Vladislav Popkov (Author), Xin Zhang (Author), Andreas Klümper (Author)

Abstract

We demonstrate the existence of a special chiral “phantom” mode with some analogy to a Goldstone mode in the anisotropic quantum XXZ Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum $k_0$. The mode exists not due to symmetry principles, but results from nontrivial scattering properties of magnons with momentum $k_0$ given by the anisotropy via $\cos{k_0}=\Delta$. Different occupations of the phantom mode lead to energetical degeneracies between different magnetization sectors in the periodic case. This mode originates from special string-type solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots (PBRs). We derive criteria under which the spectrum contains eigenstates with PBRs, both in open and periodically closed integrable systems, for spin-1/2 and higher spins, and discuss the respective chiral eigenstates. The simplest of such eigenstates, the spin helix state, which is a periodically modulated state of chiral nature, is built up from the phantom excitations exclusively. Implications of our results for experiments are discussed.

Keywords

kvantna mehanika;quantum mechanics;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 530.145
COBISS: 94433027 Link will open in a new window
ISSN: 2469-9950
Views: 110
Downloads: 40
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Other data

Secondary language: Slovenian
Secondary keywords: kvantna mehanika;
Pages: str. L081410-1-L081410-6
Volume: ǂVol. ǂ104
Issue: ǂiss. ǂ8
Chronology: 2021
DOI: 10.1103/PhysRevB.104.L081410
ID: 14316034