From Real Materials to Model Hamiltonians With Density Matrix Downfolding

Zheng, Huihuo; Changlani, Hitesh J.; Williams, Kiel T.; Busemeyer, Brian; Wagner, Lucas K.

doi:10.3389/fphy.2018.00043

Cited by 29 publications

(24 citation statements)

References 68 publications

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“…where ðr 1 ; …; r N Þ are the electron coordinates, and R a ¼ aRe z is the coordinate of the ath proton. This Hamiltonian has been studied in the finite basis or finite systems (or both) and has generated increasing interest [8,10,11,[13][14][15][16]. We use atomic units throughout, in which energies are measured in Hartrees (me 4 =ℏ 2 ) and lengths in units of the Bohr radius a B ¼ ℏ 2 =ðme 2 Þ.…”

Section: Methodsmentioning

confidence: 99%

Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases

Motta

Genovese

et al. 2020

Phys. Rev. X

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Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantummechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

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Section: Methodsmentioning

confidence: 99%

Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases

Motta

Genovese

et al. 2020

Phys. Rev. X

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“…Therefore, the singlet-triplet excitation is J ¼ 492ð24Þ meV, within two statistical error bars of the experimental result. This realization was made possible by work we have done regarding effective model fitting [3,4]. We view this as a strong motivation to have a rigorous theory of effective models as we tried to lay out in those papers.…”

mentioning

confidence: 99%

Erratum: Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles [Phys. Rev. Lett. 114 , 176401 (2015)]

Zheng¹,

Wagner

2018

Phys. Rev. Lett.

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“…To overcome these limitations, we developed a novel inverse method that automates the construction of parent Hamiltonians from wave functions by searching for models in a large space of "physically reasonable" Hamiltonians. More broadly, inverse methods have been successful in applications such as solving machine learning problems [25], targeting many-particle ordering in classical materials [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41], and promoting certain properties in quantum many-body systems [42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

Chertkov

Clark

2018

Phys. Rev. X

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Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational "inverse method," the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function jψ T i and produces as output Hamiltonians for which jψ T i is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and, in this work, we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model. EHC gives an alternative inverse approach for studying quantum many-body phenomena.

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From Real Materials to Model Hamiltonians With Density Matrix Downfolding

Cited by 29 publications

References 68 publications

Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases

Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases

Erratum: Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles [Phys. Rev. Lett. 114 , 176401 (2015)]

Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

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