Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions

• URL: http://arxiv.org/abs/2303.10491v2
• Date: Tue, 18 Jul 2023 11:43:08 GMT
• Title: Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions
• Authors: Saidakhmat N. Lakaev, Alexander K. Motovilov, Saidakbar Kh. Abdukhakimov
• Abstract summary: We study the Schroedinger operators H_lambdamu(K), with K in T, the fixed quasi-momentum of the particles pair. We establish a sharp lower bound for the number of isolated eigenvalues of H_lambdamu(K) in each connected component.
• Score: 68.8204255655161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the Schroedinger operators H_{\lambda\mu}(K), with K \in T_2 the fixed quasi-momentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice Z_2 with first and second nearest-neighboring-site interactions of magnitudes \lambda \in R and \mu \in R, respectively. We establish a partition of the (\lambda,\mu)-plane so that in each its connected component, the Schroedinger operator H_{\lambda\mu}(0) has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential spectrum and above its top. Moreover, we establish a sharp lower bound for the number of isolated eigenvalues of H_{\lambda\mu}(K) in each connected component.

Related papers

• On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions [0.0]
  We study the ground-state entanglement Hamiltonian of free nonrelativistic fermions for semi-infinite domains in one dimension. We prove that the Bisognano-Wichmann form of the entanglement Hamiltonian becomes exact.
  arXiv  Detail & Related papers  (2024-10-21T18:55:23Z)
• A two-boson lattice Hamiltonian with interactions up to next-neighboring sites [0.0]
  A partition of the $(gamma,lambda,mu)$-space into connected components is established. For each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schr"odinger operator.
  arXiv  Detail & Related papers  (2024-10-09T17:15:21Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Contact interactions, self-adjoint extensions, and low-energy scattering [0.0]
  We show that the one-dimensional scattering problem is surprisingly intricate. We show that the families of self-adjoint extensions correspond to a coupled system of symmetric and antisymmetric outgoing waves. As an application, the spectrum of a general point interaction with a harmonic trap is solved in one dimension.
  arXiv  Detail & Related papers  (2024-03-22T15:39:56Z)
• Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator [8.84834042985207]
  We propose a fermionic extension of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump.
  arXiv  Detail & Related papers  (2024-01-30T17:20:34Z)
• Energetical self-organization of a few strongly interacting particles [0.0]
  We study the quantum self-organization of a few interacting particles with strong short-range interactions. The energy of the system is determined by the number of bonds between particles that lie on adjacent sites.
  arXiv  Detail & Related papers  (2022-03-25T12:23:51Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension [68.8204255655161]
  We study two-component atomic gas mixtures in one dimension involving both bosons and fermions. We report a rich variety of coherent ground-state phases that vary with the intrinsic and relative strength of the interactions.
  arXiv  Detail & Related papers  (2021-10-26T17:52:37Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)

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.