arXiv:hep-lat/9907008 · Lectures given at

Quantum Spin-1/2 Antiferromagnetic Chains and Strongly Coupled Multiflavor Schwinger Models

F. Berruto, G. Grignani, Gordon Walter Semenoff, Pasquale Sodano

Published Jul 16, 1999• 0 citations

Abstract

We review the correspondence between strongly coupled lattice multiflavor Schwinger models and SU(N) antiferromagnetic chains. We show that finding the low lying states of the gauge models is equivalent to solving an SU(N) Heisenberg antiferromagnetic chain. For the two-flavor lattice Schwinger model the massless excitations correspond to gapless states of the Heisenberg chain, while the massive states are created by fermion transport in the ground state of the spin chain. Our analysis shows explicitly how spinons may arise in lattice gauge theories.

DOI: 10.48550/arxiv.hep-lat/9907008

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arXiv:hep-lat/9907008 · Lectures given at

Quantum Spin-1/2 Antiferromagnetic Chains and Strongly Coupled Multiflavor Schwinger Models

F. Berruto, G. Grignani, Gordon Walter Semenoff, Pasquale Sodano

Published Jul 16, 1999• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.hep-lat/9907008

Related papers

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An antiferromagnetic

S=\frac{1}{2}

Heisenberg chain is mapped to the two-flavor massless Schwinger model at $\ensuremath{\theta}=\ensuremath{\pi}.$ The electromagnetic coupling constant and velocity of light in the Schwinger model are determined in terms of the Heisenberg coupling and lattice spacing in the spin chain system.

{\mathit{J}}_{1}

) and next-nearest (

{\mathit{J}}_{2}

) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio

{\mathit{J}}_{2}

{\mathit{J}}_{1}

for the so-called s-RVB ansatz (s-RVB stands for short range resonating valence bond). A second-order phase transition exists in a flux state for

{\mathit{J}}_{2}

{\mathit{J}}_{1}

larger than the critical value (

{\mathit{J}}_{2/}

{\mathit{J}}_{1}

{)}_{\mathrm{cr}}

identify the range 0

{\mathit{J}}_{2}

{\mathit{J}}_{1}

(

{\mathit{J}}_{2}

{\mathit{J}}_{1}

{)}_{\mathrm{cr}}

as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one-dimensional quantum antiferromagnet within the same approach. We show that in the one-dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.

A class of

\mathrm{SU}(n)

antiferromagnetic quantum "spin" chains is solved in the large-

n

limit. While the low-lying spectrum of the normal spin chain (

n=2

) consists of massless solitons, in the large-

n

limit the soliton is massive. Furthermore, the models exhibit many features of the

C{P}^{n}

field theories at nonzero topological charge, which, it was recently argued, they become in the limit of a large representation.

Motivated by recent numerical and experimental studies of the spin-

1/2

Heisenberg antiferromagnet on the kagome lattice, we formulate a many-body model for fermionic spinons introduced by us earlier [Phys. Rev. Lett. 103, 187203 (2009)]. The spinons interact with an emergent

U(1)

gauge field and experience strong short-range attraction in the

S=0

channel. The ground state of the model is generically a

{Z}_{2}

liquid. We calculate the edge of the two-spinon continuum and compare the theory to the slave-fermion approach to the Heisenberg model.