Site-occupation embedding theory using Bethe ansatz local density approximations

Site-occupation embedding theory is a significantly improved formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than non-interacting) one. It provides a rigorous framework for combining wavefunction- or Green function-based methods with DFT. Exact properties of the embedding functional are discussed as well as the construction of density-functional approximations based on the Bethe ansatz solutions to both Hubbard and Anderson models.

[1]  J. Zaanen,et al.  Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. , 1995, Physical review. B, Condensed matter.

[2]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[3]  K. Karlsson Self-consistent GW combined with single-site dynamical mean field theory for a Hubbard model , 2005 .

[4]  G. Kotliar,et al.  Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective , 2017, 1710.07773.

[5]  K. Burke,et al.  Bethe ansatz approach to the Kondo effect within density-functional theory. , 2012, Physical review letters.

[6]  Emmanuel Fromager,et al.  On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation , 2014, 1409.2326.

[7]  Garnet Kin-Lic Chan,et al.  Dynamical mean-field theory from a quantum chemical perspective. , 2010, The Journal of chemical physics.

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

[9]  Ping Sun,et al.  Extended dynamical mean-field theory and GW method , 2002 .

[10]  Garnet Kin-Lic Chan,et al.  Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory , 2015, 1504.01784.

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

[12]  Vincent Robert,et al.  Local density approximation in site-occupation embedding theory , 2016, 1602.02547.

[13]  Daniel Karlsson,et al.  Time-dependent density-functional theory meets dynamical mean-field theory: real-time dynamics for the 3D Hubbard model. , 2010, Physical review letters.

[14]  M. Saubanère,et al.  Density-matrix functional study of the Hubbard model on one- and two-dimensional bipartite lattices , 2011 .

[15]  F. Aryasetiawan,et al.  When strong correlations become weak: Consistent merging of $GW$ and DMFT , 2016, 1604.02023.

[16]  A. Georges The beauty of impurities: Two revivals of Friedel's virtual bound-state concept , 2016 .

[17]  J. Chayes,et al.  Density functional approach to quantum lattice systems , 1985 .

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

[19]  S. Sanvito,et al.  Electric field response of strongly correlated one-dimensional metals: A Bethe ansatz density functional theory study , 2010, 1010.2860.

[20]  Fredrik Nilsson,et al.  Multitier self-consistent $GW$+EDMFT , 2017, 1706.06808.

[21]  Qiming Sun,et al.  Quantum Embedding Theories. , 2016, Accounts of chemical research.

[22]  N A Lima,et al.  Density functionals not based on the electron gas: local-density approximation for a Luttinger liquid. , 2003, Physical review letters.

[23]  Gustavo E. Scuseria,et al.  Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields , 2013, 1310.0051.

[24]  Elliott H. Lieb,et al.  Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension , 1968 .

[25]  Noack,et al.  Density-functional theory on a lattice: Comparison with exact numerical results for a model with strongly correlated electrons. , 1995, Physical review. B, Condensed matter.

[26]  Takashi Tsuchimochi,et al.  Bootstrap embedding: An internally consistent fragment-based method. , 2016, The Journal of chemical physics.

[27]  Qiming Sun,et al.  A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry. , 2016, Journal of chemical theory and computation.

[28]  Gunnarsson,et al.  Density-functional treatment of an exactly solvable semiconductor model. , 1986, Physical review letters.

[29]  Density-matrix functional theory of strongly correlated lattice fermions , 2002, cond-mat/0207429.

[30]  Luiz N. Oliveira,et al.  Density-functional study of the Mott gap in the Hubbard model , 2002 .

[31]  Alexei A Kananenka,et al.  Communication: Towards ab initio self-energy embedding theory in quantum chemistry. , 2015, The Journal of chemical physics.

[32]  U. Schollwoeck The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[33]  G. Stefanucci,et al.  Towards a description of the Kondo effect using time-dependent density-functional theory. , 2011, Physical review letters.

[34]  G. M. Pastor,et al.  Lattice density functional theory of the single-impurity Anderson model: Development and applications , 2011 .

[35]  M. Casula,et al.  Dynamical screening in correlated electron systems—from lattice models to realistic materials , 2016, Journal of physics. Condensed matter : an Institute of Physics journal.

[36]  J. Lorenzana,et al.  Solving lattice density functionals close to the Mott regime , 2014, 1403.5080.

[37]  Emanuel Gull,et al.  Systematically improvable multiscale solver for correlated electron systems , 2014, 1410.5118.

[38]  K. Burke,et al.  Density functional description of Coulomb blockade: Adiabatic versus dynamic exchange correlation , 2015, 1503.06222.

[39]  E K U Gross,et al.  Dynamical Coulomb blockade and the derivative discontinuity of time-dependent density functional theory. , 2009, Physical review letters.

[40]  M. Tosi,et al.  Luther-Emery phase and atomic-density waves in a trapped fermion gas. , 2006, Physical review letters.

[41]  Chem. , 2020, Catalysis from A to Z.

[42]  Claudio Verdozzi,et al.  Time-dependent density-functional theory and strongly correlated systems: insight from numerical studies. , 2007, Physical review letters.

[43]  A. Harju,et al.  Lattice density-functional theory on graphene , 2010, 1011.2892.

[44]  C. Marianetti,et al.  Electronic structure calculations with dynamical mean-field theory , 2005, cond-mat/0511085.

[45]  A Georges,et al.  First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory. , 2003, Physical review letters.

[46]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[47]  Hans-Joachim Werner,et al.  Local treatment of electron correlation in coupled cluster theory , 1996 .

[48]  V. França,et al.  Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity , 2011, 1102.5018.

[49]  K. Burke,et al.  Accuracy of density functionals for molecular electronics: The Anderson junction , 2012, 1201.1310.

[50]  K. Capelle,et al.  Phase diagram of harmonically confined one-dimensional fermions with attractive and repulsive interactions , 2005, cond-mat/0508095.

[51]  Emanuel Gull,et al.  Testing self-energy embedding theory in combination with GW , 2017 .

[52]  Effects of nanoscale spatial inhomogeneity in strongly correlated systems , 2005, cond-mat/0502355.

[53]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[54]  M. Saubanère,et al.  Scaling and transferability of the interaction-energy functional of the inhomogeneous Hubbard model , 2009 .

[55]  Godby,et al.  Density-functional theory and the v-representability problem for model strongly correlated electron systems. , 1995, Physical review. B, Condensed matter.

[56]  K. Held,et al.  Electronic structure calculations using dynamical mean field theory , 2005, cond-mat/0511293.

[57]  V. Anisimov,et al.  Band theory and Mott insulators: Hubbard U instead of Stoner I. , 1991, Physical review. B, Condensed matter.

[58]  M. Schlüter,et al.  Density-Functional Theory of the Energy Gap , 1983 .

[59]  M. Saubanère,et al.  Density-matrix functional theory of strongly correlated fermions on lattice models and minimal-basis Hamiltonians , 2013, Theoretical Chemistry Accounts.

[60]  Takashi Tsuchimochi,et al.  Density matrix embedding in an antisymmetrized geminal power bath. , 2015, The Journal of chemical physics.

[61]  Garnet Kin-Lic Chan,et al.  Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory. , 2012, Journal of chemical theory and computation.

[62]  Gao Xianlong Effects of disorder on atomic density waves and spin-singlet dimers in one-dimensional optical lattices , 2008, 0803.2312.

[63]  Bethe ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices , 2005, cond-mat/0512184.

[64]  S. Kurth,et al.  Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials , 2012, 1209.3145.

[65]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[66]  G. M. Pastor,et al.  Interaction-energy functional of the Hubbard model: Local formulation and application to low-dimensional lattices , 2016 .

[67]  Adv , 2019, International Journal of Pediatrics and Adolescent Medicine.

[68]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[69]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[70]  Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models , 2003, cond-mat/0311470.

[71]  Garnet Kin-Lic Chan,et al.  Density matrix embedding: a simple alternative to dynamical mean-field theory. , 2012, Physical review letters.

[72]  G. Stefanucci,et al.  Steady-State Density Functional Theory for Finite Bias Conductances. , 2015, Nano letters.

[73]  Н. Грейда,et al.  17 , 2019, Magical Realism for Non-Believers.

[74]  K. Capelle,et al.  Density functionals and model Hamiltonians: Pillars of many-particle physics , 2013 .