Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

Abstract

We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation TN / √ c 3 ∝ Ms near the quantum critical point (QCP) associated with dimerization. Here TN , c, and Ms are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as TN and Ms, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation TN / √ c 3 ∝ Ms near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.Introduction.-While being the simplest models, Heisenberg-type models provide qualitatively, or even quantitatively useful information regarding the properties of cuprate materials. For example, the spatially anisotropic quantum Heisenberg model with different antiferromagnetic couplings in the 1 and 2 directions is demonstrated to be relevant for the underdoped cuprate superconductor YBa 2 Cu 3 O 6.45 [1,2]. Specifically, it is argued that this model provides a possible mechanism for the newly discovered pinning effects of the electronic liquid crystal in YBa 2 Cu 3 O 6.45 [3]. Because of their phenomenological importance, these models continue to attract a lot of attention analytically and numerically. In addition to being relevant to real materials, Heisenbergtype models on geometrically nonfrustrated lattices are important from a theoretical point of view as well. This is because these models can be simulated very efficiently using first principles Monte Carlo methods. Hence they are very useful in exploring ideas and examining theoretical predictions [4][5][6][7][8][9][10][11][12].

Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

“…Due to a logarithmic decay of the renormalized interaction strength upon approaching the critical point, this field theory exhibits logarithmic corrections to a Gaussian fixed point [7][8][9][10]. This leads to characteristic multiplicative logarithmic scaling corrections to the bare mean-field behavior in various physical quantities that are in principle accessible by several experimental probes, such as in thermodynamic measurements or neutron and light scattering techniques [6,[11][12][13][14], if probed at the relevant energy scales near the quantum critical point.A well characterized example system of this scenario is provided by the dimerized spin-half compound TlCuCl 3 : under the application of hydrostatic pressure, this system features a quantum phase transition from a gapped quantum disordered state into an antiferromagnetically ordered phase [15]. The magnetic excitations across the quantum critical region have been analyzed in detail recently by inelastic neutron scattering [16][17][18].…”

“…Due to a logarithmic decay of the renormalized interaction strength upon approaching the critical point, this field theory exhibits logarithmic corrections to a Gaussian fixed point [7][8][9][10]. This leads to characteristic multiplicative logarithmic scaling corrections to the bare mean-field behavior in various physical quantities that are in principle accessible by several experimental probes, such as in thermodynamic measurements or neutron and light scattering techniques [6,[11][12][13][14], if probed at the relevant energy scales near the quantum critical point.…”

Universality in the three-dimensional random bond quantum Heisenberg antiferromagnet

“…To the best of our knowledge, most of the studies -inspired by the experimental observation of TlCuCl 3 under pressure [62][63][64] -have been recently performed on different kinds of 3D quantum antiferromagnetic pure and disordered dimerized lattices and have focused on the estimation of the scaling relations of Néel temperature (T N ) and the staggered magnetization density (M s ) near a quantum critical point [54][55][56][57][58][59][60][61] . Related to this, the first theoretical attempts have been carried out using quantum field theory, and the existence of universal behavior near the quantum critical point has been demonstrated 54,55 .…”

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

“…The former is argued to be relevant to the newly discovered pinning effects of the electronic liquid crystal in the underdoped cuprate superconductor YBa 2 Cu 3 O 6.45 [34,35], and the latter is considered to be the right model for explaining the phase diagram of TlCuCl 3 under pressure [36][37][38][39][40][41]. To conclude, despite their simplicity, the spatially anisotropic Heisenberg models are among the most important and frequently studied systems in condensed matter physics.…”