A spin- $\frac{1}{2}$ two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.A spin-$\frac{1}{2}$ two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

arXiv:0806.4416Physical Review BMar 12, 200926 citations

On the connection between spin and statistics

Annals of PhysicsSep 1, 19611 citation

Testing the validity of Bose-Einstein statistics in molecules

Pablo Cancio Pastor, Iacopo Galli, Giovanni Giusfredi +2 more

The search for small violations of the validity of the symmetrization postulate and of the spin-statistics connection (SSC) has been addressed in the last four decades by experimental tests performed in different physical systems of identical fermions or bosons. In parallel and consequently, theories extending the quantum mechanics to a more general level have been proposed to explain such possible violations. In this paper, we present the most stringent test to a possible violation of the SSC under permutation of the bosonic $^{16}\mathrm{O}$ nuclei in the $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ molecule. An upper limit of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ for an SSC-anomalous ${\mathrm{CO}}_{2}$ molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden $({00}^{0}1\ensuremath{-}{00}^{0}0) R$(25) rovibrational transition of $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ at a $4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ wavelength. Quantum mechanics implications of this result are discussed in the frame of the $q$ -mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.The search for small violations of the validity of the symmetrization postulate and of the spin-statistics connection (SSC) has been addressed in the last four decades by experimental tests performed in different physical systems of identical fermions or bosons. In parallel and consequently, theories extending the quantum mechanics to a more general level have been proposed to explain such possible violations. In this paper, we present the most stringent test to a possible violation of the SSC under permutation of the bosonic $^{16}\mathrm{O}$ nuclei in the $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ molecule. An upper limit of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ for an SSC-anomalous ${\mathrm{CO}}_{2}$ molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden $({00}^{0}1\ensuremath{-}{00}^{0}0) R$(25) rovibrational transition of $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ at a $4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ wavelength. Quantum mechanics implications of this result are discussed in the frame of the $q$-mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.

Physical Review ADec 11, 201519 citations

On the connection between spin and statistics

Gianfausto Dell’Antonio

Annals of PhysicsNov 1, 196127 citations

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring

Adeline Orieux, Joelle Boutari, Marco Barbieri +2 more

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

arXiv:1312.1102Scientific ReportsNov 24, 201410 citations

A spin-

\frac{1}{2}

two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

^{16}\mathrm{O}

nuclei in the

^{12}\mathrm{C}^{16}\mathrm{O}_{2}

molecule. An upper limit of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ for an SSC-anomalous

{\mathrm{CO}}_{2}

molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden $({00}^{0}1\ensuremath{-}{00}^{0}0) R$(25) rovibrational transition of

^{12}\mathrm{C}^{16}\mathrm{O}_{2}

at a $4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ wavelength. Quantum mechanics implications of this result are discussed in the frame of the

q

-mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.