seeming simplicity the model is believed to capture the salient features both of the
hole- and electron-doped cuprates. Concept of the electron and hole centers, differing by a
composite local boson, and electron-hole pairing are shown to explain central points of the cuprate
puzzles, in particular, the HTSC itself and pseudogap phenomena.
Making use of two different QMC methods, the standard stochastic series expansion (SSE) with loop
updates and a continuous time world-line QMC, we studied the ground-state and finite-temperature
properties of the Hamiltonian given different parameters values. Our QMC calculations for the
model CT unstable cuprates shows a step-by-step evolution under doping of the parent insulating
state into an uncoventional inhomogeneous supersolid (mixed charge order - Bose superfluid, or
CO+BS) phase formed by electron and hole CuO$_4$ centers. The simulation does reproduce main
features of the $T-x$ phase diagrams for doped cuprates, in particular, the suppression of
antiferromagnetism, a pseudogap regime due to charge ordering, formation of a local
superconductivity at $T>T_c$, and global 2D superconductivity.