Using bosonization techniques for (2 + 1)D systems, we show that the transverse conductance for a system with general current interactions, when measured between perfect Hall regions is not renormalized at low temperatures. Our method extends two results we have recently obtained on low dimensional fermionic systems: on the one hand, the relationship between universality of Landauer conductance and universality of bosonization rules for (1 + 1)D systems, and on the other hand, the universal character of the bosonized topological current associated to a (2 + 1)D fermionic system with current interactions.Using bosonization techniques for (2 + 1)D systems, we show that the transverse conductance for a system with general current interactions, when measured between perfect Hall regions is not renormalized at low temperatures. Our method extends two results we have recently obtained on low dimensional fermionic systems: on the one hand, the relationship between universality of Landauer conductance and universality of bosonization rules for (1 + 1)D systems, and on the other hand, the universal character of the bosonized topological current associated to a (2 + 1)D fermionic system with current interactions.

Jan 1, 200012 citations

Universality and phase diagram in the quantum Hall effect

L. W. Wong

Jan 1, 19970 citations

Interactions in the integer quantum Hall effect: Critical conductivity and dynamical scaling

Michael Backhaus, Bodo Huckestein

Physica B Condensed MatterDec 1, 19981 citation

Comment on “Galilean invariance at quantum Hall edge”

Judith Hoeller, N. Read

In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015)], it is claimed that the conductivity at low frequency $\ensuremath{\omega}$ and small wave vector $q$ along the edge of a quantum Hall system (that possesses Galilean invariance along the edge) contains a universal contribution of order ${q}^{2}$ that is determined by the orbital spin per particle in the bulk of the system, or alternatively by the shift of the ground state. (These quantities are known to be related to the Hall viscosity of the bulk.) In this Comment we calculate the real part of the conductivity, integrated over $\ensuremath{\omega}$, in this regime for the edge of a system of noninteracting electrons filling either the lowest, or the lowest $\ensuremath{\nu} (\ensuremath{\nu}=1,\phantom{\rule{0.16em}{0ex}}2,...)$, Landau level(s), and show that the ${q}^{2}$ term is nonuniversal and depends on details of the confining potential at the edge. In the special case of a linear potential, a form similar to the prediction is obtained; it is possible that this corrected form of the prediction may also hold for fractional quantum Hall states in systems with special forms of interactions between electrons.In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015)], it is claimed that the conductivity at low frequency $\ensuremath{\omega}$ and small wave vector $q$ along the edge of a quantum Hall system (that possesses Galilean invariance along the edge) contains a universal contribution of order ${q}^{2}$ that is determined by the orbital spin per particle in the bulk of the system, or alternatively by the shift of the ground state. (These quantities are known to be related to the Hall viscosity of the bulk.) In this Comment we calculate the real part of the conductivity, integrated over $\ensuremath{\omega}$, in this regime for the edge of a system of noninteracting electrons filling either the lowest, or the lowest $\ensuremath{\nu} (\ensuremath{\nu}=1,\phantom{\rule{0.16em}{0ex}}2,...)$, Landau level(s), and show that the ${q}^{2}$ term is nonuniversal and depends on details of the confining potential at the edge. In the special case of a linear potential, a form similar to the prediction is obtained; it is possible that this corrected form of the prediction may also hold for fractional quantum Hall states in systems with special forms of interactions between electrons.

arXiv:1605.00275Physical review. B./Physical review. BMay 23, 20165 citations

In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015)], it is claimed that the conductivity at low frequency $\ensuremath{\omega}$ and small wave vector

q

along the edge of a quantum Hall system (that possesses Galilean invariance along the edge) contains a universal contribution of order

{q}^{2}

that is determined by the orbital spin per particle in the bulk of the system, or alternatively by the shift of the ground state. (These quantities are known to be related to the Hall viscosity of the bulk.) In this Comment we calculate the real part of the conductivity, integrated over $\ensuremath{\omega}$, in this regime for the edge of a system of noninteracting electrons filling either the lowest, or the lowest $\ensuremath{\nu} (\ensuremath{\nu}=1,\phantom{\rule{0.16em}{0ex}}2,...)$, Landau level(s), and show that the

{q}^{2}

term is nonuniversal and depends on details of the confining potential at the edge. In the special case of a linear potential, a form similar to the prediction is obtained; it is possible that this corrected form of the prediction may also hold for fractional quantum Hall states in systems with special forms of interactions between electrons.