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arXiv:2004.06012 · Journal of Experimental and Theoretical Physics

Quantum Critical Dynamics and Scaling in One-Dimensional Antiferromagnets

A. Zheludev

Published Jul 1, 2020• 6 citations
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Abstract

Abstract 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 antiferromagnetic 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.

DOI
10.1134/s1063776120070183

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Abstract 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 antiferromagnetic 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.
Inelastic neutron scattering is used to study the finite-temperature scaling behavior of the local dynamic structure factor in the quasi-one-dimensional quantum antiferromagnet $\text{Ni}[N,{N}^{\ensuremath{'}}\ensuremath{-}\text{bis}(\text{3-aminopropyl})\text{propane-1,3-diamine}](\ensuremath{\mu}\text{\ensuremath{-}}{\mathrm{NO}}_{2}){\mathrm{ClO}}_{4}$ (NTENP), at its field-induced Ising quantum critical point. The validity and the limitations of the theoretically predicted scaling relations are tested.
"Critical point phenomena in magnetic systems are studied with the aid of the scaling laws. These laws relate the critical indices which describe the behavior of thermodynamic and correlation functions near T. Kadanoff's derivation of the scaling 1aw is reviewed. An experimental survey of ferromagnetic and antiferromagnetic data near T is presented. Susceptibility, correlation length, magnectization, specific heat and a magnetic equation of state are discussed. It is found that the ""critical region"" can extend as far as [equation] although frequently it is restricted to E < 10-2 The critical indices S, y, v, ~ and ~, are close to the three dimensional ISing model values. Values for 0, y' and ~ are not known as conclusively. Specific heat behavior is discussed in terms -~ of a three-parameter fit, namely C = aE + b. Varying b allows one to estimate a possible range of a's. The experimental information is consistent with the scaling law relations 2 - alpha = 2 - alpha' = dV = d gamma / (2-pi) = gamma + 2B = B(d+1) The scaling law theory is extended to predict the temperature, field and spatial dependence of various spin correlation functions. These predictions are checked by analytic calculations for the two dimensional Ising model in zero field. Results are presented for the energy density-energy density and energy density-spin correlation functions in the limit E « 1, R » 1, but the product ER arbitrary. Results are also presented for a group of two, three and four spin correlations at cT. In each case the scaling law predictions are verified."
The Widom-Kadanoff scaling laws are generalized to dynamic phenomena, by making assumptions on the structure of time-dependent correlation functions near Tc{T}_{c}Tc​. The theory is applied to isotropic Heisenberg antiferromagnet and predictions are made, which can be tested by inelastic neutron-scattering and nmr measurements. The ferromagnet is also briefly discussed.
New universality classes in two-dimensional critical phenomena have recently been discovered using methods of quantum field theory and conformal invariance. These can equally well describe classical two-dimensional systems at their critical temperature or one-dimensional gapless quantum systems at (or near) zero temperature. (The two types of systems are related by the transfer matrix or Feynman path integral.) It is argued that isotropic one-dimensional antiferromagnets are realizations of these new universality classes. Exact predictions for the low temperature specific heat, susceptibility, correlation length, and other critical properties are made. These agree exactly with exactly solveable models and well with experimental results on CuCl2⋅2(NC5H5).
In this paper, we will critically discuss recent theoretical and experimental developments on the transport of one dimensional quantum systems. In particular, we will focus on open issues and controversial results related to the finite temperature dynamics of integrable quantum models. These singular systems are commonly used in the description of quasi-one dimensional materials. They have recently attracted a lot of interest in connection to the interpretation of experiments, specially after the discovery of unusual thermal conductivity in magnetic compounds.
In this paper, we will critically discuss recent theoretical and experimental developments on the transport of one dimensional quantum systems. In particular, we will focus on open issues and controversial results related to the finite temperature dynamics of integrable quantum models. These singular systems are commonly used in the description of quasi-one dimensional materials. They have recently attracted a lot of interest in connection to the interpretation of experiments, specially after the discovery of unusual thermal conductivity in magnetic compounds.