Fundamental Building Blocks of Strongly Correlated Wave Functions

Sunko, D. K.

doi:10.1007/s10948-016-3799-1

Cited by 5 publications

(11 citation statements)

References 22 publications

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“…For large N, this is easier said than done [11], but that issue is outside the scope of this paper. The source shape is the unique shape of highest possible degree [12]. The symmetrized derivatives are iterates of the operator,…”

Section: Algorithmic Construction Of Shapesmentioning

confidence: 99%

“…The observation relevant for this work is that derivatives of polynomials obviously reduce their information content [12]. Therefore, the information content of all pure states is not the same, and some way should be found to quantify it.…”

Section: The Case Of Three Fermionsmentioning

confidence: 99%

“…While the operationalization of this idea requires some technical finesse, it should be kept in mind that there is nothing contrived about the phenomenon which it seeks to quantify. It has been rigorously proven that the polynomial D N is a shape [12], and that all its symmetrized derivatives are shapes [11]. It is an algebraic truism that taking derivatives of a polynomial reduces its information content, all the way down to the zero polynomial.…”

Section: Logical Entropy Applied To Shapes Identification Of Pauli Distinctionsmentioning

confidence: 99%

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Entropy of pure states: not all wave functions are born equal

Sunko

2022

4open

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Many-body Hilbert space has the algebraic structure of a finitely generated free module. All N-body wave functions in d dimensions can be generated by a finite number of N!d − 1 of generators called shapes, with symmetric-function coefficients. Physically the shapes are vacuum states, while the symmetric coefficients are bosonic excitations of these vacua. It is shown here that logical entropy can be used to distinguish fermion shapes by information content, although they are pure states whose usual quantum entropies are zero. The construction is based on the known algebraic structure of fermion shapes. It is presented for the case of N fermions in three dimensions. The background of this result is presented as an introductory review.

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Section: Algorithmic Construction Of Shapesmentioning

confidence: 99%

Section: The Case Of Three Fermionsmentioning

confidence: 99%

Section: Logical Entropy Applied To Shapes Identification Of Pauli Distinctionsmentioning

confidence: 99%

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Entropy of pure states: not all wave functions are born equal

Sunko

2022

4open

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“…It remains to be seen whether they will be practical. At least, there is a chance to manage complexity, because one can imagine 11 truncating the list (18) to limit the calculation to one ideal, or band of excitations. Such an approach is similar in spirit to a fixed-node approximation 24,25 in usual simulations.…”

Section: The Fermion Sign Problemmentioning

confidence: 99%

Fundamental invariants of many-body Hilbert space

Sunko

2016

Mod. Phys. Lett. B

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Many-body Hilbert space is a functional vector space with the natural structure of an algebra, in which vector multiplication is ordinary multiplication of wave functions. This algebra is finite-dimensional, with exactly $N!^{d-1}$ generators for $N$ identical particles, bosons or fermions, in $d$ dimensions. The generators are called shapes. Each shape is a possible many-body vacuum. Shapes are natural generalizations of the ground-state Slater determinant to more than one dimension. Physical states, including the ground state, are superpositions of shapes with symmetric-function coefficients, for both bosons and fermions. These symmetric functions may be interpreted as bosonic excitations of the shapes. The algebraic structure of Hilbert space described here provides qualitative insights into long-standing issues of many-body physics, including the fermion sign problem and the microscopic origin of bands in the spectra of finite systems.Comment: Invited review, author's version as accepted by Modern Physics Letters

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“…Holographic models [44] and strongly correlated electronic wave functions [45] have been discussed for disordered systems without translational invariance. The emergent domain structures at the charge order-to-superfluid transition for 2D hard-core bosons [46] and the nanoscale phase separation in ferroelectric materials [47] have been described by advanced theories.…”

mentioning

confidence: 99%

Lattice, Charge, and Spin Phase Inhomogeneity in Complex-Striped Quantum Matter

Bianconi

Ricci

2016

J Supercond Nov Magn

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Lattice, charge and spin phase inhomogeneity in complex striped quantum matter, preface of the special issue for Superstripes 2016 conference, J .Abstract The Superstripes 2016 conference, held on June 23--29, 2016 in the island of Ischia in Italy celebrated the 20th anniversary of this series of conferences. For 20 years structural, electronic, and magnetic phase inhomogeneities in quantum matter have been the scientific focus for a growing physics community interested in complexity in quantum matter. It has been the meeting point for different scientific communities facing the challenging project to unveil the complex space and time landscapes in quantum matter. The interesting spatial inhomogeneity length scale of multiple coexisting phase ranges from atomic to mesoscopic and the time fluctuations are spread over multiple time scales. The response of these materials changes using different experimental techniques with different spatial and time resolution probing different aspects of the quantum complexity.After the discovery of high temperature superconductivity Alex Müller organized two important workshops [1,2] on phase separation and Jahn-Teller polarons in cuprates superconductors bringing together scientists active in these fields.After ten years of research on the physics of cuprate perovskites, together with Alex Muller, we decided to organize the first conference on "Stripes and high temperature superconductivity" which was held in Rome in December 1996 [3]. We invited the most active research groups reporting evidence for strong magnetic interactions resulting in the formation of spin density wave, SDW, in the form of antiferromagnetic stripes intercalated by charge rich stripes observed by neutron diffraction experiments using neutrons emitted by nuclear reactors [5]. These results showed that doped holes get self organized and segregate in stripes in spite of being uniformly distributed. Clearly these results imply an unconventional strongly correlated metallic phase with breakdown of the rigid band model [6][7][8].A.Bianconi, A. Ricci, Lattice, charge and spin phase inhomogeneity in complex striped quantum matter, preface of the special issue for Superstripes 2016 conference, J ). 2 At the same time other researchers investigated copper perovskites developing the new x-ray spectroscopy methods [8-10] using x-ray emitted by large electron storage rings. XANES (x-ray absorption near edge structure) experiments provided evidence for itinerant doped holes in the oxygen 2p orbital symmetry [9]. The EXAFS (extended xray absorption fine structure) experiments reported the evidence of charge density wave, CDW, [10] with associated periodic lattice distortions or orbital density wave giving the formation of nanoscale lattice stripes and nanoscale inhomogeneity [11] in agreement with PDF analysis of neutron scattering data [12] and transport data [13,14]. These data

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Fundamental Building Blocks of Strongly Correlated Wave Functions

Cited by 5 publications

References 22 publications

Entropy of pure states: not all wave functions are born equal

Entropy of pure states: not all wave functions are born equal

Fundamental invariants of many-body Hilbert space

Lattice, Charge, and Spin Phase Inhomogeneity in Complex-Striped Quantum Matter

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