Invariant subspaces and explicit Bethe vectors in the integrable open spin $1/2$ $\XYZ$ chain

• URL: http://arxiv.org/abs/2204.05732v1
• Date: Tue, 12 Apr 2022 11:58:58 GMT
• Title: Invariant subspaces and explicit Bethe vectors in the integrable open spin $1/2$ $\XYZ$ chain
• Authors: Xin Zhang, Andreas Kl\"umper and Vladislav Popkov
• Abstract summary: We derive a criterion under which splitting of eigenstates of an open $XYZ$ Hamiltonian occurs. The splitting is governed by an integer number, which has the geometrical meaning of the maximal number of kinks in the basis states. We also describe an elliptic analogue of the spin-helix state, appearing in both the periodic and the open $XYZ$ model.
• Score: 2.69127499926164
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a criterion under which splitting of all eigenstates of an open $\XYZ$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which has the geometrical meaning of the maximal number of kinks in the basis states. We describe the generic structure of the respective Bethe vectors. We obtain explicit expressions for Bethe vectors, in the absence of Bethe roots, and those generated by one Bethe root, and investigate the \multiplet. We also describe in detail an elliptic analogue of the spin-helix state, appearing in both the periodic and the open $\XYZ$ model, and derive the eigenstate condition. The elliptic analogue of the spin-helix state is characterized by a quasi-periodic modulation of the magnetization profile, governed by Jacobi elliptic functions.

Related papers

• Bethe Ansatz, Quantum Circuits, and the F-basis [40.02298833349518]
  deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-1/2 XXZ model. We show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.
  arXiv  Detail & Related papers  (2024-11-04T19:01:41Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Chiral Virasoro algebra from a single wavefunction [14.735587711294299]
  When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to systematically extract the generators of the Virasoro algebra from a single ground state wavefunction.
  arXiv  Detail & Related papers  (2024-03-27T09:54:21Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering [0.0]
  The steering ellipsoids corresponding to the two-qubit subsystems of permutation symmetric $N$-qubit states is analysed here. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation symmetric $N$-qubit states with two distinct spinors.
  arXiv  Detail & Related papers  (2023-01-01T19:46:21Z)
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations [23.87373187143897]
  We study the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. We take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant.
  arXiv  Detail & Related papers  (2021-10-25T17:37:33Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac12$ chain [2.69127499926164]
  We construct the coordinate Bethe ansatz for all eigenstates of the open spin-$frac12$ XXZ chain. Using several simple cases as examples, we present the core elements of our generalized coordinate Bethe ansatz method.
  arXiv  Detail & Related papers  (2021-07-28T10:59:38Z)
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain [2.69127499926164]
  We investigate solutions to the Bethe Ansatz equations for open integrable $XXZ$ Heisenberg spin chains containing phantom (infinite) Bethe roots. The phantom Bethe roots do not contribute to the energy of the Bethe state, so the energy is determined exclusively by the remaining regular excitations.
  arXiv  Detail & Related papers  (2021-02-05T17:15:27Z)
• Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors [0.0]
  We prove that in order that the description of the spin will be relativistic, it is not enough to preserve the projection lattice equipped with its natural partial order and denoteity. This, in particular, extends a result of Moln'ar to the wider setting of atomic JBW$*$-triples not containing rank-one Cartan factors.
  arXiv  Detail & Related papers  (2021-01-03T17:21:02Z)
• Generalized su(1,1) algebra and the construction of nonlinear coherent states for P\"oschl-Teller potential [0.0]
  We show that a symmetry is present in the sequence of eigenvalues of one generator of the generalized su (1,1) algebra. We then construct the Barut-Girardello coherent states associated with the generalized su (1,1) algebra for a particle in a P"oschl-Teller potential.
  arXiv  Detail & Related papers  (2020-05-22T22:06:26Z)

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.