Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard–Holstein Model

Reinhard, Teresa E.; Mordovina, Uliana; Hubig, Claudius; Kretchmer, Joshua S.; Schollwöck, Ulrich; Appel, Heiko; Sentef, Michael A.; Rubio, Ángel

doi:10.1021/acs.jctc.8b01116

Cited by 37 publications

(35 citation statements)

References 58 publications

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“…As discussed in section 2.1, an electronic band structure is often modeled as the eigenval- 25 we obtain the band structure by diagonalizing a low-level Hamiltonian containing a correlation potential which is optimized by comparing the correlated and mean-field density matrices. However, we have found that the operatorĥ(k) from eq (11) utilizing the cost function of eq (12) results in unphysically dispersive bands because a change in the cost function in eq 12 can generate a drastic variation ofĥ(k) at certain k-points.…”

Section: Electronic Band Structure From Dmetmentioning

confidence: 99%

“…24,[26][27][28][29] Remarkably, DMET has inspired the development of other theories based on density matrix embedding, such as density embedding theory (DET), 30 bootstrap embedding, [31][32][33] incremental embedding, 34 localized active space self-consistent field (LASSCF), 35,36 and projected density matrix embedding theory. 37 Its extensions to the real-time formulation 38 as well as to the electron-phonon interacting system 25,39 have also been investigated. For periodic systems, DET with a coupled cluster solver has been implemented to compute correlation energy in several one-dimensional systems.…”

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confidence: 99%

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Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Pham

Hermes

Gagliardi

2019

J. Chem. Theory Comput.

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We developed a periodic version of density matrix embedding theory, DMET, with which it is possible to perform electronic structure calculations on periodic systems, and compute the band structure of solid-state materials. Electron correlation can be captured by means of a local impurity model using various wave function methods, like, for example, full configuration interaction, coupled cluster and multiconfigurational methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Our results show that DMET is in good agreement with other many-body techniques at a cheaper computational cost. We anticipate that periodic DMET can be a promising first principle method for strongly correlated materials. arXiv:1909.08783v2 [cond-mat.str-el]An accurate and affordable numerical method for strongly correlated electrons in solid-state materials remains one of the most exciting but challenging topics in computational chemistry and material science. 1 This is crucially important because electron correlation governs many exotic phenomena in condensed phases, such as metal-insulator transition, unconventional superconductivity, and magnetism. 2-4 For decades, Kohn-Sham density functional theory (KS-DFT) 5,6 has been the most successful method for solid-state materials due to its simplicity and predictive capability for many cases. 7,8 While formally exact, the practical application of KS-DFT using approximate exchange-correlation (XC) functional is unable to provide a good description for strong electronic interaction. This is often attributed to the single-determinant nature of the KS fictitious system. 9 Even within the weak correlation regime, the exact KS orbitals energy gap or simply KS band gap (≡ LU M O − HOM O , with LU M O and HOM O are the lowest unoccupied and highest occupied molecular orbital energy, respectively) cannot be interpreted as the fundamental band gap (≡ IP − EA with IP and EA are ionization potential and electron affinity, respectively) owing to the derivative discontinuity of the exchange-correlation energy (IP − EA = LU M O − HOM O + ∆, with ∆ is the derivative discontinuity). 10 Strictly speaking, KS-DFT band structure is unphysical as pointed out in the early work by Perdew and Levy, 10 Sham and Schluter, 11 and recently byBaerends. 12 This argument also applies to approximate functionals based on the local density approximation (LDA) or generalized gradient approximation (GGA). LDA/GGA usually underestimate the fundamental band gap of solids. (For solids the fundamental band gap is very close to the optical band gap which is related to the first excitation; 12 the distinction is not necessary here and we use the term 'band gap' to refer to the fundamental band gap throughout this paper.) This so-called band gap problem 13 makes KS-DFT less appealing ...

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Section: Electronic Band Structure From Dmetmentioning

confidence: 99%

mentioning

confidence: 99%

Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Pham

Hermes

Gagliardi

2019

J. Chem. Theory Comput.

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“…For instance, the formation and stability of (Bi-)Polarons is a central problem and considerable effort has been taken for its investigation [6][7][8][9][10][11][12][13][14][15]. A broad class of different methods such as quantum Monte Carlo [16,17], density-functional theory [18], density-matrix embedding theory [19], or dynamical mean-field theory [20][21][22] has been explored to study its various aspects. Evidently, the task to numerically describe such low-dimensional, strongly-correlated quantum systems has been subject to a vast development.…”

Section: Introductionmentioning

confidence: 99%

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

2021

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Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

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“…In the strong coupling limit, analytical predictions for the polaron and bipolaron properties such as their effective mass can be derived [16,17]. While the research on the static properties of different polaron models is still active and fruitful [18][19][20][21], there is a growing interest in polaron dynamics out of equilibrium. A particularly interesting scenario to consider in this context is the light-induced superconducting response of the system, which has been observed in several materials [22][23][24][25][26][27][28].…”

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confidence: 99%

Quantum simulation of extended polaron models using compound atom-ion systems

Jachymski

Negretti

2020

Phys. Rev. Research

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We consider the prospects for quantum simulation of condensed matter models exhibiting strong electronphonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally possesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.

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Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard–Holstein Model

Cited by 37 publications

References 58 publications

Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

Quantum simulation of extended polaron models using compound atom-ion systems

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