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Register a new userSpin ladders and quantum simulators for Luttinger liquids
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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.
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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.
We study spinless electrons in a single channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity-coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired, superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau level filling factors. For odd-denominator fillings $ u=1/(2n+1)$, wires at the Luttinger phase form Laughlin states while wires in the strongly paired phase form bosonic fractional quantum Hall state of strongly-bound pairs at a filling of $1/(8n+4)$. The transition between the two is of the universality class of Ising transitions in three dimensions. For even-denominator fractions $ u=1/2n$ the two single-wire phases translate into four quantum Hall states. Two of those states are bosonic fractional quantum Hall states of weakly- and strongly- bound pairs of electrons. The other two are non-Abelian quantum Hall states, which originate from coupling wires close to their critical point. One of these non-Abelian states is the Moore-Read state. The transition between all these states are of the universality class of Majorana transitions. We point out some of the properties that characterize the different phases and the phase transitions.
We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub Bose-Luttinger liquids, which in some respects can be regarded as boson
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.
Spin liquids are quantum phases of matter that exhibit a variety of novel features associated with their topological character. These include various forms of fractionalization - elementary excitations that behave as fractions of an electron. While there is not yet entirely convincing experimental evidence that any particular material has a spin liquid ground state, in the past few years, increasing evidence has accumulated for a number of materials suggesting that they have characteristics strongly reminiscent of those expected for a quantum spin liquid.
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