In this work, we perform a combination of analytical and numerical studies on the phase diagram of the spin-1/2 Kitaev-Heisenberg chain in the region of negative Kitaev and positive Heisenberg couplings. Apart from the antiferromagnetic phase, we find a magnetically ordered phase with left-left-right-right order and a gapless phase with central charge value $c=1$ , resolving the existing contradictory results in literature regarding this parameter region. In particular, the origin of the left-left-right-right order is clarified based on a perturbative Luttinger liquid analysis. The left-left-right-right phase is further shown to persist in the Kitaev-Heisenberg-Gamma model when a small nonzero Gamma interaction is introduced. Using a coupled-chain method, we also demonstrate that the one-dimensional (1D) left-left-right-right order gives a quasi-1D explanation for the 2D stripy order of the same model on the honeycomb lattice.In this work, we perform a combination of analytical and numerical studies on the phase diagram of the spin-1/2 Kitaev-Heisenberg chain in the region of negative Kitaev and positive Heisenberg couplings. Apart from the antiferromagnetic phase, we find a magnetically ordered phase with left-left-right-right order and a gapless phase with central charge value $c=1$, resolving the existing contradictory results in literature regarding this parameter region. In particular, the origin of the left-left-right-right order is clarified based on a perturbative Luttinger liquid analysis. The left-left-right-right phase is further shown to persist in the Kitaev-Heisenberg-Gamma model when a small nonzero Gamma interaction is introduced. Using a coupled-chain method, we also demonstrate that the one-dimensional (1D) left-left-right-right order gives a quasi-1D explanation for the 2D stripy order of the same model on the honeycomb lattice.

arXiv:2408.07968Physical review. B./Physical review. BJun 25, 20255 citations

Q uanta

The SciencesJul 8, 19920 citations

Can Nothing Cause Nonlocal Quantum Jumps?

Alexander Afriat

A paradox is discussed in which a photon can occupy one of two positions, ‘left’ or ‘right.’ Quantum mechanics allows the two possibilities—‘nothing left, photon right’ and ‘photon left, nothing right’—to be combined in a (coherent) superposition; or alternatively in an (incoherent) mixture, with similar terms, but no phase relation between them. As the phase relation is statistically significant, and can in principle be revealed experimentally, the two superposed possibilities must both be present in nature, together, for they somehow ‘communicate’ with one another through that relation. The eigenvalue +1 can be assigned to the presence of the photon on the right, −1 to its absence, to construct a measurable physical quantity, ‘photon‐right.’ Its expectation vanishes for the aforementioned superposition. If we look for the photon on the left and do not find it, it must be on the right. The superposition accordingly collapses to the term ‘nothing left, photon right,’ whose expectation for photon‐right jumps from zero to one right away. Only with a mixture could one ascribe the initial (vanishing) expectation to an ignorance which is then overcome once the photon is not found on the left. The issue is: what exactly happens on the left to cause the ontic (and not merely epistemic) jump on the right? Is it some mental event? Or is it nothing at all?A paradox is discussed in which a photon can occupy one of two positions, ‘left’ or ‘right.’ Quantum mechanics allows the two possibilities—‘nothing left, photon right’ and ‘photon left, nothing right’—to be combined in a (coherent) superposition; or alternatively in an (incoherent) mixture, with similar terms, but no phase relation between them. As the phase relation is statistically significant, and can in principle be revealed experimentally, the two superposed possibilities must both be present in nature, together, for they somehow ‘communicate’ with one another through that relation. The eigenvalue +1 can be assigned to the presence of the photon on the right, −1 to its absence, to construct a measurable physical quantity, ‘photon‐right.’ Its expectation vanishes for the aforementioned superposition. If we look for the photon on the left and do not find it, it must be on the right. The superposition accordingly collapses to the term ‘nothing left, photon right,’ whose expectation for photon‐right jumps from zero to one right away. Only with a mixture could one ascribe the initial (vanishing) expectation to an ignorance which is then overcome once the photon is not found on the left. The issue is: what exactly happens on the left to cause the ontic (and not merely epistemic) jump on the right? Is it some mental event? Or is it nothing at all?

AIP conference proceedingsJan 1, 20061 citation

Right here, right now

David Cohen

The New ScientistJan 1, 20050 citations

c=1

, resolving the existing contradictory results in literature regarding this parameter region. In particular, the origin of the left-left-right-right order is clarified based on a perturbative Luttinger liquid analysis. The left-left-right-right phase is further shown to persist in the Kitaev-Heisenberg-Gamma model when a small nonzero Gamma interaction is introduced. Using a coupled-chain method, we also demonstrate that the one-dimensional (1D) left-left-right-right order gives a quasi-1D explanation for the 2D stripy order of the same model on the honeycomb lattice.