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Register a new userIs the Luttinger liquid a new state of matter?
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Authors
V. V. Afonin
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We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landaus theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.
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It is well established that at low energies one-dimensional (1D) fermionic systems are described by the Luttinger liquid (LL) theory, that predicts phenomena like spin-charge separation, and charge fractionalization into chiral modes. Here we show through the time evolution of an electron injected into a 1D t-J model, obtained with time-dependent density matrix renormalization group, that a further fractionalization of both charge and spin takes place beyond the hydrodynamic limit. Its dynamics can be understood at the supersymmetric point (J=2t) in terms of the excitations of the Bethe-Ansatz solution. Furthermore we show that fractionalization with similar characteristics extends to the whole region corresponding to a repulsive LL.
We study a system of crossed spin-gapped and gapless Luttinger liquids. We establish the existence of a stable non-Fermi liquid state with a finite-temperature,long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $Tto 0$. This two-dimensional system has many properties characteristic of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. This model can easily be extended to three dimensions.
We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can {it stabilize} a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi liquid state: the crossed sliding Luttinger liquid phase (CSLL). In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T to 0$. This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.
A novel method for detecting Luttinger-liquid behavior is proposed. The idea is to measure the tunneling conductance between a quantum wire and a parallel two-dimensional electron system as a function of both the potential difference between them, $V$, and an in-plane magnetic field, $B$. We show that the two-parameter dependence on $B$ and $V$ allows for a determination of the characteristic dependence on wave vector $q$ and frequency $omega$ of the {it spectral function}, $A_{rm LL}(q,omega)$, of the quantum wire. In particular, the separation of spin and charge in the Luttinger liquid should manifest itself as singularities in the $I$-$V$-characteristic. The experimental feasibility of the proposal is discussed.
The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of great debate. We conducted 17-O single crystal NMR measurements of the S=1/2 kagome lattice in herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrate that the intrinsic local spin susceptibility $chi_{kagome}$ deduced from the 17-O NMR frequency shift asymptotes to zero below temperature T ~ 0.03 J, where J ~ 200 K is the Cu-Cu super-exchange interaction. Combined with the magnetic field dependence of $chi_{kagome}$ we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.
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