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arXiv:1702.05903 · Physical review. B./Physical review. B

Quantum criticality of spinons

Feng He, Yuzhu Jiang, Yi-Cong Yu, H. Q. Lin, Xi‐Wen Guan

Published Dec 7, 2017• 23 citations
arXivHTMLPDF

Abstract

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 ${R}_{W}=4{K}_{s}$ remains almost temperature independent, where ${K}_{s}$ 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 $\mathrm{Cu}(\mathrm{C}{}_{4}\mathrm{H}{}_{4}\mathrm{N}{}_{2})(\mathrm{NO}{}_{3}){}_{2}$, 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.

DOI
10.1103/physrevb.96.220401

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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 ground state of a one-dimensional spin-12 uniform antiferromagnetic Heisenberg chain (AfHc) is a Tomonaga–Luttinger liquid which is quantum-critical with respect to applied magnetic fields up to a saturation field μ0Hs beyond which it transforms to a fully polarized state. Wilson ratio has been predicted to be a good indicator for demarcating these phases [Phys. Rev. B 96, 220401 (2017)]. From detailed temperature and magnetic field-dependent magnetization, magnetic susceptibility and specific heat measurements in a metalorganic complex and comparisons with field theory and quantum transfer matrix method calculations, the complex was found to be a very good realization of a spin-12 AfHc. Wilson ratio obtained from experimentally obtained magnetic susceptibility and magnetic contribution of specific heat values was used to map the magnetic phase diagram of the uniform spin-12 AfHc over large regions of phase space demarcating Tomonaga–Luttinger liquid, saturation field quantum critical, and fully polarized states. Luttinger parameter and spinon velocity were found to match very well with the values predicted from conformal field theory.
Up to now, probing the quantum phase transition (QPT) and quantum critical (QC) phenomena at finite temperatures in one-dimensional (1D) spin systems still lacks an in-depth understanding. Herein, we study the QPT and thermodynamics of 1D spin-1/2 anisotropic Heisenberg antiferromagnetic chains by Green’s function theory. The quantum phase diagram is renormalized by the anisotropy (∆), which manifests a quantum critical point (QCP) hc = 1 + ∆ signaling the transition from gapless Tomonaga–Luttinger liquid (TLL) to gapped ferromagnetic (FM) state, demonstrated by the magnetic entropy and thermal Drude weight. At low temperatures, it is shown that two crossover temperatures fan out a QC regime and capture the QCP via the linear extrapolation to zero temperature. In addition, around QCP, the QC scaling is performed by analyzing the entropy and thermal Drude weight to extract the critical exponents (α, δ, and β) that fulfill the Essamm–Fisher scaling law, which provides a novel thermodynamic means to detect QPT for experiment. Furthermore, scaling hypothesis equations with two rescaled manners are proposed to testify the scaling analysis, for which all the data points fall on a universal curve or two independent branches for the plot against rescaled field or temperature, implying the self-consistency and reliability of the obtained critical exponents.
Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics, and criticality of one-dimensional (1D) spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high-precision equation of state from which the Tomonaga-Luttinger-liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent z=2z=2z=2 and correlation length exponent $\ensuremath{\nu}=1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger-liquid description.
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.
By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system (C5H12N)2CuBr4({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}(C5​H12​N)2​CuBr4​. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.
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.