MeanField Classical vs Quantum Classical case Phys Rev

Mean-Field : Classical vs Quantum Classical case Phys. Rev. B 45, 6497 Quantum case THE STATE UNIVERSITY OF NEW JERSEY RUTGERS A. Georges, G. Kotliar (1992)

Medium of free electrons : impurity model. Solve for the medium using Self Consistency THEG. STATE UNIVERSITY OF NEW G. JERSEY G. . Kotliar, S. Savrasov, Palsson and Biroli, Phys. Rev. Lett. 87, RUTGERS 186401 (2001)

Extension to clusters. Cellular DMFT. CDMFT. G. Kotliar, S. Y. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001) tˆ(K) is the hopping expressed in the superlattice notations. After evaluating cluster quntities periodize to retrieve or estimate lattice observables • Other cluster extensions (DCA, nested cluster schemes, PCMDFT ), causality issues, O. Parcollet, G. Biroli and GK cond-matt 0307587 (2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

CDMFT: Extracting Lattice qua W can be either G, S or M (cumulant, irreducible with respect to t ) so there is no uniqueness in the reconstruction of lattice quantities, e. g THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Testing CDMFT (G. . Kotliar, S. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001) ) with two sites in the Hubbard model in one dimension V. Kancharla C. Bolech and GK PRB 67, 075110 (2003)][[M. Capone M. Civelli V Kancharla C. Castellani and GK PR B 69, 195105 (2004) ] U/t=4. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

First Application: The Mott tansition problem. n n n Central Ingredient : competition bewteen the Coulomb energy and the kinetic energy. Force us to confront the difficult regime where both are of the same order of magnitude. Arguably it is the simplest and most universal “strong correlation problem “ THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

V 2 O 3 under pressure or THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ni. Se 2 -x. Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Mott transition in layered organic conductors al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS S Lefebvre et

Pressure Driven Mott trans How does the electron go from the localized to the itinerant limit ? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

M. Rozenberg et. al. Phys. Rev. Lett. 75, 105 (1995) T/W Phase diagram of a Hubbard model with partial frustration at STATE UNIVERSITY OF NEW JERSEY the Mott transition in single site integer THE filling. Thinking about RUTGERS DMFT. High temperature universality

Insights from DMFT q Low temperature Ordered phases. Stability depends on chemistry and crystal structure q. High temperature behavior around Mott endpoint, more universal regime, captured by simple models treated within DMFT. Role of magnetic THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Spectral Evolution at T=0 half filling full frustration X. Zhang M. Rozenberg G. Kotliar (PRL 1993) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Parallel development: Fujimori et. al THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Qualitative single site DMFT predictions. n n Spectra of the strongly correlated metallic regime contains both quasiparticle-like and Hubbard band-like features. Mott transition is drive by transfer of spectral weight. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange nd Rozenberg Phys. Rev. Lett. 84, 5180 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Qualitative single site DMFT predictions: Optics n n Spectra of the strongly correlated metallic regime contains both quasiparticle-like and Hubbard band-like features. Mott transition is drive by transfer of spectral weight. Consequences for optics. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weight in v 2 O 3 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

V 2 O 3: Anomalous transfer of spectral weight Th. Pruschke and D. L. Cox and M. Jarrell, Europhysics Lett. , 21 (1993), 593 M. Rozenberg G. Kotliar THE H. STATE Kajueter GOFTahomas D. Rapkikne J Honig and P UNIVERSITY NEW JERSEY RUTGERS Metcalf Phys. Rev. Lett. 75, 105 (1995)

Anomalous transfer of optical spectral weight, Ni. Se. S. [Miyasaka and Takagi 2000] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous Spectral Weight Transfer: Optics Below energy Apreciable. T dependence found. Schlesinger et. al (Fe. Si) PRL 71 , 1748 , (1993) B Bucher et. al. Ce 2 Bi 4 Pt 3 PRL 72, 522 (1994), Rozenberg et. al. PRB 54, 8452, (1996). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous Resistivity and Mott transition Ni Se 2 -x Sx Crossover from Fermi liquid to bad metal to semiconductor to paramagnetic insulator. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Single site DMFT and kappa organics THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ising critical endpoint! In V 2 O 3 P. Limelette et. al. Science 302, 89 (2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Searching for a quasiparticle peak THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

ARPES measurements on Ni. S 2 -x. Sex . Matsuura et. Al Phys. Rev B 58 (1998) 3690. Doniaach and Watanabe Phys. Rev. B 57, 3829 (1998) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Schematic DMFT phase Implications for transport. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous Resistivity and Mott transition Ni Se 2 -x Sx Crossover from Fermi liquid to bad metal to semiconductor to paramagnetic insulator. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Phase Diagram k Organics THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Transport in k organics: hysteresis. Limelette et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

The bad insulator regime. M THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ising endpoint finally found THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange nd Rozenberg Phys. Rev. Lett. 84, 5180 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

V 2 -x. Crx O 3 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ising critical endpoint! In VCr 2 O 3 Limelette et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Conclusion. n n An electronic model accounts for all the qualitative features of the finite temperature of a frustrated system at integer occupancy. The electronic degrees of freedom rather than the lattice drives the transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Conclusion n Single site DMFT describes the main features of the experiments at high temperatures using a simple model. Made non trivial predictions. Finite temperature conclusions are robust. At low temperatures clusters will bring refinements of this picture. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Comments on DMFT. n n Review of DMFT, technical tools for solving DMFT eqs. A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68, 13 (1996)] CDMFT , instead of studying finite systems with open or periodic boundary conditions, study a system in a medium. Connection with DMRG, infer the density matrix by using a Gaussian anzats, and the periodicity of the system. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

§ § § Dynamical Mean Field Theory Basic idea: reduce the quantum many body problem to a one site or a cluster of sites, in a medium of non interacting electrons obeying a self consistency condition. [A. Georges and GK Phys. Rev. B 45, 6497, 1992]. Merge atomic physics and band theory. Atom in a medium. Weiss field. = Quantum impurity model. Solid in a frequency dependent potential. Incorporate band structure and orbital degeneracy to achive a realistic description of materials. LDA +DMFT. Realistic combination with band theory: LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). . THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Spectral Density Functional n n n Determine the self energy , the density and the structure of the solid self consistently. By extremizing a functional of DENSITY +LOCAL SPECTRA. (Chitra, Kotliar, PRB 2001, Savrasov, Kotliar, PRB 2005). Coupling of electronic degrees of freedom to structural degrees of freedom. Full implementation for Pu. Savrasov and Kotliar Nature 2001. Under development. Functional of G and W, self consistent determination of the Coulomb interaction and the Greens function. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). n n The light, sp (or spd) electrons are extended, well described by LDA. The heavy, d (or f) electrons are localized treat by DMFT. Use Khon Sham Hamiltonian after substracting the average energy already contained in LDA. Add to the substracted Kohn Sham Hamiltonian a frequency dependent self energy, treat with DMFT. In this method U is either a parameter or is estimated from constrained LDA n n Describes the excitation spectra of many strongly correlated solids. . THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Mott Transition in the Actinide Series Johansen 60, kotliar Savrasov 2000 Lashley et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Pu phases: A. Lawson Los Alamos Science 26, (2000) LDA underestimates the volume of fcc Pu by 30%. Within LDA fcc Pu has a negative shear modulus. LSDA predicts d Pu to be magnetic with a 5 ub moment. Experimentally it is not. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Pu is not MAGNETIC, alpha and delta have comparable susceptibility and specific heat. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Total Energy as a function of volume for Pu W (ev) vs (a. u. 27. 2 ev) (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu.

Consequence of two DMFT solutions E U/W THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Double well structure and d Pu Qualitative explanation of negative thermal expansion[ G. Kotliar J. Low Temp. Physvol. 126, 1009 27. (2002)]See also A. Lawson et. al. Phil. Mag. B 82, 1837 ] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Phonon Spectra n n n Electrons are the glue that hold the atoms together. Vibration spectra (phonons) probe the electronic structure. Phonon spectra reveals instablities, via soft modes. Phonon spectrum of Pu had not been measured. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Phonon freq (THz) vs q in delta Pu X. Dai et. al. Science vol 300, 953, 2003 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Inelastic X Ray. Phonon energy 10 mev, photon energy 10 Kev. E = Ei - Ef Q = ki - kf THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

DMFT Phonons in fcc d-Pu C 11 (GPa) C 44 (GPa) C 12 (GPa) C'(GPa) Theory 34. 56 33. 03 26. 81 3. 88 Experiment 36. 28 33. 59 26. 73 4. 78 ( Dai, Savrasov, Kotliar, Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et. al, Science, 22 August 2003)

J. Tobin et. al. PHYSICAL REVIEW B 68, 155109 , 2003 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

K. Haule , Puphotoemission with DMFT using vertex corrected NCA. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Actinides and The Mott Phenomena Evolution of the electronic structure between the atomic limit and the band limit in an open shell situation. The “”in between regime” is ubiquitous central theme in strongly correlated systems. Actinides allow us to probe this physics in ELEMENTS. Mott transition across the actinide series [ B. Johansson Phil Mag. 30, 469 (1974)]. Revisit the problem using a new insights and new techniques from the solution of the Mott transition problem within DMFT in a model Hamiltonian. Use the ideas and concepts that resulted from this development to give physical qualitative insights into real materials. Turn the technology developed to solve simple models into a practical quantitative electronic structure method. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Conclusions and Outlook n n n Motivation: Mott transition in Americium and Plutonium. In both cases theory (DMFT) and experiment suggest gradual subtle changes. DMFT: Physical connection between spectra and structure. Studied the Mott transition open and closed shell cases. . DMFT: method under construction, but it already gives quantitative results and qualitative insights. Interactions between theory and experiments. Pu: simple picture of alpha delta and epsilon. Interplay of lattice and electronic structure near the Mott transition. Am: Rich physics, mixed valence under pressure ? Superconductivity near the Mott transition. n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Actinides and The Mott Phenomena Evolution of the electronic structure between the atomic limit and the band limit in an open shell situation. The “”in between regime” is ubiquitous central theme in strongly correlated systems. Actinides allow us to probe this physics in ELEMENTS. Mott transition across the actinide series [ B. Johansson Phil Mag. 30, 469 (1974)]. Revisit the problem using a new insights and new techniques from the solution of the Mott transition problem within DMFT in a model Hamiltonian. Use the ideas and concepts that resulted from this development to give physical qualitative insights into real materials. Turn the technology developed to solve simple models into a practical quantitative electronic structure method. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS