Matrix field theory for disordered electron systems

Karen Michaeli

H. G. Schuster, Vitor Rocha Vieira

The effect of an electron heat bath on the motion of an electron system is studied using a quantum Langevin equation and deriving the influence functional of the Feynman-Vernon approach. The generating functional for the time-dependent, finite-temperature correlation functions of a disordered electron system with interactions is written down, and some of its symmetry properties are analyzed. Since the disorder only affects the time evolution of the system our formalism avoids the replica trick and provides a natural physical framework for studying a large variety of open problems in the field of disordered systems. As an example, we give an explicit expression for the averaged generating functional for a disordered electron system in the presence of a Coulomb interaction in terms of two complex matrix fields.

Franz Wegner

E. Kolley, Winfried Kolley

Abstract A real‐time finite‐temperature field theory on the Keldysh contour is used to describe the dynamics of an electron system within a random Hubbard model. The effective, i.e. quenched‐averaged, fermionic action under the functional integral is bosonized by introducing both a matrix field and an exchange field via Hubbard‐Stratonovich transformations. The resulting collective action permits the loop expansion, giving rise to a systematic approximation scheme. The saddle point and Gaussian fluctuations around it are calculated.

Naoto Nagaosa

Patrick Tscheppe, Marcel Klett, Henri Menke +4 more

Abstract We formulate a quantum embedding algorithm in real-space for the simultaneous theoretical treatment of nonlocal electronic correlations and disorder, the coherent cellular dynamical mean-field theory (C-CDMFT). This algorithm combines the molecular coherent potential approximation (CPA) with the cellular dynamical mean-field theory. After a pedagogical review of quantum embedding theories for disordered and interacting electron systems, and a detailed discussion of its work flow, we present first results from C-CDMFT for the half-filled two-dimensional Anderson–Hubbard model on a square lattice: (i) the analysis of its Mott metal–insulator transition as a function of disorder strength, and (ii) the impact of different types of disorder on its magnetic phase diagram. For the latter, by means of a ‘disorder diagnostics’, we are able to precisely identify the contributions of different disorder configurations to the system’s magnetic response.