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Modern Physics Letters B

ON THE GAUGE THEORY OF THE RESONATING VALENCE BOND STATES

G. Baskaran, R. SHANKAR

Published Dec 1, 1988• 9 citations
Publisher

Abstract

In this brief report we review some of the basic concepts involved in the gauge theory approach to the Resonating Valence Bond State of strongly correlated electronic systems. Some general consequences of the local gauge symmetry on the nature of excitations are also discussed.
DOI
10.1142/s0217984988001156

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Quantum dimer models are believed to capture the essential physics of antiferromagnetic phases dominated by short-ranged valence bond configurations. We show that these models arise as particular limits of Ising (Z2){(Z}_{2})(Z2​) gauge theories, but that in these limits the system develops a larger local U(1) invariance that has different consequences on different lattices. Conversely, we note that the standard Z2{Z}_{2}Z2​ gauge theory is a generalized quantum dimer model, in which the particular relaxation of the hardcore constraint for the dimers breaks the U(1) down to Z2.{Z}_{2}.Z2​. These mappings indicate that at least one realization of the Senthil--Fisher proposal for fractionalization is exactly the short ranged resonating valence bond (RVB) scenario of Anderson and of Kivelson, Rokhsar and Sethna. They also suggest that other realizations will require the identification of a local low energy, Ising link variable and a natural constraint. We also discuss the notion of topological order in Z2{Z}_{2}Z2​ gauge theories and its connection to earlier ideas in RVB theory. We note that this notion is not central to the experiment proposed by Senthil and Fisher to detect vortices in the conjectured Z2{Z}_{2}Z2​ gauge field.
Aimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents in the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems. Diverse topics such as general theory of phase transitions, harmonic and anharmonic lattices, Bose condensation and superfluidity, modern aspects of magnetism including resonating valence bonds, electrons in metals, and strong electron correlations are treated using unifying concepts of order and elementary excitations. The main theoretical tools used to treat these problems are introduced and explained in a simple way, and their applications are demonstrated through concrete examples.
We consider a resonating-valence-bond state as a variational estimate for the ground state of a Heisenberg antiferromagnet. We derive an expression for the normalization of this wave function, which is a superposition of a very large number of singlet pair states, which we then use to show that the singularities, correlations, and low-lying excitations of this quantum system can be calculated from the partition function of a related dimerlike classical statistical mechanics problem. Possible calculational schemes are discussed.