Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

Abstract

The S = 1/2 and S = 1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S = 1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchaincoupling, case.

Quantum phases and phase transitions of Mott insulators

“…The spin correlation length will diverge at the quantum critical point with the exponent [34] ν = 0.7048 (30). The spin gap of the paramagnet, ∆, vanishes as ∆ ∼ (λ c − λ) zν , and this prediction is in excellent agreement with the numerical study of the dimerized antiferromagnet [28].…”

“…The very distinct symmetry signatures of the ground states and excitations between λ ≈ 1 and λ ≈ 0 make it clear that the two limits cannot be continuously connected. It is known that there is an intermediate secondorder phase transition at [25,28] λ = λ c = 0.52337(3) between these states as shown in Fig 4. Both the spin gap ∆ and the Néel order parameter N 0 vanish continuously as λ c is approached from either side.…”

Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

“…Still, since the conventional method of using r = 1 in Eqs. (4) and (5) has successfully led to correct determination of some critical exponents for anisotropic systems 10,15,25 , it might be desirable to reexamine these studies to some extent.…”

“…Although for anisotropic systems and for the observables ρ si L with i ∈ {1, 2}, one can argue theoretically that the unconventional method we use is the correct approach for performing finite-size scaling, still, we can arrive at a correct value for ν from ρ s2 2L using the conventional method. Further, since the conventional method has successfully led to correct determination of some critical exponents for anisotropic systems 10,15,25 , it will be desirable to examine the results obtained from these two methods in a more detailed manner. This paper is organized as follows.…”

“…Specifically, the spin-1/2 Heisenberg model on the square lattice is the appropriate model for understanding the undoped precursors of high T c cuprates (undoped antiferromagnets). Second, because of the availability of efficient Monte Carlo algorithms as well as the increased power of computing resources, properties of undoped antiferromagnets on geometrically non-frustrated lattices can be simulated with unprecedented accuracy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . As a consequence, these models are particular suitable for examining theoretical predictions and exploring ideas.…”