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arXiv:1806.04913 · Physical review. B./Physical review. B

Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets

Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie, E. Orignac

Published Sep 5, 2018• 19 citations
arXivHTMLPDF

Abstract

At low temperature, critical one-dimensional (1D) quantum systems, such as spin chains, are theoretically described by the Tomonaga-Luttinger liquid (TLL) theory. In realistic quasi-1D materials, however, residual couplings are always present, and these systems eventually escape the theoretical 1D world to get eventually ordered at lower temperature. In order to define a genuine ``1D temperature window'' in quasi-1D systems for dynamical quantities such as the NMR relaxation rate or the dynamical structure factor that is probed by inelastic neutron scattering, the authors present a comprehensive theoretical study based on analytical as well as numerical approaches. They are able to describe the full temperature crossover for weakly coupled chains and, in particular, the universal 1D window where the TLL picture can be experimentally observed.

DOI
10.1103/physrevb.98.094403

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At low temperature, critical one-dimensional (1D) quantum systems, such as spin chains, are theoretically described by the Tomonaga-Luttinger liquid (TLL) theory. In realistic quasi-1D materials, however, residual couplings are always present, and these systems eventually escape the theoretical 1D world to get eventually ordered at lower temperature. In order to define a genuine ``1D temperature window'' in quasi-1D systems for dynamical quantities such as the NMR relaxation rate or the dynamical structure factor that is probed by inelastic neutron scattering, the authors present a comprehensive theoretical study based on analytical as well as numerical approaches. They are able to describe the full temperature crossover for weakly coupled chains and, in particular, the universal 1D window where the TLL picture can be experimentally observed.
Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl2{}_{2}2​-4SC(NH2{}_{2}2​)2{}_{2}2​ (DTN), made of weakly coupled spin S=1S=1S=1 chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below 111 K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate 1/T11/{T}_{1}1/T1​, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely 111D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by 333D long-range order in materials such as DTN.
Recently, it has been shown that spin nematic (quadrupolar) or higher multipolar correlation functions exhibit a quasi-long-range order in the wide region of the field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-12\frac{1}{2}21​ zigzag chains. In this Rapid Communication, we point out that the temperature dependence of the NMR relaxation rate 1/T11/{T}_{1}1/T1​ in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin-12\frac{1}{2}21​ Heisenberg chain); 1/T11/{T}_{1}1/T1​ decreases with lowering temperature in multipolar TLL. We also discuss low-energy features in spin dynamical structure factors which are characteristic of the multipolar TLL phases.
Magnon bound states emerging in one-dimensional (1D) spin chains still lack a rigorous understanding. In this Rapid Communication we show that the length-1 spin strings significantly dominate the critical properties of spinons, magnons, and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution, we analytically calculate the scaling functions of the thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double maxima in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), the quantum critical, and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio RW=4Ks{R}_{W}=4{K}_{s}RW​=4Ks​ remains almost temperature independent, where Ks{K}_{s}Ks​ is the Luttinger parameter. Furthermore, by applying our results, we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C4H4N2)(NO3)2\mathrm{Cu}(\mathrm{C}{}_{4}\mathrm{H}{}_{4}\mathrm{N}{}_{2})(\mathrm{NO}{}_{3}){}_{2}Cu(C4​H4​N2​)(NO3​)2​, recently studied by Kono et al. [Phys. Rev. Lett. 114, 037202 (2015)]. We further find that the magnetization maximum used in experiments is not a good quantity to map out the finite-temperature TLL phase boundary.
Abstract The Tomonaga–Luttinger liquid (TLL) theory describes the low-energy excitations of strongly correlated one-dimensional (1D) fermions. In the past years, a number of studies have provided a detailed understanding of this universality class. More recently, theoretical investigations that go beyond the standard low-temperature, linear-response TLL regime have been developed. While these provide a basis for understanding the dynamics of the spin-incoherent Luttinger liquid, there are few experimental investigations in this regime. Here we report the observation of a thermally induced, spin-incoherent Luttinger liquid in a 6Li atomic Fermi gas confined to 1D. We use Bragg spectroscopy to measure the suppression of spin-charge separation and the decay of correlations as the temperature is increased. Our results probe the crossover between the coherent and incoherent regimes of the Luttinger liquid and elucidate the roles of the charge and the spin degrees of freedom in this regime.
The quantum many-body interactions in one-dimensional spin-12\frac{1}{2}21​ systems are subject to Tomonaga-Luttinger liquid (TLL) physics, which predict an array of multiparticle excitations that form continua in momentum-energy space. Here we use inelastic neutron spectroscopy to study the TLL spin dynamics in SrCo2V2O8{\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrCo2​V2​O8​, a compound which contains weakly coupled spin-12\frac{1}{2}21​ chains of Co atoms, at 0.05 K and in a longitudinal magnetic field up to 9.0 T. The measurements were performed above 3.9 T, where the ground-state N\'eel antiferromagnetic (AFM) order is completely suppressed and the multiparticle excitations are exclusively of the TLL type. In this region and below 7.0 T, the longitudinal TLL mode---psinon/antipsinon (P/AP)---is unexpectedly well described by a damped harmonic oscillator (DHO) while approaching the zone center defining the static spin-spin correlations. A non-DHO-type, continuumlike signal is seen at higher fields, but deviations from the ideal one-dimensional TLL still remain. This change in the P/AP mode coincides with the phase transition between the longitudinal spin density wave (LSDW) and transverse AFM order. Inside the LSDW state, the DHO-type P/AP spectral weight increases and the linewidth broadens as the magnetic order parameter decreases. These results reveal the impact of three-dimensional magnetic order on the TLL spin dynamics; they call for beyond-mean-field treatment for the interchain exchange interactions.
We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The 1/T11/{T}_{1}1/T1​ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter KKK. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the 1/T11/{T}_{1}1/T1​ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.