Towards a Coupled Cluster Gauge-Field Approach to Quantum Hydrodynamics

Arponen, J.; Bishop, R. F.; Pajanne, E.; Robinson, N. I.

doi:10.1007/978-1-4613-0971-0_5

Cited by 3 publications

(6 citation statements)

References 9 publications

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“…The overall structure of the ECCM is indicated schematically in Fig. 3, and the interested reader is referred to the literature [74,75,80,[99][100][101][102][103][104] for further details. We note here only that the ECCM is, to the best of our knowledge, unique as a formulation of quantum many-body theory in which every fundamental amplitude exactly obeys the cluster property at all levels of approximation.…”

Section: Overview Of CC Theory: the Formalismmentioning

confidence: 99%

“…Finally, we turn our attention to two specific applications of the ECCM which have shown how the basic formalism may fairly easily be integrated with rather important gauge-fieM techniques. The two very different, specific problems concerned are: (i) the (zero-temperature) quantum fluid dynamics of a stronglyinteracting condensed Bose fluid [100]; and (ii) a charged impurity in a polarizable medium [101]. In the former case the gauge fields are external, and correspond to the scalar and vector potentials (arising from the U(1) symmetry of number conservation, and hence exactly as met in electromagnetism) which serve to set the system into its most general state of motion.…”

Section: Other Formal Applications Of the Eccmmentioning

confidence: 99%

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An overview of coupled cluster theory and its applications in physics

Bishop

1991

Theoret. Chim. Acta

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348

391

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What has since become known as the normal coupled cluster method (NCCM) was invented about thirty years ago to calculate ground-state energies of closed-shell atomic nuclei. Coupled duster (CC) techniques have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within the NCCM. Further extensions deal both with systems at nonzero temperature ar.:l with general dynamical behaviour. More recently, a new version of CC theory, the so-called extended coupled cluster method (ECCM) has been introduced. It has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. CC techniques are now widely recognized as providing one of the most universally applicable, most powerful, and most accurate of all microscopic ab initio methods in quantum many-body theory. The number of successful applications within physics is now impressively large. In most such cases the numerical results are either the best or among the best available. A typical case is the electron gas, where the CC results for the correlation energy agree over the entire metallic density range to within less than 1 millihartree (or < 1%) with the essentially exact Green's function Monte Carlo results. The role of CC theory within modern quantum many-body theory is first surveyed, by a comparison with other techniques. Its full range of applications in physics is then reviewed. These include problems in nuclear physics, both for finite nuclei and infinite nuclear matter; the electron gas; various integrable and nonintegrable models; various relativistic quantum field theories; and quantum spin chain and lattice models. Particular applications of the ECCM include the quantum hydrodynamics o f a zero-temperature, strongly-interacting condensed Bose fluid; a charged impurity in a polarizable medium (e.g., positron annihilation in metals); and various anharmonic oscillator and spin systems.

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Section: Overview Of CC Theory: the Formalismmentioning

confidence: 99%

Section: Other Formal Applications Of the Eccmmentioning

confidence: 99%

An overview of coupled cluster theory and its applications in physics

Bishop

1991

Theoret. Chim. Acta

Self Cite

348

391

View full text Add to dashboard Cite

show abstract

“…Proof of Theorem 1. To eliminate the p P eod pGq we impose the condition for the B operator p P eod pGq " p P eod pe B He ´Bq " 0 , (24) which can explicitly be expanded in terms of multi-commutator expansion using Hausdorff expansion p P eod pHq ´p P eod prH, Bsq `1 2 p P eod prrH, Bs, Bsq ´. .…”

Section: Schrieffer-wolff Rank-reducing Similarity Transformationsmentioning

confidence: 99%

“…The coupled-cluster (CC) theory [1][2][3][4][5][6][7][8][9][10][11] has assumed a preeminent role in providing a high-accuracy description of diversified classes of many-body systems [6,[12][13][14][15][16][17][18], quantum field theory [19][20][21][22][23], quantum hydrodynamics [24,25], nuclear structure theory [26][27][28], quantum chemistry [29][30][31][32][33][34][35][36], and material sciences [37][38][39][40][41][42][43][44][45][46][47]. Many strengths of the singlereference CC formalism (SR-CC) originate in the exponential parametrization of the groundstate wave function and closely related linked cluster theorem…”

Section: Introductionmentioning

confidence: 99%

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Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

Kowalski

Bauman

2022

Applied Sciences

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We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

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Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

Bauman

Kowalski

2022

Mater Theory

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The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.

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Towards a Coupled Cluster Gauge-Field Approach to Quantum Hydrodynamics

Cited by 3 publications

References 9 publications

An overview of coupled cluster theory and its applications in physics

An overview of coupled cluster theory and its applications in physics

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

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