Dynamics of local symmetry correlators for interacting many-particle systems

Schmelcher, Peter; Krönke, Sven; Diakonos, F. K.

doi:10.1063/1.4974096

Cited by 7 publications

(4 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also think that our results further underline the important role played by symmetries in molecular theories of the one-body reduced density matrix 64,[75][76][77] . All our findings can be rewritten in linear response theory, such that the computational burden can be further relieved.…”

Section: Discussionsupporting

confidence: 67%

See 1 more Smart Citation

On the time evolution of fermionic occupation numbers

Benavides-Riveros

Marques

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

We derive an equation for the time evolution of the natural occupation numbers for fermionic systems with more than two electrons. The evolution of such numbers is connected with the symmetry-adapted generalized Pauli exclusion principle, as well as with the evolution of the natural orbitals and a set of many-body relative phases. We then relate the evolution of these phases to a geometrical and a dynamical term, attached to each one of the Slater determinants appearing in the configuration-interaction expansion of the wave function. arXiv:1902.08794v2 [quant-ph]

show abstract

Section: Discussionsupporting

confidence: 67%

“…The missed diagonal terms ϕ k |φ k can be removed as convenient phase factors 64 (see below). The equations of motion of ξ and f can be derived from the stationary condition of the time-dependent quantum mechanical action…”

Section: A Formula For the Time Evolution Of The Fermionic Occupmentioning

confidence: 99%

On the time evolution of fermionic occupation numbers

Benavides-Riveros

Marques

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Furthermore, recently it has been shown that these currents are obtained, as a special case, from a more general continuity equation involv-ing currents constructed from wave fields satisfying two different wave equations [10]. Even more, as shown in [10][11][12] such currents can be defined for arbitrary spatial dimensions d and number of degrees of freedom N . The only significant change for d > 1 is that these generalized currents are not spatially constant any more but they possess a vanishing divergence.…”

Section: Introductionmentioning

confidence: 99%

Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering

Metaxas,

Schmelcher,

Diakonos

2020

Preprint

View full text Add to dashboard Cite

We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic scattering conditions do not respect the symmetries of the potential and there is no systematic way to predetermine their imprint on the scattered wave field. Here we show that symmetry induced, non-local, divergence-free currents can be a useful tool for the description of the consequences of symmetries on higher dimensional wave scattering, focusing on the two-dimensional case.The condition of a vanishing divergence of these non-local currents, being in one-to-one correspondence with the presence of a symmetry in the scattering potential, provides a systematic pathway to to take account if the symmetries in the scattering solution. It leads to a description of the scattering process which is valid in the entire space including the near field regime. Furthermore, we argue that the usual asymptotic representation of the scattering wave function does not account for insufficient account for a proper description of the underlying potential symmetries. Within our approach we derive symmetry induced conditions for the coefficients in the wave field expansion with respect to the angular momentum basis in two dimensions, which determine the transition probabilities between different angular momentum states.

show abstract

“…on the invariance of a subset of matrix elements under a site permutation. In general, local symmetries of the underlying Hamiltonian are indirectly encoded into its eigenstates, as has been demonstrated recently in various contexts [30][31][32][33][34][35][36][37][38]. However, not every locally symmetric system features CLSs, and a systematic framework linking a theory of local symmetries to the formation and control of both CLSs and the resulting flat bands is still missing.…”

Section: Introductionmentioning

confidence: 99%

Compact localized states and flat bands from local symmetry partitioning

2018

Self Cite

View full text Add to dashboard Cite

Journal reference: Phys. Rev. B 97, 035161 (2018) We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one-and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

show abstract

Dynamics of local symmetry correlators for interacting many-particle systems

Cited by 7 publications

References 38 publications

On the time evolution of fermionic occupation numbers

On the time evolution of fermionic occupation numbers

Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering

Compact localized states and flat bands from local symmetry partitioning

Contact Info

Product

Resources

About