Solving one-body ensemble N-representability problems with spin

• URL: http://arxiv.org/abs/2412.01805v1
• Date: Mon, 02 Dec 2024 18:50:01 GMT
• Title: Solving one-body ensemble N-representability problems with spin
• Authors: Julia Liebert, Federico Castillo, Jean-Philippe Labbé, Tomasz Maciazek, Christian Schilling,
• Abstract summary: We show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.
• Score: 1.0485739694839669
• License:
• Abstract: The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies $n_i$ of orbitals $\varphi_i$ according to $0 \leq n_i \leq 2$. In this work, we first refine the underlying one-body $N$-representability problem by taking into account simultaneously spin symmetries and a potential degree of mixedness $\boldsymbol w$ of the $N$-electron quantum state. We then derive a comprehensive solution to this problem by using basic tools from representation theory, convex analysis and discrete geometry. Specifically, we show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers, defining a convex polytope $\Sigma_{N,S}(\boldsymbol w) \subset [0,2]^d$. These constraints are independent of $M$ and the number $d$ of orbitals, while their dependence on $N, S$ is linear, and we can thus calculate them for arbitrary system sizes and spin quantum numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.

Related papers

• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality [0.0]
  We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. We compute the critical exponents $z$, $beta$, $gamma$ and $nu$, and the central charge $c$. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates.
  arXiv  Detail & Related papers  (2023-07-20T18:00:05Z)
• 1-matrix functional for long-range interaction energy of two hydrogen atoms [0.0]
  Minimization of the resulting explicit functional yields the large-$R$s for the occupation numbers of the weakly occupied NOs. The radial components of the $p$-type "half-space" orbitals and the corresponding occupation numbers (that decay like $R-6$) are available for the first time thanks to the development of the present formalism.
  arXiv  Detail & Related papers  (2023-03-11T12:30:01Z)
• Near-optimal fitting of ellipsoids to random points [68.12685213894112]
  A basic problem of fitting an ellipsoid to random points has connections to low-rank matrix decompositions, independent component analysis, and principal component analysis. We resolve this conjecture up to logarithmic factors by constructing a fitting ellipsoid for some $n = Omega(, d2/mathrmpolylog(d),)$. Our proof demonstrates feasibility of the least squares construction of Saunderson et al. using a convenient decomposition of a certain non-standard random matrix.
  arXiv  Detail & Related papers  (2022-08-19T18:00:34Z)
• Spectral properties of sample covariance matrices arising from random matrices with independent non identically distributed columns [50.053491972003656]
  It was previously shown that the functionals $texttr(AR(z))$, for $R(z) = (frac1nXXT- zI_p)-1$ and $Ain mathcal M_p$ deterministic, have a standard deviation of order $O(|A|_* / sqrt n)$. Here, we show that $|mathbb E[R(z)] - tilde R(z)|_F
  arXiv  Detail & Related papers  (2021-09-06T14:21:43Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• An effective solution to convex $1$-body $N$-representability [0.0]
  We study the generalization of the $1$-body $N$-representability problem to ensemble states with fixed spectrum $mathbfw$. We adapt and further develop tools such as symmetric polytopes, sweep polytopes, and Gale order.
  arXiv  Detail & Related papers  (2021-05-13T17:56:14Z)
• Universal scattering with general dispersion relations [0.15749416770494704]
  We show that when there are no bright zero-energy eigenstates, the $S$-matrix evaluated at an energy $Eto 0$ converges to a universal limit. We extend these results to general integer dimensions $D geq 1$, dispersion relations $epsilon(boldsymbolk) = |boldsymbolk|a$ for a $D$-dimensional momentum vector.
  arXiv  Detail & Related papers  (2021-03-17T18:00:03Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Emergent universality in critical quantum spin chains: entanglement Virasoro algebra [1.9336815376402714]
  Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. We show that the Schmidt vectors $|v_alpharangle$ display an emergent universal structure, corresponding to a realization of the Virasoro algebra of a boundary CFT.
  arXiv  Detail & Related papers  (2020-09-23T21:22:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.