We investigate the quantum phase transition in an $S=1/2$ dimerized Heisenberg antiferromagnet in three spatial dimensions. By performing large-scale quantum Monte Carlo simulations and detailed finite-size scaling analyses, we obtain high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the antiferromagnetically ordered N\'eel phase. This transition breaks $\text{O}(N)$ symmetry with $N=3$ in $D=3+1$ dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization ${m}_{s}$ and the N\'eel temperature ${T}_{N}$ . We present a scaling ansatz for ${T}_{N}$ , including logarithmic corrections, which agrees with our data and indicates exact linearity with ${m}_{s}$ , implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted $N$ -independent leading and subleading logarithmic corrections in the size dependence of the staggered magnetic susceptibility. These logarithmic scaling forms have not previously been identified or verified by unbiased numerical methods, and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as ${\mathrm{TlCuCl}}_{3}$ .We investigate the quantum phase transition in an $S=1/2$ dimerized Heisenberg antiferromagnet in three spatial dimensions. By performing large-scale quantum Monte Carlo simulations and detailed finite-size scaling analyses, we obtain high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the antiferromagnetically ordered N\'eel phase. This transition breaks $\text{O}(N)$ symmetry with $N=3$ in $D=3+1$ dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization ${m}_{s}$ and the N\'eel temperature ${T}_{N}$. We present a scaling ansatz for ${T}_{N}$, including logarithmic corrections, which agrees with our data and indicates exact linearity with ${m}_{s}$, implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted $N$-independent leading and subleading logarithmic corrections in the size dependence of the staggered magnetic susceptibility. These logarithmic scaling forms have not previously been identified or verified by unbiased numerical methods, and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as ${\mathrm{TlCuCl}}_{3}$.

arXiv:1506.06073Physical Review BDec 2, 201529 citations

Cubic interactions and quantum criticality in dimerized antiferromagnets

Lars Fritz, R. L. Doretto, Stefan Weßel +3 more

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

arXiv:1101.3784Physical Review BMay 6, 201141 citations

Cubic Interactions and Quantum Criticality in Dimerized Antiferromagnets

Stefan Weßel, Lars Fritz, R. L. Doretto +3 more

Bulletin of the American Physical SocietyFeb 29, 20120 citations

We investigate the quantum phase transition in an

S=1/2

dimerized Heisenberg antiferromagnet in three spatial dimensions. By performing large-scale quantum Monte Carlo simulations and detailed finite-size scaling analyses, we obtain high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the antiferromagnetically ordered N\'eel phase. This transition breaks

\text{O}(N)

symmetry with

N=3

D=3+1

dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization

{m}_{s}

and the N\'eel temperature

{T}_{N}

. We present a scaling ansatz for

{T}_{N}

, including logarithmic corrections, which agrees with our data and indicates exact linearity with

{m}_{s}

, implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted

N

-independent leading and subleading logarithmic corrections in the size dependence of the staggered magnetic susceptibility. These logarithmic scaling forms have not previously been identified or verified by unbiased numerical methods, and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as

{\mathrm{TlCuCl}}_{3}