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Scott CJC, Booth GH. Rigorous Screened Interactions for Realistic Correlated Electron Systems. PHYSICAL REVIEW LETTERS 2024; 132:076401. [PMID: 38427856 DOI: 10.1103/physrevlett.132.076401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 12/05/2023] [Accepted: 01/19/2024] [Indexed: 03/03/2024]
Abstract
We derive a widely applicable first-principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous two-point correlation functions in a chosen model space at the level of the random phase approximation, improving upon the traditional uncontrolled static approximations. Applied to screened interactions within a quantum embedding framework, we demonstrate these faithfully describe the relaxation of local subspaces via downfolding high-energy physics in molecular systems, as well as enabling a systematically improvable description of the long-range plasmonic contributions in extended graphene.
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Affiliation(s)
- Charles J C Scott
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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Sadigh B, Åberg D, Pask J. Spectral-partitioned Kohn-Sham density functional theory. Phys Rev E 2023; 108:045204. [PMID: 37978681 DOI: 10.1103/physreve.108.045204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
We introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.
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Affiliation(s)
- Babak Sadigh
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Daniel Åberg
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - John Pask
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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3
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Weng G, Romanova M, Apelian A, Song H, Vlček V. Reduced Scaling of Optimal Regional Orbital Localization via Sequential Exhaustion of the Single-Particle Space. J Chem Theory Comput 2022; 18:4960-4972. [PMID: 35817013 PMCID: PMC9367006 DOI: 10.1021/acs.jctc.2c00315] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Wannier functions have become a powerful tool in the
electronic
structure calculations of extended systems. The generalized Pipek-Mezey
Wannier functions exhibit appealing characteristics (e.g., reaching
an optimal localization and the separation of the σ–π
orbitals) compared with other schemes. However, when applied to giant
nanoscale systems, the orbital localization suffers from a large computational
cost overhead if one is interested in localized states in a small
fragment of the system. Herein, we present a swift, efficient, and
robust approach for obtaining regionally localized orbitals of a subsystem
within the generalized Pipek-Mezey scheme. The proposed algorithm
introduces a reduced work space and sequentially exhausts the entire
orbital space until the convergence of the localization functional.
It tackles systems with ∼10000 electrons within 0.5 h with
no loss in localization quality compared to the traditional approach.
Regionally localized orbitals with a higher extent of localization
are obtained via judiciously extending the subsystem’s size.
Exemplifying on large bulk and a 4 nm wide slab of diamond with an
NV– center, we demonstrate the methodology and discuss
how the choice of the localization region affects the excitation energy
of the defect. Furthermore, we show how the sequential algorithm is
easily extended to stochastic methodologies that do not provide individual
single-particle eigenstates. It is thus a promising tool to obtain
regionally localized states for solving the electronic structure problems
of a subsystem embedded in giant condensed systems.
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Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Mariya Romanova
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Arsineh Apelian
- Department of Materials, University of California, Santa Barbara, California 93106-9510, United States
| | - Hanbin Song
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
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Vorwerk C, Sheng N, Govoni M, Huang B, Galli G. Quantum embedding theories to simulate condensed systems on quantum computers. NATURE COMPUTATIONAL SCIENCE 2022; 2:424-432. [PMID: 38177872 DOI: 10.1038/s43588-022-00279-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 06/14/2022] [Indexed: 01/06/2024]
Abstract
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.
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Affiliation(s)
- Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Marco Govoni
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
| | - Benchen Huang
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
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Ma H, Sheng N, Govoni M, Galli G. Quantum Embedding Theory for Strongly Correlated States in Materials. J Chem Theory Comput 2021; 17:2116-2125. [DOI: 10.1021/acs.jctc.0c01258] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- He Ma
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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Ma H, Sheng N, Govoni M, Galli G. First-principles studies of strongly correlated states in defect spin qubits in diamond. Phys Chem Chem Phys 2020; 22:25522-25527. [PMID: 33084673 DOI: 10.1039/d0cp04585c] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Using a recently developed quantum embedding theory, we present first-principles calculations of strongly correlated states of spin defects in diamond. Using this theory, effective Hamiltonians are constructed, which can be solved by classical and quantum computers; the latter promise a much more favorable scaling as a function of system size than the former. In particular, we report a study on the neutral group-IV vacancy complexes in diamond, and we discuss their strongly correlated spin-singlet and spin-triplet excited states. Our results provide valuable predictions for experiments aimed at optical manipulation of these defects for quantum information technology applications.
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Affiliation(s)
- He Ma
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
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Tomczak JM. Thermoelectricity in correlated narrow-gap semiconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:183001. [PMID: 29633717 DOI: 10.1088/1361-648x/aab284] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We review many-body effects, their microscopic origin, as well as their impact on thermoelectricity in correlated narrow-gap semiconductors. Members of this class-such as FeSi and FeSb2-display an unusual temperature dependence in various observables: insulating with large thermopowers at low temperatures, they turn bad metals at temperatures much smaller than the size of their gaps. This insulator-to-metal crossover is accompanied by spectral weight-transfers over large energies in the optical conductivity and by a gradual transition from activated to Curie-Weiss-like behaviour in the magnetic susceptibility. We show a retrospective of the understanding of these phenomena, discuss the relation to heavy-fermion Kondo insulators-such as Ce3Bi4Pt3 for which we present new results-and propose a general classification of paramagnetic insulators. From the latter, FeSi emerges as an orbital-selective Kondo insulator. Focussing on intermetallics such as silicides, antimonides, skutterudites, and Heusler compounds we showcase successes and challenges for the realistic simulation of transport properties in the presence of electronic correlations. Further, we explore new avenues in which electronic correlations may contribute to the improvement of thermoelectric performance.
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Affiliation(s)
- Jan M Tomczak
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
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Recent Progress in First-Principles Methods for Computing the Electronic Structure of Correlated Materials. COMPUTATION 2018. [DOI: 10.3390/computation6010026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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10
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Dynamical mean field theory-based electronic structure calculations for correlated materials. Top Curr Chem (Cham) 2014; 347:303-45. [PMID: 24842620 DOI: 10.1007/128_2014_530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
Abstract
We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.
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Tomczak JM, van Schilfgaarde M, Kotliar G. Many-body effects in iron pnictides and chalcogenides: nonlocal versus dynamic origin of effective masses. PHYSICAL REVIEW LETTERS 2012; 109:237010. [PMID: 23368252 DOI: 10.1103/physrevlett.109.237010] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2012] [Indexed: 06/01/2023]
Abstract
We apply the quasiparticle self-consistent GW approximation (QSGW) to some of the iron pnictide and chalcogenide superconductors. We compute Fermi surfaces and density of states, and find excellent agreement with experiment, substantially improving over standard band-structure methods. Analyzing the QSGW self-energy we discuss nonlocal and dynamic contributions to effective masses. We present evidence that the two contributions are mostly separable, since the quasiparticle weight is found to be essentially independent of momentum. The main effect of nonlocality is captured by the static but nonlocal QSGW effective potential. Moreover, these nonlocal self-energy corrections, absent in, e.g., dynamical mean field theory, can be relatively large. We show, on the other hand, that QSGW only partially accounts for dynamic renormalizations at low energies. These findings suggest that QSGW combined with dynamical mean field theory will capture most of the many-body physics in the iron pnictides and chalcogenides.
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Affiliation(s)
- Jan M Tomczak
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
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