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arXiv:1803.02041 · Physical review. B./Physical review. B

Numerical investigations of SO(4) emergent extended symmetry in spin- 12 Heisenberg antiferromagnetic chains

Pranay Patil, Emanuel Katz, Anders W. Sandvik

Published Jul 10, 2018• 15 citations
arXivHTMLPDF

Abstract

The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, $[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)]/{\mathrm{Z}}_{2}$, in the infrared limit whose physical interpretation is that the spin and dimer order parameters form the components of a common four-dimensional pseudovector. Here we numerically investigate this emergent symmetry using quantum Monte Carlo simulations of a modified Heisenberg chain (the $J\text{\ensuremath{-}}Q$ model) in which the logarithmic scaling corrections of the conventional Heisenberg chain can be avoided. We show how the two- and three-point spin and dimer correlation functions approach their forms constrained by conformal field theory as the system size increases and numerically confirm the expected effects of the extended symmetry on various correlation functions. We stress that sometimes the leading power laws of three-point (and higher) correlations are not given simply by the scaling dimensions of the lattice operators involved but can be faster decaying because of exact cancellations of contributions from the fields and currents under conformal symmetry.

DOI
10.1103/physrevb.98.014414

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Correlation functions of dimer operators, the product operators of spins on two adjacent sites, are studied in the spin-12\frac{1}{2}21​ XXZ chain in the critical regime. The amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field through the combined use of bosonization and density-matrix renormalization-group methods. In particular, for the antiferromagnetic Heisenberg model with SU(2) symmetry, logarithmic corrections to the dimer correlations due to the marginally irrelevant operator are studied, and the asymptotic form of the dimer correlation function is obtained. The asymptotic form of the spin-Peierls excitation gap including logarithmic corrections is also derived.
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