Coherent-State Representation of Many-Fermion Quantum Mechanics

Rowe, D.J.; Ryman, A.

doi:10.1103/physrevlett.45.406

Cited by 20 publications

(6 citation statements)

References 9 publications

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“…L E C Rosales-Zárate and P D Drummond normalization by the determinant given in equation (28). Hence the integral over the variables λ is ∞ −∞ dλ 2 (λ 2 )P (1)…”

Section: Evaluation Of Integralsmentioning

confidence: 98%

“…These are obtained as the action of a representation of a Lie group on an extremal state. This definition is related to the dynamical structure of the corresponding creation and annihilation operators, using U (N) Lie group methods [7][8][9]18,[26][27][28][29][30] . In this approach, an integral over the coherent state projectors appears, but it does not generate an identity operator for all fermion states, due to number conservation.…”

Section: Introductionmentioning

confidence: 99%

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Resolution of unity for fermionic Gaussian operators

Rosales-Zárate¹,

Drummond²

2013

J. Phys. A: Math. Theor.

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The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory.We prove that a resolution of unity exists for any even distribution of eigenvalues over hermitian fermionic Gaussian operators in the nonstandard symmetry classes. This has some important consequences. It demonstrates a useful technique for constructing fundamental mathematical identities in an exponentially complex Hilbert space. It also shows that, to obtain nontrivial results for random matrix canonical ensembles in the nonstandard symmetry classes, it is necessary to consider ensembles that are not even functions of the eigenvalues. We show that the same restriction does not apply to the standard Wigner-Dyson symmetry classes of random matrices.

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“…L E C Rosales-Zárate and P D Drummond normalization by the determinant given in equation (28). Hence the integral over the variables λ is ∞ −∞ dλ 2 (λ 2 )P (1)…”

Section: Evaluation Of Integralsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Resolution of unity for fermionic Gaussian operators

Rosales-Zárate¹,

Drummond²

2013

J. Phys. A: Math. Theor.

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“…It has the useful property of being the set of all independent-particle states. The classical Hamiltonian on this manifold is then defined by the expectation values of the quantum mechanical Hamiltonian in its coherent states and the classical Hamiltonian equations of motion, defined by time-dependent HF theory, are identical to the corresponding equations of motion of constrained quantum mechanics as shown in references [44][45][46] and reviewed in chapter 6 of [47]. Thus, a classical equilibrium state on this manifold is a state for which the expectation value of the quantum mechanical Hamiltonian is a (local) minimum.…”

Section: A Classical Mean-field Perspectivementioning

confidence: 99%

Nuclear shape coexistence from the perspective of an algebraic many-nucleon version of the Bohr-Mottelson unified model

Rowe

2019

Preprint

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A fully quantal algebraic version of the Bohr-Mottelson unified model is presented with the important property that its quantisation is defined by its irreducible unitary representations which span the many-nucleon Hilbert space of every nucleus. The model is uniquely defined by the requirement that its Lie algebra of observables includes the nuclear quadrupole moments and kinetic energy. It then follows that there can be no non-zero isoscalar E2 transitions between any states belonging to its different irreducible representations and, as a result, the states of the model are uniquely defined with the property that observed transitions between rotational states of nuclei are to be expressed in terms of mixtures of the model irreps. The algebraic version of the unified model parallels the Bohr-Mottelson model in most respects, including the possibility of including the effects of Coriolis and centrifugal forces as subsequent perturbations. However, it corrects its treatment of angular momentum quantisation and no longer uses an over-complete set of coordinates. These changes have significant implications for the dynamics of nuclear rotations which are hidden when its moments of inertia are considered as inertial masses in the standard expression of rotational kinetic energies. Thus, the developments put a new perspective on the phenomenon of shape coexistence.

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“…It is convenient to introduce fermionic creation and annihilation operatorsf † i , f j , (1 ≤ i, j ≤ N ), which obey standard anticommutation rules {f † i , f j } = δ ij . It is well known that the family of Slater determinants provides an over-complete basis in F(M, N ), which behaves in many ways as the family of coherent states for a bosonic system 2,[11][12][13][14] . The Slater determinants for M fermions are defined, up to a global phase, by the M -dimensional subspace in C N spanned by the occupied single particle states.…”

Section: B Gr(m N) Coherent Statesmentioning

confidence: 99%

Zero point fluctuations for magnetic spirals and Skyrmions, and the fate of the Casimir energy in the continuum limit

2018

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We study the role of zero-point quantum fluctuations in a range of magnetic states which on the classical level are close to spin-aligned ferromagnets. These include Skyrmion textures characterized by nonzero topological charge, and topologically-trivial spirals arising from the competition of the Heisenberg and Dzyaloshinskii-Moriya interactions. For the former, we extend our previous results on quantum exactness of classical Bogomolny-Prasad-Sommerfield (BPS) ground-state degeneracies to the general case of Kähler manifolds, with a specific example of Grassmann manifolds Gr(M, N). These are relevant to quantum Hall ferromagnets with N internal states and integer filling factor M. A promising candidate for their experimental implementation is monolayer graphene with N = 4 corresponding to spin and valley degrees of freedom at the charge neutrality point with M = 2 filled Landau levels. We find that the vanishing of the zero-point fluctuations in taking the continuum limit occurs differently in the case of BPS states compared to the case of more general smooth textures, with the latter exhibiting more pronounced lattice effects. This motivates us to consider the vanishing of zero-point fluctuations in such near-ferromagnets more generally. We present a family of lattice spin models for which the vanishing of zero-point fluctuations is evident, and show that some spirals can be thought of as having nonzero but weak zero-point fluctuations on account of their closeness to this family. Between them, these instances provide concrete illustrations of how the Casimir energy, dependent on the full UV-structure of the theory, evolves as the continuum limit is taken. 1 2 .

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Coherent-State Representation of Many-Fermion Quantum Mechanics

Cited by 20 publications

References 9 publications

Resolution of unity for fermionic Gaussian operators

Resolution of unity for fermionic Gaussian operators

Nuclear shape coexistence from the perspective of an algebraic many-nucleon version of the Bohr-Mottelson unified model

Zero point fluctuations for magnetic spirals and Skyrmions, and the fate of the Casimir energy in the continuum limit

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