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

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

At the Moment

Mark A. Fischetti

Scientific AmericanDec 1, 20030 citations

A novel identicication scheme for post-quantum secure digital right management

Sedat Akleylek, Meryem Soysaldı

With the progress of technology and widespread use of internet, the data has become digital. It is getting easier day by day to copy, modify and transform digital data / applications into another form. The term of digital rights management (DRM) has been suggested to limit the use of data in digital media and to protect copyrights. Different architectures / technologies are used to provide DRM. In existing architectures, the user is unaware whether the license, which was purchased, is used by an unauthorized party. In this paper, a structure is given to resolve this problem and fairness property is added for DRM architectures. Moreover, a post-quantum reliable identification protocol based on multivariate quadratic systems, which can be used for access control in DRM architecture, is proposed.With the progress of technology and widespread use of internet, the data has become digital. It is getting easier day by day to copy, modify and transform digital data / applications into another form. The term of digital rights management (DRM) has been suggested to limit the use of data in digital media and to protect copyrights. Different architectures / technologies are used to provide DRM. In existing architectures, the user is unaware whether the license, which was purchased, is used by an unauthorized party. In this paper, a structure is given to resolve this problem and fairness property is added for DRM architectures. Moreover, a post-quantum reliable identification protocol based on multivariate quadratic systems, which can be used for access control in DRM architecture, is proposed.

Oct 1, 20171 citation

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.