Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

Dobrautz, Werner; Katukuri, Vamshi M.; Bogdanov, Nikolay A.; Kats, Daniel; Manni, Giovanni Li; Alavi, Ali

doi:10.1103/physrevb.105.195123

Cited by 20 publications

(57 citation statements)

References 174 publications

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“…Recently, we have discovered a strategy within GUGA that allows an unprecedented reduction of the multireference character (compression) − of ground- and excited-state wave functions and the unique possibility to perform state-specific optimizations of ground- and excited-state wave functions. , These properties arise from a unique block-diagonal structure of the GUGA Hamiltonian matrix, even within the same spin-symmetry sector, that follows chemically/physically motivated molecular orbital transformations . This strategy has been applied to exchange-coupled polynuclear transition metal clusters with a large number of localized open-shell orbitals − and to one-dimensional Heisenberg and Hubbard model Hamiltonians . In the latter cases, a connection with the concept of alternancy symmetry can be envisioned. , Other sparse FCI solvers ,− could also benefit from the enhanced sparsity of the Hamiltonian and wave functions that follow the above-mentioned strategy.…”

Section: Introductionmentioning

confidence: 99%

Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

et al. 2022

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In this article, we demonstrate that a first-order spin penalty scheme can be efficiently applied to the Slater determinant based Full-CI Quantum Monte Carlo (FCIQMC) algorithm, as a practical route toward spin purification. Two crucial applications are presented to demonstrate the validity and robustness of this scheme: the 1 Δ g ← 3 Σ g vertical excitation in O 2 and key spin gaps in a [Mn 3 (IV) O 4 ] cluster. In the absence of a robust spin adaptation/purification technique, both applications would be unattainable by Slater determinant based ground state methods, with any starting wave function collapsing into the higher-spin ground state during the optimization. This strategy can be coupled to other algorithms that use the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver, including the Stochastic Generalized Active Space, the similarity-transformed FCIQMC, the tailored-CC, and second-order perturbation theory approaches. Moreover, in contrast to the GUGA-FCIQMC technique, this strategy features both spin projection and total spin adaptation, making it appealing when solving anisotropic Hamiltonians. It also provides spin-resolved reduced density matrices, important for the investigation of spin-dependent properties in polynuclear transition metal clusters, such as the hyperfine-coupling constants.

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Section: Introductionmentioning

confidence: 99%

Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

et al. 2022

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“…We found that specific chemically and physically motivated site permutations bring the Hamiltonian matrices into a unique (quasi -)block-diagonal structure, and many-body wave functions into embarrassingly compact forms, indicated by larger leading CI coefficients, small L 1 -norm and large L 4 -norms of normalized eigenvectors. [25,28] As a direct consequence of the block-diagonal structure of the Hamiltonian matrices, it is possible to selectively optimize electronic excited states without the overhead of calculating the lowerenergy states, by simply relying on the initial ansatz for the targeted wave function. This strategy has been numerically shown for the singlet low-energy excited states of two Fe 4 S 4 cubane clusters.…”

Section: Introductionmentioning

confidence: 99%

“…[27] We have also applied this strategy to the one-dimensional s-1 2 isotropic Heisenberg model with nearest-neighbor (NN) interactions (single J magnetic coupling constant), to the spin-free form of the Hubbard model with NN interactions in a real-space representation, and to ab initio Hamiltonians in the form of chains of equally spaced hydrogen atoms. [28,36] For all the cases above we discussed the rationale behind the spin-adapted ground state wave function compression as a function of the permutational symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…[23,26,27] Similarly, for the one-dimensional Heisenberg chain conclusions were obtained following a thorough exploration of the permutational space, also adopting a simulated annealing strategy. [28] In the present work we undertake a more rigorous and funda-mental strategy to the block-diagonal structure of the electronic Hamiltonian within a spin-adapted formulation, based on commutation relations between partial cumulative spin operators and the Hamiltonian operator. These commutation relations represent a new tool to predict orbital/site permutations that lead to wave function compression without necessarily explore numerically the permutational space.…”

Section: Introductionmentioning

confidence: 99%

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Resolution of Ground and Excited Electronic States within the Unitary Group Approach

Manni

Kats

Liebermann

2022

Preprint

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In this work ground and excited electronic states of Heisenberg cluster models, in the form of con- figuration interaction many-body wave functions, are characterized within the spin-adapted Graph- ical Unitary Group Approach framework, and relying on a novel combined unitary and symmetric group approach. Finite-size cluster models of well-defined point-group symmetry and of general local-spin Slocal ≥ 21 are presented, including J1–J2 triangular and tetrahedral clusters, which are often used to describe magnetic interactions in biological and bio-mimetic polynuclear transition metal clusters with unique catalytic activity, such as nitrogen fixation and photosynthesis. We show that a unique block-diagonal structure of the underlying Hamiltonian matrix in the spin-adapted basis emerges when an optimal lattice site ordering is chosen that reflects the internal symmetries of the model investigated. The block-diagonal structure is bound to the commutation relations between cumulative spin operators and the Hamiltonian operator, that in turn depend on the geometry of the cluster investigated. The many-body basis transformation, in the form of the orbital/site reorder- ing, exposes such commutation relations. These commutation relations represent a rigorous and formal demonstration of the block-diagonal structure in Hamiltonian matrices and the compression of the corresponding spin-adapted many-body wave functions. As a direct consequence of the block- diagonal structure of the Hamiltonian matrix it is possible to selectively optimize electronic excited states without the overhead of calculating the lower-energy states by simply relying on the initial ansatz for the targeted wave function. Additionally, more compact many-body wave functions are obtained. In extreme cases, electronic states are precisely described by a single configuration state function, despite the curse of dimensionality of the corresponding Hilbert space. These findings are crucial in the electronic structure theory framework, for they offer a conceptual route towards wave functions of reduced multi-reference character, that can be optimized more easily by approximated eigensolvers and are of more facile physical interpretation. They open the way to study larger ab initio and model Hamiltonians of increasingly larger number of correlated electrons, while keeping the computational costs at their lowest.

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“…The FCIQMC method has been used with success previously both for a wide array of fermionic models [79][80][81][82], as well as applied to bosons [83,84], however has not to date been applied to mixed-species systems. In particular, we believe that an application of FCIQMC to coupled electron-boson systems is particularly appealing, since it is not expected to require an explicit truncation of the bosonic mode occupation, allowing a sampling over all relevant bosonic degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces

Scott¹,

Booth²

2022

Preprint

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We extend the scope of full configuration interaction quantum Monte Carlo (FCIQMC) to be applied to coupled fermion-boson hamiltonians, alleviating the a priori truncation in boson occupation which is necessary for many other wave function based approaches to be tractable. Detailing the required algorithmic changes for efficient excitation generation, we apply FCIQMC in two contrasting settings. The first is a sign-problem-free Hubbard-Holstein model of local electron-phonon interactions, where we show that with care to control for population bias via importance sampling and/or reweighting, the method can achieve unbiased energies extrapolated to the thermodynamic limit, without suffering additional computational overheads from relaxing boson occupation constraints. Secondly, we apply the method as a 'solver' within a quantum embedding scheme which maps electronic systems to local electron-boson auxiliary models, with the bosons representing coupling to long-range plasmonic-like fluctuations. We are able to sample these general electron-boson hamiltonians with ease despite a formal sign problem, including a faithful reconstruction of converged reduced density matrices of the system.

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Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

Cited by 20 publications

References 174 publications

Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

Resolution of Ground and Excited Electronic States within the Unitary Group Approach

Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces

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