### ΘΦ: Solid State Quantum Chemistry Package Allowing RVB and BCS Ground States

### Evgeny Plekhanov^{1,3), Andrei Tchougreeff^{2,3,4}

*1)King's College London, Theory and Simulation of Condensed Matter (TSCM), The Strand, London WC2R 2LS, United Kingdom
2)Institut für anorganische Chemie RWTH - Aachen University, Landoltweg 1, D-52056, Aachen, Germany
3)Moscow Center for Continuous Mathematical Education, Bol. Vlasevskiy per. , 119002, Moscow, Russia
4)A.N. Frumkin Institute of Physical Chemistry and Electrochemistry of RAS, Moscow, Russia*

**Abstract:**

We present here a new program package called ThPh. It is designed for studying the ground state and finite temperature
properties of spinfull multi-orbital lattice models within generalised mean-field theories. We formulate the mean-field
theory in a general form through the generalized density matrix and allow for spin- and charge-density waves with
arbitrary incommensurate wave-vectors, as well as all possible superconducting orders. The inner loop self-consistency
equations are solved by use of the "globally convergent modified Newton-Raphson method", while the external free-energy
optimization is performed by using the multidimensional simplex method. We have implemented a number of Brillouin zone
integration schemes in order to contrast the problem of finite-size effects and low-temperature singularities. We
implemented basic types of fundamental interaction terms: general multi-orbital hopping term, multi-orbital local
Coulomb and Heisenberg exchange terms.
We illustrate the use of ThPh by showing the results of a few well known example systems: i) attractive s-wave
superconducting Hubbard model; ii) the competition between various incommensurate AF spin-density waves in 2D Hubbard
model [1]; iii) slave-boson type Resonating Valence Bonds (RVB) states in CuNCN [2,3]; iv) various symmetry
superconducting states in graphene [4]. Finally, we discuss prospectives
and possible new applications of ThPh.
[1] E. Arrigoni and G.C. Strinati Phys. Rev. B 44, 7455 (1991).
[2] A. L. Tchougreeff and R. Dronskowski J. Phys. Condens. Mater 25 435602 (2013).
[3] E. Plekhanov, A. L. Tchougreeff, Resonating Valence Bonds in Chemistry and Solid State.
in Handbook of Solid State Chemistry, Volume 5 Theoretical Description (R. Dronskowski Ed.) Wiley (2016).
[4] A. M. Black-Schaffer and S. Doniach Phys. Rev. B, 75, 134512, (2007).