One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D\GammaA) and the dual fermion (DF) scheme, yielding a consistent formulation of non-local correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D\GammaA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF and D\GammaA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.

[1]  M I Katsnelson,et al.  Efficient perturbation theory for quantum lattice models. , 2008, Physical review letters.

[2]  A. Tremblay,et al.  Theoretical methods for strongly correlated electrons , 2004 .

[3]  K. Held,et al.  Ab initio calculations with the dynamical vertex approximation , 2011, 1104.2188.

[4]  Georges,et al.  Hubbard model in infinite dimensions. , 1992, Physical review. B, Condensed matter.

[5]  H. R. Krishnamurthy,et al.  Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems , 1998 .

[6]  D. Vollhardt,et al.  Correlated Lattice Fermions in High Dimensions , 1989 .

[7]  Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: A nonlinear sigma model approach , 2003, cond-mat/0307238.

[8]  A. Katanin.  The effect of six-point one-particle reducible local interactions in the dual fermion approach , 2012, 1209.6285.

[9]  A. Georges,et al.  Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs , 2008, 0810.3819.

[10]  G. Kotliar,et al.  Cluster dynamical mean field theory of the Mott transition. , 2008, Physical review letters.

[11]  T. Pruschke,et al.  Dual fermion dynamical cluster approach for strongly correlated systems , 2011, 1104.3854.

[12]  A. D. Jackson,et al.  Variational and perturbation theories made planar , 1982 .

[13]  J. P. Remeika,et al.  Metal-Insulator Transitions in Pure and Doped V 2 O 3 , 1973 .

[14]  M. Salmhofer,et al.  Functional renormalization group approach to correlated fermion systems , 2011, 1105.5289.

[15]  White,et al.  Conserving approximations for strongly fluctuating electron systems. II. Numerical results and parquet extension. , 1991, Physical review. B, Condensed matter.

[16]  K. Held,et al.  Comparing pertinent effects of antiferromagnetic fluctuations in the two- and three-dimensional Hubbard model , 2008, 0808.0689.

[17]  T. Maier,et al.  Multi-scale extensions to quantum cluster methods for strongly correlated electron systems , 2006, Journal of physics. Condensed matter : an Institute of Physics journal.

[18]  Influence of Spatial Correlations in Strongly Correlated Electron Systems : Extension to Dynamical Mean Field Approximation(Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties) , 2006, cond-mat/0602451.

[19]  C. Dominicis.  Variational Formulations of Equilibrium Statistical Mechanics , 1962 .

[20]  N. Blumer,et al.  Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model , 2012, 1205.6788.

[21]  R. Bishop,et al.  Quantum many-particle systems , 1990 .

[22]  V. Janiš,et al.  Mean-field theories for disordered electrons: Diffusion pole and Anderson localization , 2005, cond-mat/0501586.

[23]  G. Kotliar,et al.  Cellular Dynamical Mean Field Approach to Strongly Correlated Systems , 2000, cond-mat/0010328.

[24]  Hyowon Park,et al.  The study of two-particle response functions in strongly correlated electron systems within the dynamical mean field theory , 2011 .

[25]  K. Held,et al.  Critical properties of the half-filled Hubbard model in three dimensions. , 2011, Physical review letters.

[26]  M. Katsnelson,et al.  Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions , 2007, 0711.3647.

[27]  W. Krauth,et al.  Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions , 1996 .

[28]  K. Held,et al.  Dynamical vertex approximation : A step beyond dynamical mean-field theory , 2006, cond-mat/0603100.

[29]  T. Maier,et al.  Structure of the pairing interaction in the two-dimensional Hubbard model. , 2005, Physical review letters.

[30]  Nevill Mott,et al.  Metal-Insulator Transition , 1968 .

[31]  K. Held,et al.  Dynamical vertex approximation for nanoscopic systems. , 2010, Physical review letters.

[32]  J Liu,et al.  Parquet approximation for the 4x4 Hubbard cluster. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  A. Georges,et al.  Signature of antiferromagnetic long-range order in the optical spectrum of strongly correlated electron systems , 2011, 1112.5003.

[34]  Nevill Mott,et al.  Metal-insulator transitions , 1974 .

[35]  J. Ramanujam,et al.  Solving the parquet equations for the Hubbard model beyond weak coupling. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Gabriel Kotliar,et al.  Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory , 2004 .

[37]  A. I. Lichtenstein,et al.  Antiferromagnetism and d -wave superconductivity in cuprates: A cluster dynamical mean-field theory , 1999, cond-mat/9911320.

[38]  Smith,et al.  Two-body and three-body parquet theory. , 1992, Physical Review A. Atomic, Molecular, and Optical Physics.

[39]  K. Held,et al.  Dynamical Vertex Approximation , 2008, 0807.1860.

[40]  Alessandro Toschi,et al.  Local electronic correlation at the two-particle level , 2012, Physical Review B.

[41]  N. E. Bickers.  PARQUET EQUATIONS FOR NUMERICAL SELF-CONSISTENT-FIELD THEORY , 1991 .

[42]  T. Pruschke,et al.  Thermodynamics of the 3D Hubbard model on approaching the Néel transition. , 2010, Physical review letters.

[43]  S. Ciuchi,et al.  Divergent precursors of the Mott-Hubbard transition at the two-particle level. , 2013, Physical review letters.

[44]  Schiller,et al.  Systematic 1/d corrections to the infinite-dimensional limit of correlated lattice electron models. , 1995, Physical review letters.

[45]  Paul C. Martin,et al.  Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation , 1964 .

[46]  H. Monien,et al.  Determination of the lattice susceptibility within the dual fermion method , 2008 .

[47]  T. Pruschke,et al.  Quantum cluster theories , 2004, cond-mat/0404055.

[48]  A. I. Lichtenstein,et al.  Dual fermion approach to nonlocal correlations in the Hubbard model , 2006, cond-mat/0612196.