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Journal Club for Condensed Matter Physics

RVB, spin liquids, and topological order

Published Nov 30, 2012• 0 citations
Publisher

Abstract

1. Resonating Valence Bond States in the PEPS Formalism. Authors: Norbert Schuch, Didier Poilblanc, J. Ignacio Cirac, and David Perez-Garcia. Phys. Rev. B 86, 115108 (2012). Recommeded and a Commentary by David DiVincenzo, RWTH Aachen | View Commentary (pdf) | DOI: 10.36471/JCCM_November_2012_02 https://doi.org/10.36471/JCCM_November_2012_02

DOI
10.36471/jccm_november_2012_02

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  1. Resonating Valence Bond States in the PEPS Formalism. Authors: Norbert Schuch, Didier Poilblanc, J. Ignacio Cirac, and David Perez-Garcia. Phys. Rev. B 86, 115108 (2012). Recommeded and a Commentary by David DiVincenzo, RWTH Aachen | View Commentary (pdf) | DOI: 10.36471/JCCM_November_2012_02 https://doi.org/10.36471/JCCM_November_2012_02
In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.
Very soon after the discovery of the high-Tc cuprate superconductors Anderson proposed the key to understanding their highly unusual properties lay in the ansatz that they were hole doped spin liquids in which the spins are bound in singlet pairs resonating between different configurations. This RVB concept is generally formulated for a doped Mott insulator, i.e. for a system with a strong onsite Coulomb interaction. It is instructive to explore the approach from weak Coulomb interaction to see if similar behavior can also occur case. Quasi-one dimensional systems in the form of finite width ladders do indeed show such behavior with a continuous crossover from weak to strong interaction limits. In two dimensions functional renormalization group methods have recently been developed to treat weak to moderately strong interactions. These show that similar behavior can occur in the case that the Fermi energy lies near the logarithmically divergent van Hove singularity in the density of states when the band is nearly half-filled. These methods are limited to a description of the flow to strong coupling as the energy or temperature scale is lowered. The form of the strong coupling phase can be explored by numerical techniques. However a proper theory of this phase is lacking and even a consistent phenomenological description has not yet been achieved.