Quantum phase transitions of 2-d dimerized spin-1/2 Heisenberg models with spatial anisotropy

Details Quantum phase transitions of 2-d dimerized spin-1/2 Heisenberg models with spatial anisotropy Quantum phase transitions of 2-d dimerized spin-1/2 Heisenberg models with spatial anisotropy

2012-02-06

arxiv.org/abs/1202.1057v1

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages, 18 figures, 8 tables

Scientific paper

Motivated by the unexpected Monte Carlo results as well as the theoretical proposal of a large correction to scaling for the critical theory of the 2-d staggered-dimer spin-1/2 Heisenberg model on the square lattice, we study the phase transitions induced by dimerization of several dimerized quantum Heisenberg models with spatial anisotropy using first principles Monte Carlo method. We focus on investigating the finite-size scaling of the observables $\rho_{s1}2L$ and $\rho_{s2}2L$ since such strategy might reveal the subtlety of determining the corresponding critical theory. Here, $\rho_{si}$ with $i \in {1,2}$ and $L$ refer to the spin stiffness in the $i$ direction and the spatial box size used in the simulations, respectively. Remarkably, while the Monte Carlo data we obtain for all the models considered here, including the herringbone- and ladder-dimer models on the square lattice, seem to be compatible with the recently proposed scenario of an enhanced correction to scaling, our data are in consistence with the established numerical values for the critical exponents in the O(3) universality class as well. To explain the results presented in this study, a more detailed numerical study, and possibly a better theoretical understanding, for the critical theories of the models investigated here is required.

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