Conjectured Bounds for 2-Local Hamiltonians via Token Graphs

• URL: http://arxiv.org/abs/2506.03441v1
• Date: Tue, 03 Jun 2025 22:52:10 GMT
• Title: Conjectured Bounds for 2-Local Hamiltonians via Token Graphs
• Authors: Anuj Apte, Ojas Parekh, James Sud,
• Abstract summary: We show how the maximum energy of the Quantum MaxCut, XY, and EPR Hamiltonians on a graph $G$ are related to the spectral radii of the token graphs of $G$.<n>We conjecture new bounds for these spectral radii based on properties of $G$.<n>Our conjectures also provide simple bounds on the ground state energy of the antiferromagnetic Heisenberg model.
• Score: 0.08192907805418585
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explain how the maximum energy of the Quantum MaxCut, XY, and EPR Hamiltonians on a graph $G$ are related to the spectral radii of the token graphs of $G$. From numerical study, we conjecture new bounds for these spectral radii based on properties of $G$. We show how these conjectures tighten the analysis of existing algorithms, implying state-of-the-art approximation ratios for all three Hamiltonians. Our conjectures also provide simple combinatorial bounds on the ground state energy of the antiferromagnetic Heisenberg model, which we prove for bipartite graphs.

Related papers

• Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians [37.96754147111215]
  We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms.<n>In particular, we certify the ground state energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares.
  arXiv  Detail & Related papers  (2024-10-21T00:10:51Z)
• Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
  We study the Hamiltonian for a three-dimensional Bose gas of $N geq 3$ spinless particles interacting via zero-range (also known as contact) interactions.<n>Such interactions are encoded by (singular) boundary conditions imposed on the coincidence hyperplanes, i.e., when the coordinates of two particles coincide.<n>We construct a class of Hamiltonians characterized by such modified boundary conditions, that are self-adjoint and bounded from below.
  arXiv  Detail & Related papers  (2024-03-19T10:00:12Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Calculating composite-particle spectra in Hamiltonian formalism and demonstration in 2-flavor QED$_{1+1\text{d}}$ [0.0]
  We consider three distinct methods to compute the mass spectrum of gauge theories in the Hamiltonian formalism. We find that the mass of $sigma$ meson is lighter than twice the pion mass, and thus $sigma$ is stable against the decay process. Our numerical results are so close to the WKB-based formula between the pion and sigma-meson masses, $M_sigma/M_pi=sqrt3$.
  arXiv  Detail & Related papers  (2023-07-31T13:38:23Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Improved Product-state Approximation Algorithms for Quantum Local Hamiltonians [0.15229257192293202]
  Ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics. We develop new techniques to find classical, additive error product-state approximations for these quantities on certain families of Quantum $k$-Local Hamiltonians.
  arXiv  Detail & Related papers  (2022-10-17T00:55:35Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• Application of quotient graph theory to three-edge star graphs [0.0]
  We find quotient graphs for the three-edge star quantum graph with Neumann boundary conditions at the loose ends. These quotient graphs are smaller than the original graph and the direct sum of quotient graph Hamiltonians is unitarily equivalent to the original Hamiltonian.
  arXiv  Detail & Related papers  (2021-08-11T14:48:52Z)
• Energy spectrum of massive Dirac particles in gapped graphene with Morse potential [0.0]
  We study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. We investigate the graphene band structure by a linear dispersion relation which creates an energy gap in the Dirac points called gapped graphene.
  arXiv  Detail & Related papers  (2021-04-14T09:26:56Z)
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs [62.997667081978825]
  We study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph.
  arXiv  Detail & Related papers  (2020-03-25T02:46:14Z)

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.