Quantum-critical dynamics
Is it possible to make quantitative predictions for experiments based on only qualitative information about the material under study? Actually yes, under so-called critical conditions, which are often realized near phase transitions. Very different systems with a few qualitative similarities will at long wavelengths and long time scales show quantitatively identical (universal) behavior. Quantum criticality that occurs in the limit of very low temperatures is particularly interesting, because a single universality class defines not only the static but also the dynamic properties.
Case in point: one dimensional spin systems. Their low-temperature low-energy long-wavelength properties are universal regardless of the details of magnetic interactions. Even better, they are identical to those of interacting impenetrable Bosons, which in one dimension can be mapped to Fermions. For the Fermionic model there are specific analytical predictions for the specific heat, density and correlation functions, the details of interaction potential being irrelevant. These calculations are directly carried over to spin systems and describe the heat capacity, magnetization and inelastic neutron scattering, respectively. We have performed a series of experiments to verify these long-standing theoretical results in real quasi-one-dimensional quantum magnetic materials [1].
[1] A. Zheludev, external pagearXiv:2004.06012 (2020).
Tomonaga-Luttinger spin liquids
![Enlarged view: Scaling of critical temporal spin correlations in the magnetized phase of DIMPY. The solid line is the exact analytiycal result for attractive Fermions result expressed through Euler's Gamma-functions below [3].](/highlights/universal-critical-dynamics/_jcr_content/par/textimage_1937818856/image.imageformat.lightbox.1863087877.png)
One very nice example is our study of partially magnetized spin chains and spin ladders. These are in the same universality class as the so-called Tomonaga-Luttinger liquid, a concept that replaces Landau's Fermi liquid theory in one dimension. Even the humble Heisenberg antiferromagnetic spin chain such as 2(1,4-Dioxane)·2(H2O)·CuCl2 is a Tomonaga-Luttinger spin liquid (TLSL) and maps
into repulsive Fermions [2]. In contrast, a partially magnetized strong-led spin ladder such as realized in the compound DIMPY is equivalent to a TLSL with attraction [3]. For this material we employed inelastic neutron scattering [3] and NMR [4] to study critical dynamics, and calorimetry and magnetometry [4] to probe static critical properties. The results are in a staggeringly good agreement with theory that is applied without any input on the actual spin Hamiltonian.
[2] M. Haelg, D. Hüvonen, N. P. Butch, F. Demmel, A. Zheludev, external pagePhys. Rev. B 92, 104416 (2015).
[3] K. Yu. Povarov, D. Schmidiger, N. Reynolds, A. Zheludev, R. Bewley, external pagePhys. Rev. B 91, 020406(R) (2015)
[4] M. Jeong (정민기), D. Schmidiger, H. Mayaffre, M. Klanjšek, C. Berthier, W. Knafo, G. Ballon, B. Vignolle, S. Krämer, A. Zheludev, and M. Horvatić, external pagePhys. Rev. Lett.117, 106402 (2016).
Scale factor-free universality
![Enlarged view: Top: Excitation spectrum measured in BPCB near the quantum critical point of magnon condensation. Bottom: universal scaling behavior of the transverse low-energy excitations. The solid line is the exact theoretical result for free Fermions [6].](/highlights/universal-critical-dynamics/_jcr_content/par/textimage_1829147129/image.imageformat.lightbox.1685733732.png)
Different and even "more universal" behavior is observed in one-dimensional magnets near field-induced quantum phase transitions known as magnon condensations. The Fermionic correspondence remains valid, but at these transitions the density goes to zero. In one dimension this means that interactions are totally irrelevant and the system is like free Fermions. All thermodynamics and the correlations functions can be calculated exactly. It was actuallly us who were first to actually evaluate the latter numerically [5]. In our first attempt we tried to measure this universal critical dynamics in the spin chain material K2CuSO4Cl2 [5]. We largely failed due to a seemingly unavoidable "contamination" by non-universal excitations. We later came up with a clever trick to avoid this problem by using a spin laddrer, namely the strong-rung ladder compound BPCB [6]. The correlation functions for hard-core Bosons/ Fermions in one dimension were experimentally measured for the first time.
[5] Dominic Blosser, Noam Kestin, Kirill Yu. Povarov, Robert Bewley, Emanuele Coira, Thierry Giamarchi and Andrey Zheludev, external pagePhys Rev B 96, 134406 (2017).
[6] D. Blosser, V. K. Bhartiya, D. J. Voneshen, A. Zheludev, external pagePhys. Rev. Lett. 121, 247201 (2018).