Multipoint correlation functions: spectral representation and numerical evaluation

• URL: http://arxiv.org/abs/2101.00707v2
• Date: Wed, 13 Oct 2021 19:02:44 GMT
• Title: Multipoint correlation functions: spectral representation and numerical evaluation
• Authors: Fabian B. Kugler and Seung-Sup B. Lee and Jan von Delft
• Abstract summary: We derivation generalized spectral representations for multipoint correlation functions that apply to many-body frameworks. Our approach separates spectral from time-ordering properties and thereby elucidates the relation between the three formalisms. Using a numerical renormalization group (NRG) method, we present numerical results for selected quantum impurity models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlation functions. Here, we complete this picture by deriving generalized spectral representations for multipoint correlation functions that apply in all of the commonly used many-body frameworks: the imaginary-frequency Matsubara and the real-frequency zero-temperature and Keldysh formalisms. Our approach separates spectral from time-ordering properties and thereby elucidates the relation between the three formalisms. The spectral representations of multipoint correlation functions consist of partial spectral functions and convolution kernels. The former are formalism independent but system specific; the latter are system independent but formalism specific. Using a numerical renormalization group (NRG) method described in the accompanying paper, we present numerical results for selected quantum impurity models. We focus on the four-point vertex (effective interaction) obtained for the single-impurity Anderson model and for the dynamical mean-field theory (DMFT) solution of the one-band Hubbard model. In the Matsubara formalism, we analyze the evolution of the vertex down to very low temperatures and describe the crossover from strongly interacting particles to weakly interacting quasiparticles. In the Keldysh formalism, we first benchmark our results at weak and infinitely strong interaction and then reveal the rich real-frequency structure of the DMFT vertex in the coexistence regime of a metallic and insulating solution.

Related papers

• Modeling Non-Covalent Interatomic Interactions on a Photonic Quantum Computer [50.24983453990065]
  We show that the cQDO model lends itself naturally to simulation on a photonic quantum computer. We calculate the binding energy curve of diatomic systems by leveraging Xanadu's Strawberry Fields photonics library. Remarkably, we find that two coupled bosonic QDOs exhibit a stable bond.
  arXiv  Detail & Related papers  (2023-06-14T14:44:12Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Dilute neutron star matter from neural-network quantum states [58.720142291102135]
  Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
  arXiv  Detail & Related papers  (2022-12-08T17:55:25Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Multipartite correlations in quantum collision models [0.0]
  A challenge in the standard collision model is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Here we develop a tensor network formalism to address both challenges. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory- kernel master equation.
  arXiv  Detail & Related papers  (2022-04-05T17:06:27Z)
• Computing local multipoint correlators using the numerical renormalization group [0.0]
  We develop a numerical renormalization group (NRG) approach to compute local three- and four-point correlators of quantum impurity models. Our method can treat temperatures and frequencies -- imaginary or real -- of all magnitudes, from large to arbitrarily small ones.
  arXiv  Detail & Related papers  (2021-01-03T21:35:56Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Recent advances in the calculation of dynamical correlation functions [0.0]
  Time-dependent correlation functions play a central role in both the theoretical and experimental understanding of dynamic properties. The method of recurrence relation has, at its foundation, the solution of Heisenberg equation of motion of an operator in a many-body interacting system. In this work, we discuss the most relevant applications of the method of recurrence relations and numerical calculations based on exact diagonalizations.
  arXiv  Detail & Related papers  (2020-05-28T18:33:22Z)
• Exact spectral function of a Tonks-Girardeau gas in a lattice [0.0]
  We calculate the exact spectral function of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime. We show that the spectral function displays a power-law behaviour close to the Lieb-I and Lieb-II singularities. In particular, the Lieb-II mode shows a divergence in the spectral function, differently from what happens in the dynamical structure factor.
  arXiv  Detail & Related papers  (2020-05-27T20:50:37Z)
• Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath [0.0]
  This work addresses quantum adiabatic decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system-environment interaction Hamiltonian that represents a partition of non-interacting subsystems.
  arXiv  Detail & Related papers  (2019-12-30T16:39:38Z)

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.