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computed for the plasmon model, but the high energy feature appears as a broad tail and not as a separate peak. 

In summary, we have described a simple and effi- cient algorithm to treat fermionic lattice models with arbitrary frequency dependent interactions within single- site DMFT. The only restrictions are that the external screening degrees of freedom may be represented as non- interacting bosons, have an analytically known commu- tator with electron creation operators and couple to a quantity which is conserved by the on-site Hamiltonian (this last restriction prevents a direct application of our formalism to clusters). While we have presented results for the one-band Hubbard model, we emphasize that our method is applicable to multi-orbital models with gen- eral Slater-Kamanori interactions. The method there- fore opens the door for efficient DMFT simulations of the properties of strongly correlated compounds with ar- bitrary energy dependence of the interaction parameters, as well as self-consistent GW+DMFT calculations. We also note that the extended-DMFT variants of dynam- ical mean field theory lead to bosonic problems with a structure very similar to the problem we have considered [14]. 

The frequency dependent U ( ω ) may be characterized by three numbers: a bare (unscreened) interaction, a screened interaction, and a screening frequency. If the screening frequency is very high compared to both the conduction electron bandwidth and the screened inter- action, then the physics is well described by an effec- tive model with an instantaneous interaction equal to the screened U$_{scr}$ . If the screening frequency is very low compared to these scales, then one recovers the familiar electron-phonon physics. We have shown here that the crossover between the two regimes is very broad. Over wide parameter ranges the dynamical nature of the in- 

teraction is important: a model with effective interaction equal to the screened one provides poor estimates of the location of the metal-insulator transition, the value of the Mott Hubbard gaps and the locations and line shapes of the shakeoff features in the spectral function. In partic- ular, the peak positions in the spectal functions do not provide quantitative estimates of either the screened or unscreened U values. 

Our work suggests several directions for future re- search. Application of the method to real materials is in progress. Our approach may also be useful as a solver for E-DMFT calculations. Finally, we note that Assaad and Lang have presented a method for treating bosons within the weak coupling formalism [15]. While the weak cou- pling approach is less efficient than the hybridization ex- pansion for single-site (multiorbital) calculations, it can be applied to cluster dynamical mean field theory. An extension of Assaad’s method to investigate the effects of screening in clusters would be of interest. 

Acknowledgements The spectral functions have been obtained using a maximum entropy code implemented by A. Comanac. The calculations were performed on the Brutus cluster at ETH Zurich using a code based on ALPS [16]. PW is supported by SNF-PP002-118866 and AJM acknowledges support from NSF-DMR-0705847. 

[1] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70 , 1039 (1998). 

[2] R. Hesper, L. H. Tjeng and G. A. Sawatzky, Europhys. Lett. 40 ,177 (1997). 

[3] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Phys. Rev. B 70 , 195104 (2004). 

[4] F. Aryasetiawan, K. Karlsson, O. Jepsen, and U. Sch¨ onberger, Phys. Rev. B 74 , 125106 (2006). 

[5] T. Miyake and F. Aryasetiawan, Phys. Rev. B. 77 , 085122 (2008). 

[6] A. Georges et al. , Rev. Mod. Phys. 68 , 13 (1996). 

[7] J. E. Hirsch and R. M. Fye, Phys. Rev. Lett. 56 , 2521 (1986). 

[8] P. Werner, A. Comanac, L. de’ Medici, M. Troyer and A. J. Millis, Phys. Rev. Lett. 97 , 076405 (2006). 

[9] P. Werner and A. J. Millis, Phys. Rev. B 74 , 155107 (2006). 

[10] E. Zurek, O. Jepsen, O. K. Andersen, ChemPhysChem 6 , 1934 (2005). 

[11] G. Kotliar et al. , Rev. Mod. Phys. 78 , 865 (2006). 

[12] P. Werner and A. J. Millis, Phys. Rev. Lett. 99 , 146404 (2007). 

[13] E. Gull, P. Werner, A. J. Millis, and M. Troyer, Phys. Rev. B 76 , 235123 (2007). 

[14] R. Chitra and G. Kotliar, Phys. Rev. B63 , 115110 (2001). 

[15] F. F. Assaad and T. C. Lang, Phys. Rev. B 76 , 035116 (2007). 

[16] A. F. Albuquerque et al. , J. Magn. Magn. Mater. 310 , 1187 (2007). 

