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18
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5answers
2k views

Simple models that exhibit topological phase transitions

There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
17
votes
2answers
341 views

Edge theory of FQHE - Unable to produce Green's function from anticommutation relations and equation of motion?

I'm studying the edge theory of the fractional quantum Hall effect (FQHE) and I've stumbled on a peculiar contradiction concerning the bosonization procedure which I am unable to resolve. Help! In ...
15
votes
4answers
2k views

Quantum Hall effect for dummies

In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all ...
15
votes
2answers
1k views

Topological Charge. What is it Physically?

I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
10
votes
2answers
987 views

Why quantum hall effect has chiral edge state?

The most popular explaination may be the following: in magnetic field, electrons move in cycolotron orbits, such cycolotron orbits ensure electrons to move in one direction at the edge. That is why ...
8
votes
1answer
244 views

Resistance of a two-dimensional sample

In this review of the QHE, Steve Girvin makes the following statement (bottom of pg. 6, beginning of Sec. 1.1.1): As one learns in the study of scaling in the localization transition, resistivity ...
7
votes
1answer
779 views

Questions about Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper

I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I ...
6
votes
3answers
292 views

Whis is the difference between charge fractionalization in 1D and 2D?

Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations. But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
6
votes
1answer
377 views

Aharonov-Bohm Effect and Integer Quantum Hall Effect

What is the relationship between Aharonov-Bohm effect and Integer Quantum Hall effect?
6
votes
2answers
300 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where ...
6
votes
1answer
266 views

What is parafermion in condensed matter physics?

Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, ...
6
votes
1answer
163 views

How to understand topological order at finite temperature?

I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features ...
5
votes
1answer
214 views

The bijective correspondence between a symmetric polynomial and edge excitation of the fractional quantum hall droplet

I am recently reading Xiao-Gang Wen's paper (http://dao.mit.edu/~wen/pub/edgere.pdf) on edge excitation for fractional quantum hall effect. On page 25, he claimed that it is easy to show that there ...
5
votes
1answer
194 views

Curvature and edge state

If the boundary of quantum hall fluid has non-constant curvature, how will it affect the edge state which is usually described in chiral Luttinger fluid?
5
votes
1answer
122 views

Why Landau Level quantization is observed only in low temperature and strong magnetic field in real experiment?

I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization. In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of ...
5
votes
1answer
182 views

A simple conjecture on the Chern number of a 2-level Hamiltonian $H(\mathbf{k})$?

For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian ...
5
votes
1answer
194 views

What is the energy functional for $\nu=5/2$ Moore-Read state?

I am trying to do some Monte Carlo simulations for Pfaffian state from Fractional Quantum Hall effect. I am wondering what is the energy functional for $\nu=5/2$ Moore-Read state?
5
votes
0answers
128 views

Hall conductivity from Kubo: Bulk or edge?

Using the Kubo formula, Thouless, Kohmoto, Nightingale, and den Nijs (TKNN, PRL 49 405-408 (1982)), proved that upon summing all the contributions of the filled states of an insulator, the Hall ...
4
votes
1answer
152 views

Are Hall edge currents truly dissipationless?

Integer quantum Hall states has integer number of chiral edge current channels flowing around like supercurrent in a superconductor. Are they truly dissipationless? If so, what is the mechanism that ...
4
votes
1answer
233 views

Edge channels in Quantum Hall effect

Why is the value of Hall conductance directly proportional to the number of edge channels in the sample?
4
votes
1answer
119 views

Simple uncertaintly calculation of the center coordinates of a Landau Level

I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long. In equation 2.39, the ...
4
votes
1answer
788 views

First Chern number, monoples and quantum Hall states

The first Chern number $\cal C$ is known to be related to various physical objects. Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to ...
4
votes
1answer
159 views

What is the mass of the emergent magnetic monopoles in spin ice and how is the mass of an emergent particle determined?

In solid state physics emergent particles are very common. How one determines if they are gap-less excitations? Do the defects in spin ice called magnetic monopoles have mass? What is the mass of ...
4
votes
0answers
54 views

Why can interactions be neglected for the Integer Quantum Hall effect?

Though the statement is made often, I've not seen any justification for neglecting electron-electron (Coulumb) interactions in the fully filled $\nu =1$ IQH state. I would highly appreciate if someone ...
4
votes
0answers
530 views

What is the Laughlin argument?

The fundamental question is Why is Hall conductance quantized? Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the ...
3
votes
1answer
446 views

Zero Resistance in Quantum Hall Effect and Superconductivity

What is the difference between the zero resistance of $R_{xx}$ in integer quantum Hall effect and the zero resistance in superconductivity?
3
votes
2answers
129 views

Equivilence of One Flux Quantum and Zero Flux

In Ady Stern's review of the Quantum Hall effect, he says of a quantum hall system "The spectrum at $\Phi = \Phi_0$ is the same as the spectrum at $\Phi = 0$..." Can someone explain why this is? It ...
3
votes
1answer
117 views

How to determine the orientation of the massive Dirac Hamiltonian?

In the calculation of the Chern number within a 2D lattice model, let's take the Haldane model for example, the Chern number$=\pm1$ has 2 contributions coming from 2 Dirac points described by ...
3
votes
1answer
137 views

Difference between Wigner crystal state and fractional quantum Hall (FQH) state

Wigner crystal and FQH effect are both due to strong electron-electron interaction under magnetic field. As we know, Landau's symmetry-breaking cannot be used to describe FQH state. But can it be used ...
3
votes
1answer
127 views

Why FQHE need a lower energy state?

There are a lot papers explaining why Laughlin's wavefunction are energetically favorable, but seldom explain why a lower energy state could explain the plateau at $\nu=1/3$. I met at several places ...
3
votes
1answer
543 views

Chern number in condensed matter physics

In mathematics, the Chern number is defined in terms of the Chern class of a manifold. What is the exact definition of Chern number in condensed matter physics, i.e. quantum hall system?
3
votes
1answer
175 views

Laplacian of a delta function as an interaction potential for Laughlin state

I am reading Xiao-Gang Wen's paper "Pattern-of-zeros approach to Fractional quantum Hall states and a classification of symmetric polynomial of infinite variables", on page 8, he gives three ...
3
votes
0answers
70 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
3
votes
0answers
120 views

Quantum Hall Effect and Edge States

In quantum hall effect we measure the hall conductance (in transverse direction) which is quantized. My question how do they take care of the edge states that are in the longitudinal side?
3
votes
0answers
116 views

Flux quantization and AB effect and Laughlin's argument of IQHE

I have a question essentially the same with this one "Aharonov-Bohm Effect and Flux Quantization in superconductors" which is why we can say the flux is quantized in superconducting disk but not in AB ...
2
votes
1answer
211 views

Is Fractional quantum Hall effect proof that leptons are composite particles?

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values. Should this be considered ...
2
votes
1answer
163 views

A naive question on the Quantum Hall Effect(QHE) and the confinement in gauge theory?

The non-interacting 2D lattice QH system is described by the Hamiltonian $H=\sum t_{ij}e^{iA_{ij}}c_i^\dagger c_j+H.c$ My confusion is: Does this imply that the $2D$ lattice QHE is described by the ...
2
votes
1answer
178 views

Rewriting Creation and Annihilation Operators

I am playing with the Landau Level problem and Algebraic solutions to it. I am given $$a=\frac{l_{b}}{\sqrt{2}\hbar}(\pi_{x}-i\pi_{y}) ...
2
votes
1answer
86 views

FQH Edge Theory as decoupled chiral bosons

The action describing the edge theory of the Fractional Quantum Hall effect is given by \begin{equation} S = \frac{1}{4\pi} \int \mathrm{d}x \ \mathrm{d}t \left[ K_{IJ} \ \partial_{t}\phi_{RI} ...
2
votes
1answer
216 views

What is nonlocal resistance?

We are first taught to calculate local resistance, where current and voltage are on the same part of the material. But many experiments measure nonlocal resistance, where current and voltage are ...
2
votes
1answer
544 views

How do you obtain the commutation relations at non-equal times (for the edge of a fractional quantum Hall state)?

The edge of a fractional quantum Hall state is an example of a chiral Luttinger liquid. Take, for the sake of simplicity, the edge of the Laughlin state. The Hamiltonian is: $$H = ...
2
votes
1answer
167 views

What is the operator for the edge current of a fracional quantum Hall state?

The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson, $$ S = \frac{1}{4\pi} \int dt dx ...
2
votes
0answers
58 views

Laughlin state unique ground state?

In the FQHE, one typically encounters the statement that the $\nu = 1/3$ Laughlin state is a unique exact ground state of a model Hamiltonian where the Haldane pseudopotentials $V_1 \neq 0$ and $V_m = ...
2
votes
0answers
334 views

Simple model of edge states for a two-dimensional topological insulator

Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features? See e.g. the ...
2
votes
0answers
154 views

Are the electrons in a quantum hall edge state entangled?

I am reading the paper on Quantum Energy Teleportation by Yusa, Izumida and Hotta(This article), and it seems that they are assuming that the quantum hall edge state is a quantum correlated state, ...
2
votes
0answers
208 views

Analytic form of the normalization constant for Laughlin wavefunction

Is there any analytic form of the normalization constant for Laughlin wavefunction $$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$ where $\nu$ is the filling factor?
1
vote
1answer
102 views

Why is planar geometry preferred to observe ordinary Hall effect?

In the Physics Today article by Avron et.al. "A Topological Look at the Quantum Hall Effect" Physics Today (2003) it is suggested that to observe ordinary Hall effect, planar geometry is preferred to ...
1
vote
1answer
269 views

“Classical” limit of Quantum Hall Effect

Imagine a partially filled $\nu=1$ state of the integer quantum Hall effect (IQHE). One way to think about it is to imagine a gas of electrons where each particle is locked to the lowest quantum state ...
1
vote
1answer
94 views

Isn't it incorrect for the minimal gauge coupling and related calculations in Prof. Ezawa's book on quantum Hall effect?

He is CORRECT. I use $\mathbf{B}=\left(0,0,B_{\perp}\right)$ and he use $\mathbf{B}=\left(0,0,-B_{\perp}\right)$. $B_{\perp}>0$. Nov.28.2012 Basically I got mad with conventions. 1.Here is the ...
1
vote
1answer
25 views

What is the quantum Hall resistance R_H as a function of magnetic field?

For the integer quantum Hall effect, the resistance $R_H = h/(ne^2)$, where $n$ is some integer. All of the graphs of $R_H$ as a function of magnetic field, $B$, that I've seen show that at $B = 0$, ...