Quantum signature of exciton condensation

Safaei, Shiva; Mazziotti, David A.

doi:10.1103/physrevb.98.045122

Cited by 38 publications

(38 citation statements)

References 60 publications

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“…The 2-RDM method exploits the pairwise nature of the electron-electron interaction in the electronic Hamiltonian. Variational calculation of the 2-RDM has been applied to the accurate computation of a range of strongly correlated phenomena including polyradical character in conjugated polyaromatic hydrocarbons [19], non-innocent ligand effects in transition-metal complexes [37,38], entanglement-driven non-superexchange mechanisms in bridged transition- * damazz@uchicago.edu metal dimers [39,40], and exciton condensation in molecular-scale electron double layers [41,42].…”

Section: Introductionmentioning

confidence: 99%

Dual-cone variational calculation of the two-electron reduced density matrix

Mazziotti

2020

Phys. Rev. A

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The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher N -representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. We apply the method to computing the energies and properties of strongly correlated electrons-including atomic charges, electron densities, dipole moments, and orbital occupations-in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

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Section: Introductionmentioning

confidence: 99%

Dual-cone variational calculation of the two-electron reduced density matrix

Mazziotti

2020

Phys. Rev. A

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“…On a classical computer necessary N -representability conditions allow us to compute a lower bound on the groundstate energy and an approximate 2-RDM without computation or storage of the N -electron wave function [21,[23][24][25][26][27][28][29][30][31][32][33][34]. The variational calculation of the 2-RDM subject to approx- * damazz@uchicago.edu imate N -representability conditions can capture strong electron correlation in molecular systems at a computational cost that scales polynomially with the number N of electrons [35][36][37][38][39][40]. While a perfect quantum computer would be able to operate with the variational principle of the wave function, near-term quantum computers operate with substantial noise that disrupts the N -representability of the measured 2-RDM.…”

Section: Introductionmentioning

confidence: 99%

Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition

Smart

Mazziotti

2019

Phys. Rev. A

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Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that compute the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by N-representability conditions, conditions for representing an N-electron wave function, that mitigates noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of "chemical accuracy," even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.

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“…Introduction: Ample experimental and theoretical investigation has centered around the condensation of fermion pairs [1][2][3][4] and excitons [5][6][7][8][9][10][11]. Fermion pair condensates-the most familiar of which include the class of Bardeen-Cooper-Schrieffer (BCS) superconductors [1]-occur when particle-particle pairs condense into a single quantum state to create a superfluid.…”

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confidence: 99%

“…1). To this end, we use the theoretical signatures of fermion pair condensation-independently discovered by Yang [24] and Sasaki [25]-and exciton condensation-derived by Garrod and Rosina [8,26]-to explore the fermion pair and exciton character of few-particle systems. Furthermore, we prove that a large class of fermion-exciton condensate wavefunctions can be constructed by entangling any fermion-pair condensate wavefunction with any exciton-condensate wavefunction, from which we establish the dual condensate's existence in the large-N thermodynamic limit.…”

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Potential coexistence of exciton and fermion-pair condensations

2020

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Extensive theoretical and experimental investigation has been conducted on fermion pair condensation and exciton condensation as distinct classes of Bose-Einstein-like condensation. In this work, the existence of a fermion-exciton condensate-a single quantum state in which character of both fermion pair and exciton condensates coexist-is established computationally in the low-particlenumber (N ) limit and theoretically in the large-N thermodynamic limit. The trade-off between the fermion pair and excitonic character of the fermion-exciton condensate is shown to be elliptic in nature. The possibility that the properties of fermion-exciton condensates could be a hybrid of the properties of fermion pair condensates and exciton condensates is discussed, and future experimental and computational exploration of this new class of condensate, which may potentially be realizable in a bilayer of superconductors, is anticipated.

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Quantum signature of exciton condensation

Cited by 38 publications

References 60 publications

Dual-cone variational calculation of the two-electron reduced density matrix

Dual-cone variational calculation of the two-electron reduced density matrix

Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition

Potential coexistence of exciton and fermion-pair condensations

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