We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger-liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single-channel Kondo type, we infer that the universality we found implies that Luttinger-liquid physics has no qualitative effect on these properties, in contrast with perturbative results.We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger-liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single-channel Kondo type, we infer that the universality we found implies that Luttinger-liquid physics has no qualitative effect on these properties, in contrast with perturbative results.

arXiv:0808.0849Europhysics Letters (EPL)Jun 1, 200929 citations

Probing the Excitations of the Luttinger Liquids

孫允武

Jan 1, 20080 citations

Universal Symmetry-Protected Resonances in a Spinful Luttinger Liquid

Yichen Hu, C. L. Kane

We study the problem of resonant tunneling through a quantum dot in a spinful Luttinger liquid. For a range of repulsive interactions, we find that for symmetric barriers there exist resonances with a universal peak conductance $2g^* e^2/h$ that are controlled by a non-trivial intermediate fixed point. This fixed point is also a quantum critical point separating symmetry-protected topological phases. By tuning the system through resonance, all SPT phases can be accessed. For a particular interaction strength with Luttinger parameters $g_ρ=1/3$ and $g_σ=1$ , we show that the problem is equivalent to a two channel $SU(3)$ Kondo problem( $SU(3)_2$ CFT). At the Toulouse limit, both problems can be mapped to a quantum Brownian motion model on a Kagome lattice, which in turn is related to the quantum Brownian motion on a honeycomb lattice and the three-channel $SU(2)$ Kondo problem( $SU(2)_3$ CFT). "Level-rank duality" in the quantum Brownian motion model relating $SU(2)_k$ CFT to $SU(k)_2$ CFT is also explored. Utilizing the boundary conformal field theory, the on-resonance conductance of our resonant tunneling problem is calculated as well as the scaling dimension of the leading relevant operator. This allows us to compute the scaling behavior of the resonance line-shape as a function of temperature.We study the problem of resonant tunneling through a quantum dot in a spinful Luttinger liquid. For a range of repulsive interactions, we find that for symmetric barriers there exist resonances with a universal peak conductance $2g^* e^2/h$ that are controlled by a non-trivial intermediate fixed point. This fixed point is also a quantum critical point separating symmetry-protected topological phases. By tuning the system through resonance, all SPT phases can be accessed. For a particular interaction strength with Luttinger parameters $g_ρ=1/3$ and $g_σ=1$, we show that the problem is equivalent to a two channel $SU(3)$ Kondo problem($SU(3)_2$ CFT). At the Toulouse limit, both problems can be mapped to a quantum Brownian motion model on a Kagome lattice, which in turn is related to the quantum Brownian motion on a honeycomb lattice and the three-channel $SU(2)$ Kondo problem($SU(2)_3$ CFT). "Level-rank duality" in the quantum Brownian motion model relating $SU(2)_k$ CFT to $SU(k)_2$ CFT is also explored. Utilizing the boundary conformal field theory, the on-resonance conductance of our resonant tunneling problem is calculated as well as the scaling dimension of the leading relevant operator. This allows us to compute the scaling behavior of the resonance line-shape as a function of temperature.

arXiv:1604.08280Bulletin of the American Physical SocietyApr 28, 20163 citations

Theory of Nonlinear Luttinger Liquids

L. I. Glazman

Bulletin of the American Physical SocietyMar 16, 20100 citations

Universality classes, statistical exclusion principle, and properties of interacting fermions

Krzysztof Byczuk, Józef Spałek

We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi- or Luttinger-liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger, and spin liquids) represents a universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi- or Luttinger-liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger, and spin liquids) represents a universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.

arXiv:cond-mat/9411125Physical review. B, Condensed matterMar 15, 199514 citations

Probing Luttinger Liquids

ScienceMar 31, 20050 citations

2g^* e^2/h

that are controlled by a non-trivial intermediate fixed point. This fixed point is also a quantum critical point separating symmetry-protected topological phases. By tuning the system through resonance, all SPT phases can be accessed. For a particular interaction strength with Luttinger parameters

g_ρ=1/3

and

g_σ=1

, we show that the problem is equivalent to a two channel

SU(3)

Kondo problem(

SU(3)_2

CFT). At the Toulouse limit, both problems can be mapped to a quantum Brownian motion model on a Kagome lattice, which in turn is related to the quantum Brownian motion on a honeycomb lattice and the three-channel

SU(2)

Kondo problem(

SU(2)_3

CFT). "Level-rank duality" in the quantum Brownian motion model relating

SU(2)_k

CFT to

SU(k)_2

CFT is also explored. Utilizing the boundary conformal field theory, the on-resonance conductance of our resonant tunneling problem is calculated as well as the scaling dimension of the leading relevant operator. This allows us to compute the scaling behavior of the resonance line-shape as a function of temperature.