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arXiv:cond-mat/0402352 · Physical Review Letters

Exotic Versus Conventional Scaling and Universality in a Disordered Bilayer Quantum Heisenberg Antiferromagnet

Rastko Sknepnek, Thomas Vojta, Matthias Vojta C

Published Aug 23, 2004• 45 citations
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Abstract

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.

DOI
10.1103/physrevlett.93.097201

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We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.
Using a numerical implementation of a strong-disorder renormalization group, we study the low-energy, long-distance properties of layers and bilayers of S=1∕2S=1∕2S=1∕2 Heisenberg antiferromagnets with different types of disorder: bond randomness, site dilution, and dimer dilution. Generally the systems exhibit an ordered and a disordered phase separated by a phase boundary on which the static critical exponents appear to be independent of bond randomness in the strong-disorder regime, while the dynamical exponent is a continuous function of the bond disorder strength. The low-energy fixed points of the off-critical phases are affected by the actual form of the disorder, and the disorder-induced dynamical exponent depends on the disorder strength. As the strength of the bond disorder is increased, there is a set of crossovers in the properties of the low-energy singularities. For weak disorder quantum fluctuations play the dominant role. For intermediate disorder nonlocalized disorder fluctuations are relevant, which become localized for even stronger bond disorder. We also present some quantum Monte Carlo simulation results to support the strong-disorder renormalization approach.
We study the Néel-paramagnetic quantum phase transition in two-dimensional dimerized S=1/2 Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long-standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find nonmonotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is a new irrelevant field in the staggered model, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is ω_{2}≈1.25 and the prefactor of the correction L^{-ω_{2}} is large and comes with a different sign from that of the conventional correction with ω_{1}≈0.78. Our study highlights competing scaling corrections at quantum critical points.
We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1∕2S=1∕2S=1∕2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with intraplane and interplane couplings JJJ and ${J}_{\ensuremath{\perp}}$. We discuss the ground-state finite-size scaling properties of three different quantities---the Binder moment ratio, the spin stiffness, and the long-wavelength magnetic susceptibility---which we use to extract the critical value of the coupling ratio $g={J}_{\ensuremath{\perp}}∕J$. The individual estimates of gc{g}_{c}gc​ are consistent provided that subleading finite-size corrections are properly taken into account. For both models, we find that the spin stiffness has the smallest subleading finite-size corrections; in the case of the incomplete bilayer we find that the first subleading correction vanishes or is extremely small. In agreement with predictions, we find that at the critical point the Binder ratio has a universal value and the product of the spin stiffness and the long-wavelength susceptibility scales as 1∕L21∕{L}^{2}1∕L2 with a universal prefactor. Our results for the critical coupling ratios are gc=2.5220(1){g}_{c}=2.5220(1)gc​=2.5220(1) (full bilayer) and gc=1.3888(1){g}_{c}=1.3888(1)gc​=1.3888(1) (incomplete bilayer), which represent improvements of more than an order of magnitude over the previous best estimates. For the correlation length exponent we obtain $\ensuremath{\nu}=0.7106(9)$, consistent with the expected three-dimensional Heisenberg universality class.
We employ the stochastic series expansion quantum Monte Carlo method to investigate the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a N\'eel-ordered phase to a quantum disordered phase, consistent with the O(3)O(3)O(3) universality class. In contrast, random dilution gives rise to a two-step transition: from the N\'eel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence ${\ensuremath{\chi}}_{u}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}}), 0<\ensuremath{\alpha}<1$. At the N\'eel-to-glass transition, the quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.
The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.
The two-dimensional $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\ensuremath{\alpha}={J}^{\ensuremath{'}}/J$. The critical point of the order-disorder quantum phase transition in the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model is determined as ${\ensuremath{\alpha}}_{c}=2.5196(2)$ by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.