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 RW = 4Ks remains almost temperature-independent, here Ks 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(C4H4N2)(NO3)2 recently studied in Phys. Rev. Lett. 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. Of central importance to the study of the 1D spin-1/2 antiferromagnetic Heisenberg chain is the understanding of spin excitations [1,[3][4][5][6][7][8][9][10][11][12][13]. Elementary spin excitations in this model may exhibit quasi-particle behaviour which is described by spinons carrying half a unit of spin. Such fractional quasiparticles are responsible for the TLL in the model [10,14,15].Regarding to the Bethe ansatz solution of the 1D spin-1/2 chain, a significant development is Takahashi's discovery of spin string patterns [2], i.e., magnon bound states with different string lengths. Takahashi's spin strings give one full access to the thermodynamics of the model through Yang and Yang's grand canonical approach [18], namely the so-called thermodynamic Bethe ansatz (TBA) equations [2]. However, the problems of how such spin strings determine the free fermion nature of spinons and how spin strings comprise universal scalings of thermal and magnetic properties still lack a rigorous understanding. In this paper we present a full answer to these questions.Using spin string solutions to the TBA equations, we obtain the following results: I) we obtain exact scaling functions, critical exponents and a benchmark of quantum magnetism for the 1D spin-1/2 Heisenberg chain, revealing the microscopic origin of the quasiparticle spinons, free fermions and magnons that emerge in different physical regimes; II) We find that the Wilson ratio [19,20], the ratio between the susceptibility χ and the specific heat c v divided by the temperature T ,πkB gµB 2 χ/(c v /T ), significantly characterises the TLL of spinons and marks the crossover temperature between the quantum critical phase and the TLL [21], see Fig. 1. When the magnetic field is larger than the saturation field, dilute magnon beh...

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