Application of Wave Functions Containing Interelectron Coordinates. I. The Ground-State Energy of Lithium

Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N-qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H4 is presented.

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The ground state energy of the ±J spin glass from the genetic algorithm

Journal de Physique I ◽

10.1051/jp1:1994112 ◽

1994 ◽

Vol 4 (9) ◽

pp. 1281-1285 ◽

Cited By ~ 15

Author(s):

P. Sutton ◽

D. L. Hunter ◽

N. Jan

Keyword(s):

Genetic Algorithm ◽

Spin Glass ◽

Ground State Energy ◽

Ground State ◽

State Energy

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GROUND-STATE ENERGY OF FRÖHLICH ELECTRON-PHONON SYSTEM

Le Journal de Physique Colloques ◽

10.1051/jphyscol:19816140 ◽

1981 ◽

Vol 42 (C6) ◽

pp. C6-481-C6-483

Author(s):

Chih-Yuan Lu

Keyword(s):

Ground State Energy ◽

Ground State ◽

State Energy

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POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

Modern Physics Letters B ◽

10.1142/s0217984907014012 ◽

2007 ◽

Vol 21 (24) ◽

pp. 1635-1642

Author(s):

MIAN LIU ◽

WENDONG MA ◽

ZIJUN LI

Keyword(s):

Quantum Dot ◽

Electric Field ◽

Field Intensity ◽

Ground State Energy ◽

Ground State ◽

Electric Field Intensity ◽

State Energy ◽

Theoretical Study ◽

The Moment ◽

Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

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Effects of a scattering center on the ground-state energy of quantum-dot lithium

Modern Physics Letters B ◽

10.1142/s0217984917500713 ◽

2017 ◽

Vol 31 (07) ◽

pp. 1750071

Author(s):

Z. D. Vatansever ◽

S. Sakiroglu ◽

I. Sokmen

Keyword(s):

Quantum Dot ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

Electronic Charge ◽

Strongly Correlated ◽

Configuration Interaction Method ◽

Charge Localization ◽

Scattering Center ◽

Spin Properties

In this paper, the effects of a repulsive scattering center on the ground-state energy and spin properties of a three-electron parabolic quantum dot are investigated theoretically by means of configuration interaction method. Phase transition from a weakly correlated regime to a strongly correlated regime is examined from several strengths and positions of Gaussian impurity. Numerical results reveal that the transition from spin-1/2 to spin-3/2 state depends strongly on the location of the impurity which accordingly states the controllability of the spin polarization. Moreover, broken circular symmetry results in more pronounced electronic charge localization.

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Observables in inhomogeneous ground states at large global charge

Journal of High Energy Physics ◽

10.1007/jhep08(2021)079 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Simeon Hellerman ◽

Nozomu Kobayashi ◽

Shunsuke Maeda ◽

Masataka Watanabe

Keyword(s):

Ground State Energy ◽

Ground State ◽

State Energy ◽

Point Function ◽

Ground State Configuration ◽

Charge Densities ◽

Direct Extension ◽

Fixed Set ◽

State Configuration ◽

Large Charge

Abstract As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ1/ρ2, the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ1/ρ2 ≪ 1. We also compute, at fixed set of charges, ρ1, ρ2, the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ1 + ρ2)3/2, as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

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THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

Modern Physics Letters B ◽

10.1142/s0217984905009389 ◽

2005 ◽

Vol 19 (30) ◽

pp. 1793-1802 ◽

Cited By ~ 5

Author(s):

M. MODARRES

Keyword(s):

Angular Momentum ◽

Ground State Energy ◽

Ground State ◽

Correlation Functions ◽

State Energy ◽

Interatomic Potentials ◽

Channel Correlation ◽

P Waves ◽

Effective Interactions ◽

Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

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