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Register a new userQuantum critical dynamics and scaling in one-dimensional antiferromagnets
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Authors
Andrey Zheludev
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For a number of quantum critical points in one dimension quantum field theory has provided exact results for the scaling of spatial and temporal correlation functions. Experimental realizations of these models can be found in certain quasi one dimensional antiferromagnetc materials. Measuring the predicted scaling laws experimentally presents formidable technical challenges. In many cases it only became possible recently, thanks to qualitative progress in the development of inelastic neutron scattering techniques and to the discovery of new model compounds. Here we review some of the recent experimental studies of this type.
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By means of nuclear spin-lattice relaxation rate 1/T1, we follow the spin dynamics as a function of the applied magnetic field in two gapped one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladder system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapples Tomonaga-Luttinger-liquid state. In between, 1/T1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for 1/T1, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum critical behavior.
We study the Neel-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 non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is an irrelevant field in the staggered model that is not present in the columnar case, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is $omega_2 approx 1.25$ and the prefactor of the correction $L^{-omega_2}$ is large and comes with a different sign from that of the formally leading conventional correction with exponent $omega_1 approx 0.78$. Our study highlights the possibility of competing scaling corrections at quantum critical points.
Of great recent interest in condensed matter physics are phenomena of coexistence of quantum and classical properties in the same material. Such duality occurs in certain mixed-spin antiferromagnets composed of quantum spin chains interacting through ``auxiliary magnetic ions. In this category are linear-chain rare earth nickelates that exhibit a seemingly paradoxical co-existence of long-range magnetic order and one-dimensional gapped quantum spin excitations at low temperatures. In the present paper we propose a unified physical description of these compounds, supported by recent neutron diffraction and inelastic scattering studies. Our basic concept is the effective separation between low-frequency classical and high-frequency quantum spin correlations. This interpretation enables experimental measurements of some previously inaccessible fundamental properties of quantum spin chains, and predicts new exotic magnetic excitations and mechanisms of long-range ordering in complex quantum magnets.
We use a quantum Monte Carlo method to calculate the Neel temperature T_N of weakly coupled S=1/2 Heisenberg antiferromagnetic layers consisting of coupled ladders. This system can be tuned to different two-dimensional scaling regimes for T > T_N. In a single-layer mean-field theory, chi_s^{2D}(T_N)=(z_2J)^{-1}, where chi_s^{2D} is the exact staggered susceptibility of an isolated layer, J the inter-layer coupling, and z_2=2 the layer coordination number. With a renormalized z_2, we find that this relationship applies not only in the renormalized-classical regime, as shown previously, but also in the quantum-critical regime and part of the quantum-disordered regime. The renormalization is nearly constant; k_2 ~ 0.65-0.70. We also study other universal scaling functions.
We re-examine the experimental results for the magnetic response function $chi({bf q}, E, T)$, for ${bf q}$ around the anti-ferromagnetic vectors ${bf Q}$, in the quantum-critical region, obtained by inelastic neutron scattering, on an Fe-based superconductor, and on a heavy Fermion compound. The motivation is to compare the results with a recent theory, which shows that the fluctuations in a generic anti-ferromagnetic model for itinerant fermions map to those in the universality class of the dissipative quantum-XY model. The quantum-critical fluctuations in this model, in a range of parameters, are given by the correlations of spatial and of temporal topological defects. The theory predicts a $chi({bf q}, E, T)$ (i) which is a separable function of $({bf q -Q})$ and of ($E$,$T$), (ii) at crticality, the energy dependent part is $propto tanh (E/2T)$ below a cut-off energy, (iii) the correlation time departs from its infinite value at criticality on the disordered side by an essential singularity, and (iv) the correlation length depends logarithmically on the correlation time, so that the dynamical critical exponent $z$ is $infty$ . The limited existing experimental results are found to be consistent with the first two unusual predictions from which the linear dependence of the resistivity on T and the $T ln T$ dependence of the entropy also follow. More experiments are suggested, especially to test the theory of variations on the correlation time and length on the departure from criticality.
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