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Register a new userElectron Spin Resonance of the Interacting Spinon Liquid
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Quasiparticles of the Heisenberg spin-1/2 chain - spinons - represent the best experimentally accessible example of fractionalized excitations known to date. Dynamic spin response of the spin chain is typically dominated by the broad multi-spinon continuum that often masks subtle features, such as edge singularities, induced by the interaction between spinons. This, however, is not the case in the small momentum region of the magnetized spin chain where strong interaction between spinons leads to {em qualitative} changes to the response. Here we report experimental verification of the recently predicted collective modes of spinons in a model material K$_2$CuSO$_4$Br$_2$ by means of the electron spin resonance (ESR). We exploit the unique feature of the material - the uniform Dzyaloshinskii-Moriya interaction between chains spins - in order to access small momentum regime of the dynamic spin susceptibility. By measuring interaction-induced splitting between the two components of the ESR doublet we directly determine the magnitude of the marginally irrelevant backscattering interaction between spinons for the first time. We find it to be in an excellent agreement with the predictions of the effective field theory. Our results point out an intriguing similarity between the one-dimensional interacting liquid of neutral spinons and the Landau Fermi liquid of electrons.
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We study the interplay of competing interactions in spin-$1/2$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_3$) couplings. Based on large-scale density matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a new {it gapless} chiral spin liquid (CSL) phase in the intermediate $J_2$ and $J_3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin liquid state, the $U(1)$ staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the $U(1)$ Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. To our knowledge, this is the first example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of novel phases emergent from competing interactions in triangular-lattice magnets.
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