Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains

Abstract

We demonstrate the existence of special phantom excitations for open and periodically closed integrable systems at the example of the $XXZ$ Heisenberg spin chain. The phantom excitations do not contribute to the energy of the Bethe state and correspond to special solutions to the Bethe Ansatz equations with infinite "phantom" Bethe roots. The phantom Bethe roots lead to degeneracies between different magnetization sectors in the periodic case and to the appearance of spin helix states (SHS), i.e. periodically modulated states of chiral nature in both open and closed systems. For the periodic chain, phantom Bethe root (PBR) solutions appear for anisotropies $\De=\coshη$ with $\exp (\eta )$ being a root of unity, thus restricting the phenomenon to the critical region $|\De|<1$. For the open chain, PBR solutions appear for any value of anisotropy, both in the critical and in the non-critical region, provided that the boundary fields satisfy a criterion which we derive in this paper. There exist PBR solutions with all Bethe roots being phantom, and PBR solutions that consist of phantom roots as well as regular (finite) roots. Implications of our results for an experiment are discussed.

arXiv comment6 pages, 1 Figure, the version accepted by Letters to PRB

References in corpus (23)

• How Algebraic Bethe Ansatz works for integrable model
• Finite-temperature transport in one-dimensional quantum lattice models
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Families of quasi-local conservation laws and quantum spin transport
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Matrix product solutions of boundary driven quantum chains
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Bethe's equation is incomplete for the XXZ model at roots of unity
• Constructing Integrable Lindblad Superoperators
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Yang-Baxter integrable Lindblad equations
• Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Exact nonequilibrium steady state of open XXZ/XYZ spin-1/2 chain with Dirichlet boundary conditions
• Solution of the Lindblad equation for spin helix states
• The sl_2 loop algebra symmetry of the six-vertex model at roots of unity
• Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Completeness of the Bethe ansatz for the six and eight-vertex models
• On the Spectrum of the XXZ-chain at roots of unity

Cited by in corpus (24)

• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Hydrodynamic relaxation of spin helices
• Quantum spin helices more stable than the ground state: onset of helical protection
• Boundary driven $XYZ$ chain: Exact inhomogeneous triangular matrix product ansatz
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Spin dynamics dominated by superexchange via virtual molecules
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Chiral basis for qubits and spin-helix decay
• Invariant subspaces and explicit Bethe vectors in the integrable open spin $1/2$ $\XYZ$ chain
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• All product eigenstates in Heisenberg models from a graphical construction
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Rational Q-systems at Root of Unity I. Closed Chains
• Quantum scar affecting the motion of three interacting particles in a circular trap
• Dissipative cooling towards phantom Bethe states in boundary driven XXZ spin chain
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation