We investigate the quantum phase transition from antiferromagnetism ( $AF$ ) to algebraic spin liquid ( $ASL$ ). {\it We propose that spin 1/2 fermionic spinons in the $ASL$ fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point ( $QCP$ ) between the $AF$ and the $ASL$ }. Condensation of the bosonic spinons leads to the $AF$ , where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the $AF$ . {\it Approaching the $QCP$ from the $AF$ , spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the $QCP$ . This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the $ASL$ is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the $ASL$ .We investigate the quantum phase transition from antiferromagnetism ($AF$) to algebraic spin liquid ($ASL$). {\it We propose that spin 1/2 fermionic spinons in the $ASL$ fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point ($QCP$) between the $AF$ and the $ASL$}. Condensation of the bosonic spinons leads to the $AF$, where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the $AF$. {\it Approaching the $QCP$ from the $AF$, spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the $QCP$. This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the $ASL$ is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the $ASL$.

arXiv:cond-mat/0504541Apr 21, 20050 citations

Quantum Electrodynamics Without Potentials

S. Mandelstam

WORLD SCIENTIFIC eBooksAug 1, 20172 citations

Quantum electrodynamics without potentials

Mathematical Physics

Annals of PhysicsApr 1, 19629 citations

Anyons: a possible mechanism for binding charged particles

D. Schmeltzer, A. R. Bishop

The hard core boson gas in (2+1)-dimensions in the presence of a Chern-Simons term is considered, we find that the long wave description is given in terms of Coulomb (longitudinal) and transversal electrodynamics. The longitudinal part is described in terms of electric charges which carry vorticity. When binding of electrical charges occurs the transversal part is described by a photon field and corresponds to a superfluid. Using the same language we find that a spinless fermion is described by a massive photon. We use these concepts to understand the relation between the negative-U Hubbard model in the presence of a magnetic field, and vortices which carry electric charge induced by doping in the repulsive Hubbard model.The hard core boson gas in (2+1)-dimensions in the presence of a Chern-Simons term is considered, we find that the long wave description is given in terms of Coulomb (longitudinal) and transversal electrodynamics. The longitudinal part is described in terms of electric charges which carry vorticity. When binding of electrical charges occurs the transversal part is described by a photon field and corresponds to a superfluid. Using the same language we find that a spinless fermion is described by a massive photon. We use these concepts to understand the relation between the negative-U Hubbard model in the presence of a magnetic field, and vortices which carry electric charge induced by doping in the repulsive Hubbard model.

International Journal of Modern Physics BJun 1, 19912 citations

Quantum information with single fermions: teleportation and fermion-boson entanglement conversion

O. Morgenshtern, Benni Reznik, I. Zalzberg

While single boson entanglement is known to be equivalent to standard non-identical particle entanglement, the use of fermionic entanglement is constrained by a parity superselection rule. Nevertheless we show that within the framework of second quantization, where local modes play the role of qubits, the analogy with ordinary entanglement holds: two entangled spinless fermion modes can be used to teleport a single local fermion mode and to perform standard dense coding. Entanglement concentration and dilution are possible for fermions. We clarify the meaning of our results by discussing the connection with quantum reference frames and conversion between spinless fermion entanglement and spinless boson entanglement.While single boson entanglement is known to be equivalent to standard non-identical particle entanglement, the use of fermionic entanglement is constrained by a parity superselection rule. Nevertheless we show that within the framework of second quantization, where local modes play the role of qubits, the analogy with ordinary entanglement holds: two entangled spinless fermion modes can be used to teleport a single local fermion mode and to perform standard dense coding. Entanglement concentration and dilution are possible for fermions. We clarify the meaning of our results by discussing the connection with quantum reference frames and conversion between spinless fermion entanglement and spinless boson entanglement.

arXiv:0807.0850Jul 5, 20081 citation

THE NEW QUANTUM ELECTRODYNAMICS

George William Series

WORLD SCIENTIFIC eBooksJun 1, 19880 citations

We investigate the quantum phase transition from antiferromagnetism (

AF

) to algebraic spin liquid (

ASL

). {\it We propose that spin 1/2 fermionic spinons in the

ASL

fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point (

QCP

) between the

AF

and the

ASL

}. Condensation of the bosonic spinons leads to the

AF

, where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the

AF

. {\it Approaching the

QCP

from the

AF

, spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the

QCP

. This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the

ASL

is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the

ASL