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Register a new userControlling Luttinger liquid physics in spin ladders under a magnetic field
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We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate 1/T_1 at 250 mK and for (ii) the phase transition to a 3D ordered phase occuring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and Luttinger liquid model tested in detail over the whole fermion band.
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We investigate electronic correlation effects on edge states of quantum spin-Hall insulators within the Kane-Mele-Hubbard model by means of quantum Monte Carlo simulations. Given the U(1) spin symmetry and time-reversal invariance, the low-energy theory is the helical Tomanaga-Luttinger model, with forward scattering only. For weak to intermediate interactions, this model correctly describes equal-time spin and charge correlations, including their doping dependence. As apparent from the Drude weight, bulk states become relevant in the presence of electron-electron interactions, rendering the forward-scattering model incomplete. Strong correlations give rise to slowly decaying transverse spin fluctuations, and inelastic spin-flip scattering strongly modifies the single-particle spectrum, leading to graphene-like edge state signatures. The helical Tomanaga-Luttinger model is completely valid only asymptotically in the weak-coupling limit.
Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ (short (Hpip)$_{2}$CuBr$_{4}$) was shown to be a remarkable realization of a Tomonaga-Luttinger liquid (TLL) and allowed to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and allows thus to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as the formation of the Bose glass. As a first step in this direction we present in this paper a study of the properties of the related (Hpip)$_{2}$CuCl$_{4}$ compound. We determine the exchange couplings and compute the temperature and magnetic field dependence of the specific heat, using a finite temperature Density Matrix Renormalization group (DMRG) procedure. Comparison with the measured specific heat at zero magnetic field confirms the exchange parameters and Hamiltonian for the (Hpip)$_{2}$CuCl$_{4}$ compound, giving the basis needed to start studying the disorder effects.
In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger Liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically-gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunnelling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.
We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines we determine the phase boundary and the order parameter of the low-temperature (3-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1 T^(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1<K<2 range which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.
We present two methods to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg antiferromagnetic ladder are attractive or repulsive. The first method combines two bulk measurements, of magnetization and specific heat, to deduce the TLL parameter that distinguishes between the attraction and repulsion. The second one is based on a local-probe, NMR measurements of the spin-lattice relaxation. For the strong-leg spin ladder compound $mathrm{(C_7H_{10}N)_2CuBr_4}$ we find that the isothermal magnetic field dependence of the relaxation rate, $T_1^{-1}(H)$, displays a concave curve between the two critical fields that bound the TLL regime. This is in sharp contrast to the convex curve previously reported for a strong-rung ladder $mathrm{(C_5H_{12}N)_2CuBr_4}$. Within the TLL description, we show that the concavity directly reflects the attractive interactions, while the convexity reflects the repulsive ones.
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