Only selected papers are listed here. For other publications, please see the publication list. Recent publications are also available at the arXiv.

My very first work [1]
"**Thermodynamical description of incommensurate phase in
prustite**" (as an undergraduate student with
V. L. Pokrovsky, then at the Landau Institute)
described the Landau theory of the incommensurate phase in prustite
(Ag_{3}AsS_{3}). In particular, effect of thermal
fluctuations on the evolution of the incommensuration vector was
analyzed. Unfortunately, we could not explain the "invar"
effect: the lattice constant of the material mysteriously remains
constant (the isobaric thermal expansion coefficient vanishes)
throughout the incommensurate phase. The effect was also seen in
other incommensurate materials, see, e.g., B. Sh. Bagautdinov and
V. Sh. Shekhtman, "The invar effect and phase
transitions in Cs_{2}ZnI_{4} crystals",
Phys. Sol. State, **41**, 123 (1999). As far as I know, the puzzle
of the invar effect remains unsolved.

In the work [5]
"**Fluctuation-induced first order transition between the quantum
Hall liquid and insulator**" (with S.-C. Zhang, then my
Ph.D. advisor at Stanford) we studied a field theory of relativistic
charged boson minimally coupled with abelian Chern-Simons gauge field.
This can be viewed as an effective model corresponding to quantum Hall
to an Insulator transition in the presence of commensurated potential.
The transition where the expectation value of the field φ vanishes
is associated with the transition quantum Hall liquid to an Insulator.
To avoid dimensional regularization, the calculation was done in a
vicinity of the tricritical point (thus the need to study
φ^{6} theory). A renormalization group analysis involving
the second-loop β-function demonstrated that fluctuations drive
the transition to first order. In regular QED this mechanism was
invented by S. Coleman and E. Weinberg, see "Radiative Corrections
as the Origin of Spontaneous Symmetry Breaking", Phys. Rev. D
**7**, 1888 (1973).

The study continued in the work [7] "**Duality and Universality for the
Chern-Simons bosons**", where a closely related model was
studied on a lattice. Namely, the model was the (Villain) lattice
`X`−`Y` model coupled with the Chern-Simons
field. *In the assumption that the transitions
are continuous*, the analysis of two symmetries,
"duality" (symmetry between particles and vortices, which
results θ → −(2π)^{2}/θ) and
"flux attachment" (periodicity with respect to the mutual
statistics of the particles, θ→θ+4π) demonstrated
that the transitions in the models with any rational value of the
Chern-Simons coefficient can be mapped onto only two universality
classes.

The next paper in the series is [8] "**Global symmetries of quantum Hall
systems: lattice description**". Here I studied
the same model but with symmetry closer to that of the quantum Hall
effect: the Lorentz invariance (more precisely, its Euclidean version)
was assumed to be broken by non-zero charge and current densities, as
well as external magnetic field. It turned out that the two
transformations not only affect the Chern-Simons coupling θ (the
statistics of the quasiparticles) but also the global currents and
fluxes, which results in mappings for the conductivities
σ_{xx} and σ_{xy} which are enticingly
similar to the correspondence rules. However, because the statistics
of the particles changes at the same time, the symmetry arguments
alone were insufficient to prove the universality of the
transitions.

This story continues in the section on edge
states, where totally different methods were used. Also, the
assumption that the transition is second order turned out to be not so
innocuous: many closely related models feature first
order transitions. Please see discussion on high-T_{c}
stripes and lattice bosons below.

If it was the statistics of quasiparticles which prevented the universality between different transitions, perhaps the universality in the experiment was due to the presence of disorder which would localize the quasiparticles and thus conveniently suppress their exchange statistics. To account for disorder seriously, in the case of integer quantum Hall effect an entirely different model is used, where incompressible quantum Hall liquid in two dimensions is separated into puddles by strong self-consistent potential. Then, at low temperatures the excitations within each puddle are gapped, and dissipative charge transport can only occur along the edges of the puddles. As a result, the quantum Hall to insulator transition driven by gating (electron density reduction) can be viewed as the (quantum) percolation transition.

In the paper [9] "**Network of
edge states: random Josephson junction array description**"
(with Karén Chaltikian), we constructed a version of the Chalker-Coddington
model applicable for the fractional quantum Hall effect. The model
consists of chiral (particles move one-way) edges connected by
occasional saddle points where tunneling between the edges occur. We
demonstrated that the duality of a sort works for each saddle point,
no matter how complicated the system of edges is: if the tunneling
of electrons through an insulating region between two nearby edges
becomes too strong, one can reconnect the edges and consider the
tunneling of quasiparticles in the transverse direction through
quantum Hall liquid.

In fact, the quantum Hall symmetries, including the quantization of
the Hall resistance well into the insulator phase, come out of a very
similar *classical* model: a collection of chiral edges
connected at saddle points [E. Shimshoni and A. Auerbach, "Quantized Hall
insulator: Transverse and longitudinal transport" Phys. Rev. B 55,
9817 (1997)]. The only difference is that the quantum interference is
suppressed. In the paper [11] "**Hall
Resistivity and Dephasing in the Quantum Hall Insulator**" (with
A. Auerbach), we demonstrated that the absence of the quantum
interference is required: a simple numerical simulation (within a
simpler Chalker-Coddington model applicable for integer quantum Hall
effect) showed that the Hall resistance quantization disappeared as
long as the effects of quantum interference were included. This
indicates that some kind of phase-breaking mechanism is in play.

In the paper [16] "**Coulomb
interaction and delocalization in quantum Hall constrictions**"
(with A. Auerbach and E. Shimshoni), we tried to figure out whether
this mysterious phase breaking could originate from the long-range
Coulomb interaction. In short, the answer was no. However, we
discovered that the duality between weak and strong tunneling remains
in the presence of the Coulomb interactions. Namely, in an
X-shaped geometry, duality relates junctions with opening angles α
and (π − α). The Coulomb interaction effect is
precisely cancelled in the self-dual geometry of a junction with
α = π/2, where the tunneling problem becomes exactly solvable
using the Wiener-Hopf method.

Series of papers on correlated bilayers and
multilayers with J. D. Naud and S. L. Sondhi. Please see our letter
[21] "**Fractional quantum
Hall effect in infinite layer systems**" for a short summary.

[10] "

[12] "

[18] "

[26] "

**UNDER CONSTRUCTION**

Leonid Pryadko <my first name at landau dot ucr dot edu> Last modified: Mon Sep 05 15:30:41 Pacific Daylight Time 2005