1,754 research outputs found

### Scaling and diffusion of Dirac composite fermions

We study the effects of quenched disorder and a dissipative Coulomb interaction on an anyon gas in a periodic potential undergoing a quantum phase transition. We use a (2+1)âˆ’dimensional low-energy effective description that involves Nf=1 Dirac fermion coupled to a U(1) Chern-Simons gauge field at level (Î¸âˆ’1/2). When Î¸=1/2 the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when Î¸=1 the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the three-dimensional XY model. Using the large Nf approximation we perform a renormalization-group analysis. We find the Coulomb interaction to be an irrelevant perturbation of the clean fixed point for any Î¸. The dissipative Coulomb interaction allows for two classes of IR stable fixed points in the presence of disorder: those with a finite nonzero Coulomb coupling and dynamical critical exponent z=1 and those with an effectively infinite Coulomb coupling and 1<z<2. At Î¸=1/2 the clean fixed point is stable to charge-conjugation preserving (random mass) disorder, while a line of diffusive fixed points is obtained when the product of charge-conjugation and time-reversal symmetries is preserved. At Î¸=1 we find a finite disorder fixed point with unbroken charge-conjugation symmetry whether or not the Coulomb interaction is present. Other cases result in runaway flows. We comment on the relation of our results to other theoretical studies and the relevancy to experiment

### The Partially-Split Hall Bar: Tunneling in the Bosonic Integer Quantum Hall Effect

We study point-contact tunneling in the integer quantum Hall state of bosons.
This symmetry-protected topological state has electrical Hall conductivity
equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the
integer quantum Hall state of fermions, a point contact can have a dramatic
effect on the low energy physics. In the absence of disorder, a point contact
generically leads to a partially-split Hall bar geometry. We describe the
resulting intermediate fixed point via the two-terminal electrical (Hall)
conductance of the edge modes. Disorder along the edge, however, both restores
the universality of the two-terminal conductance and helps preserve the
integrity of the Hall bar within the relevant parameter regime.Comment: 12 pages, 5 figures; v.2: typos fixed and clarified some argument

### An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State

We study a novel abelian gauge theory in 2+1 dimensions which has surprising
theoretical and phenomenological features. The theory has a vanishing
coefficient for the square of the electric field $e_i^2$, characteristic of a
quantum critical point with dynamical critical exponent $z=2$, and a level-$k$
Chern-Simons coupling, which is {\it marginal} at this critical point. For
$k=0$, this theory is dual to a free $z=2$ scalar field theory describing a
quantum Lifshitz transition, but $k \neq 0$ renders the scalar description
non-local. The $k \neq 0$ theory exhibits properties intermediate between the
(topological) pure Chern-Simons theory and the scalar theory. For instance, the
Chern-Simons term does not make the gauge field massive. Nevertheless, there
are chiral edge modes when the theory is placed on a space with boundary, and a
non-trivial ground state degeneracy $k^g$ when it is placed on a finite-size
Riemann surface of genus $g$. The coefficient of $e_i^2$ is the only relevant
coupling; it tunes the system through a quantum phase transition between an
isotropic fractional quantum Hall state and an anisotropic fractional quantum
Hall state. We compute zero-temperature transport coefficients in both phases
and at the critical point, and comment briefly on the relevance of our results
to recent experiments.Comment: 29 pages, 1 figur

### Interactions and the Theta Term in One-Dimensional Gapped Systems

We study how the \theta -term is affected by interactions in certain
one-dimensional gapped systems that preserve charge-conjugation, parity, and
time-reversal invariance. We exploit the relation between the chiral anomaly of
a fermionic system and the classical shift symmetry of its bosonized dual. The
vacuum expectation value of the dual boson is identified with the value of the
\theta -term for the corresponding fermionic system. Two (related) examples
illustrate the identification. We first consider the massive Luttinger liquid
and find the \theta -term to be insensitive to the strength of the interaction.
Next, we study the continuum limit of the Heisenberg XXZ spin-1/2 chain,
perturbed by a second nearest-neighbor spin interaction. For a certain range of
the XXZ anisotropy, we find that we can tune between two distinct sets of
topological phases by varying the second nearest-neighbor coupling. In the
first, we find the standard vacua at \theta = 0, \pi, while the second contains
vacua that spontaneously break charge-conjugation and parity with fractional
\theta / \pi = 1/ 2, 3/2. We also study quantized pumping in both examples
following recent work.Comment: 17 pages, harvmac; v.2 typo corrected and slight re-wording

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