Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g., quark with fractional electric charge). A condensed-matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of N\'eel configurations carrying spin- $\frac{1}{2}$ . Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin- $\frac{1}{2}$ ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of ${}^{87}$ Rb.Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g., quark with fractional electric charge). A condensed-matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of N\'eel configurations carrying spin-$\frac{1}{2}$. Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin-$\frac{1}{2}$ ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of ${}^{87}$Rb.

arXiv:1111.0275Physical Review BFeb 2, 201211 citations

Relativistic quantum mechanics with trapped ions

Lucas Lamata, Jorge Casanova, R. Gerritsma +3 more

We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.

arXiv:1106.6222New Journal of PhysicsSep 6, 201179 citations

Confinement in the Bulk, Deconfinement on the Wall: Infrared Equivalence between Compactified QCD and Quantum Magnets

Tin Sulejmanpašić, Hui Shao, Anders W. Sandvik +1 more

In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-Abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-Abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.

arXiv:1608.09011Physical Review LettersSep 1, 201771 citations

The Weyl representation in classical and quantum mechanics

Alfredo M. Ozorio de Almeida

Physics ReportsMar 1, 1998212 citations

\frac{1}{2}

. Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin-

\frac{1}{2}

ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of

{}^{87}

Rb.