Quantum criticality of spinons

Abstract

The free fermion nature of interacting spins in one dimensional (1D) spin chains still lacks a rigorous study. In this letter we show that the length-$1$ spin strings significantly dominate critical properties of spinons, magnons and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution we analytically calculate exact scaling functions of thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double peaks in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), quantum critical and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio $R_W=4K_s$ remains almost temperature-independent, here $K_s$ is the Luttinger parameter. Furthermore, 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(C${}_4$H${}_4$N${}_2$)(NO${}_3$)${}_2$ recently studied in Phys. Rev. Lett. {\bf 114}, 037202 (2015)]. We further find that the magnetization peak used in experiments is not a good quantity to map out the finite temperature TLL phase boundary.

6 pages + 10 pages, 4 figures + 4 figures

References in corpus (6)

• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
• Universal temperature dependence of the magnetization of gapped spin chains
• Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields
• Magneto-caloric effects, quantum critical points, and the Berezinsky-Kosterlitz-Thouless transition in 2D coupled spin dimer systems

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• Grüneisen parameters for Lieb-Liniger and Yang-Gaudin models
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
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• Tomonaga-Luttinger liquid and quantum criticality in spin-1/2 antiferromagnetic Heisenberg chain C14H18CuN4O10 via Wilson ratio
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory