Majorana fermions solve the tetrahedron equations as well as higher simplex equations

• URL: http://arxiv.org/abs/2410.20328v1
• Date: Sun, 27 Oct 2024 03:58:30 GMT
• Title: Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Authors: Pramod Padmanabhan, Vladimir Korepin,
• Abstract summary: Yang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. We develop a systematic method - constructing higher simplex operators from lower simplex ones.
• Score: 0.0
• License:
• Abstract: Yang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. Finding the solutions of these equations is a formidable task. In this work we develop a systematic method - constructing higher simplex operators [solutions of corresponding simplex equations] from lower simplex ones. We call it lifting. By starting from a solution of Yang-Baxter equations we can construct [lift] a solution of the tetrahedron equation and simplex equation in any dimension. We then generalize this by starting from a solution of any lower simplex equation and lifting it [construct solution] to another simplex equation in higher dimension. This process introduces several constraints among the different lower simplex operators that are lifted to form the higher simplex operators. We show that braided Yang-Baxter operators [solutions of Yang-Baxter equations independent of spectral parameters] constructed using Majorana fermions satisfy these constraints, thus solving the higher simplex equations. As a consequence these solutions help us understand the action of an higher simplex operator on Majorana fermions. Furthermore we show that operators constructed using Dirac (complex) fermions satisfy these constraints as well.

Related papers

• Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN [55.2480439325792]
  We show that every computation problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any problem, both inversion, constraint satisfaction and optimization.
  arXiv  Detail & Related papers  (2025-02-09T18:16:53Z)
• Self-distributive structures, braces & the Yang-Baxter equation [0.0]
  The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. The notion of braces is also presented as the suitable algebraic structure associated to involutive set-theoretic solutions. The quantum algebra as well as the integrability of Baxterized involutive set-theoretic solutions is also discussed.
  arXiv  Detail & Related papers  (2024-09-30T16:40:41Z)
• Unitary tetrahedron quantum gates [3.117417023918577]
  Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems.
  arXiv  Detail & Related papers  (2024-07-15T13:58:33Z)
• MultiSTOP: Solving Functional Equations with Reinforcement Learning [56.073581097785016]
  We develop MultiSTOP, a Reinforcement Learning framework for solving functional equations in physics. This new methodology produces actual numerical solutions instead of bounds on them.
  arXiv  Detail & Related papers  (2024-04-23T10:51:31Z)
• Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras [0.0]
  Yang-Baxter equation, Zamalodchikov's tetrahedron equation and Bazhanov-Stroganov equation are special cases. We describe a universal method to solve these equations using Clifford algebras.
  arXiv  Detail & Related papers  (2024-04-17T15:56:16Z)
• D-CIPHER: Discovery of Closed-form Partial Differential Equations [80.46395274587098]
  We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations. We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
  arXiv  Detail & Related papers  (2022-06-21T17:59:20Z)
• Algebraic Bethe Circuits [58.720142291102135]
  We bring the Algebraic Bethe Ansatz (ABA) into unitary form, for its direct implementation on a quantum computer. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.
  arXiv  Detail & Related papers  (2022-02-09T19:00:21Z)
• Automatic differentiation of Sylvester, Lyapunov, and algebraic Riccati equations [5.584060970507506]
  These equations are used to compute infinite-horizon Gramians, solve optimal control problems in continuous or discrete time, and design observers. We derive the forward and reverse-mode derivatives of the solutions to all three types of equations, and showcase their application on an inverse control problem.
  arXiv  Detail & Related papers  (2020-11-23T14:33:31Z)
• Fourier Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  We formulate a new neural operator by parameterizing the integral kernel directly in Fourier space. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. It is up to three orders of magnitude faster compared to traditional PDE solvers.
  arXiv  Detail & Related papers  (2020-10-18T00:34:21Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)
• Irreversible quantum evolution with quadratic generator: Review [0.0]
  We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and operators. The Gaussian solutions are obtained in terms of equations for the first and the second moments.
  arXiv  Detail & Related papers  (2019-12-30T21:04:18Z)

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.