Spectral functions of strongly correlated extended systems via an exact quantum embedding

Density matrix embedding theory (DMET) [Phys. Rev. Lett., 109, 186404 (2012)], introduced a new approach to quantum cluster embedding methods, whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost, but was inherently limited by the construction of a bath designed to reproduce ground state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the 1D and 2D Hubbard model, where we obtain zero temperature, thermodynamic limit spectral functions, and show the trivial extension to two-particle Green functions. This advance therefore extends the scope and applicability of DMET in condensed matter problems as a computationally tractable route to correlated spectral functions of extended systems, and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.