The study of physical properties condensed phases of matter, including solids and liquids.

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75 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
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2answers
53 views

Free electron gas in two dimensions

Can someone give a qualitative description on why the density of states for a two dimensional free electron gas is independent of energy while it is not in one and three dimensions? In one dimension ...
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0answers
29 views

Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...
2
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1answer
40 views

Out-of-Plane Phonons

I am trying to derive the out-of-plane phonon dispersion relation for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form: ...
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1answer
67 views

Diagonalization of Hamiltonian

Typically, one way of understanding the physics of an interacting quantum system is by diagonalizing the Hamiltonian. In principle, can we always diagonalize a Hamiltonian, such that it is expressed ...
3
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1answer
86 views

Naive questions on the ground states of Kitaev model

I got some naive questions on the ground states of honeycomb Kitaev model (with open boundary conditions): (1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ ...
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23 views

Help with 1D and 2D density of states

I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions $$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i ...
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16 views

Pseudocubic unit cells: how to construct one?

I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation ...
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0answers
19 views

How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...
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1answer
30 views

Why can't a dislocation terminate in the bulk?

We are told that they can only terminate on surfaces, grain boundaries or other dislocations but we are not told why they can't terminate inside the crystal.
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1answer
40 views

What does (001) Silicon mean?

If someone gives me a thin film of Si, and they tell me it's (001) Si, does that mean that the (001) planes of Si are the ones making up the surface of the film?
3
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1answer
50 views

What is an electron/hole pocket and what is the significance?

What is an electron/hole pocket and what is the significance? I'm trying to get my head around this. I've read what Ashcroft and Mermin have to say on the subject, but it's a little convoluted. They ...
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33 views

Symmetry argument about degeneracy of graphene energy band at Dirac point

This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points ...
2
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34 views

Why p-wave superconductors are rare in nature?

I have the basic question that why so many superconducting materials are s-wave and d-wave pairing, but the p-wave superconductors are so rare in nature? An equivalent question may be that why ...
4
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2answers
91 views

How to conclude that an interaction is attractive from its Fourier transform (momentum space representation)?

Background: In the book by Altland and Simons, Condensed matter field theory, in exercise 4.5.7, one is supposed to use the effective field theory method to integrate out the phonon field in an ...
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2answers
61 views

Is this two forms of Hubbard model equivalent?

I have seen two form of Hubbard model, one is: $$H=-t\sum_{<ij>s}c_{is}^\dagger c_{js}+h.c.+U\sum_i(n_{i\uparrow}-1/2)(n_{i\downarrow}-1/2)-\mu\sum_{is}n_{is}$$ The other is a more familiar ...
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0answers
83 views

How should I regularize this integral?

I need to calculate the following integral (which is divergent): \begin{equation} I(m,C)=\int_{-\infty}^\infty {\rm d}\omega\int_{\rm space}{\rm d^3 ...
8
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1answer
184 views

Understanding Elitzur's theorem from Polyakov's simple argument?

I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
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0answers
38 views

How Does The Macroscopic Wavefunction Build Up?

How does the macroscopic wavefunction (the order parameter) builds up from zero value to the a finite value when liquid He undergoes a transition from normal to the superfluid state? How does it ...
5
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2answers
110 views

Symmetry Breaking And Phase transition

Is every phase transition associated with a symmetry breaking? If yes, what is the symmetry that a gaseous phase have but the liquid phase does not? What is the extra symmetry that normal $\bf He$ ...
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0answers
76 views

Intro to Solid State Physics

I didn't see this listed on the books page so here it is. I'm currently in an introductory Solid State course, and we are using Kittel's book. I have been having a rough time with this book although I ...
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0answers
11 views

The temperature dependence of the electron-hole (or particle-hole) continuum

In the theory of the electron gas, the particle-hole pairs are possible elementary excitations. I would like to know how the temperature T affects the particle-hole continuum which defines the domain ...
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0answers
28 views

band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?
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1answer
29 views

How to obtain band dispersion from a band structure diagram?

Reading about bands dispersion, I came across the following (Computational Chemsitry of Solid State Materials): ...
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40 views

Debye Hückel Theory valid for ions?

I am wondering about the following: Is Debye Hückel Theory only used if you look at how an external "strong" field(like a potential by a sphere that has a charge that is 1000times higher than the ...
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1answer
69 views
+50

Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations

In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step: $H_{MF-eff} = \int ...
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0answers
54 views

What is the meaning of inflection points in the dispersion relation inside the first Brillouin zone?

I have a question regarding the $E$ vs $k$ curve in the first Brillouin zone. Why does the curve have an inflection point at some value of $k$ in the curve? How does it physically support it?
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30 views

A small contradiction between periodic boundary condition and first Brilliouin zone

In condensed matter, one usually considers Bloch states inside the first Brilliouin zone, which, for 1d system with lattice constant $a$, is $-\pi/a<k<\pi/a$. But the basis of this, Bloch ...
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0answers
47 views

Good introduction to many-body Green's function via path integral formulation?

Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ...
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1answer
36 views

List of experimental band gap

does anyone know where one can find a list, database, book of experimental bandgap values of semiconductors? Is there such a collection? Or do I need to scour papers one at a time to get the values?
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1answer
71 views

Band gaps: are they at the centre or at the edge of the Brillouin zone?

Reading about electronic band structures, I came across the following: Band gaps open at the edges of the Brillouin zone (BZ), since that is where the Bragg scattering occurs. I am slightly ...
6
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1answer
135 views

Topological insulators: why K-theory classification rather than homotopy classification?

I am reading a 2009 paper by Kitaev on K-theory classification of topological insulators. In the 4th page, 1st paragraph in the section "Classification principles", he says, Continuous ...
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0answers
61 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
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0answers
49 views

How much merit is there in the heuristic argument of bulk-edge relation for topological insulators?

Take 2D quantum hall insulator for example. The typical argument goes like this: We have a Hamiltonian that has translation symmetry in both directions on a infinite lattice, and we assign a integer ...
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27 views

Quantum Hall Effect Dark Matter Detector?

Has anyone used a Quantum Hall effect detector to detect dark matter? I was looking at the following animation on wikipedia: ...
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17 views

Can the short-time dynamics of an open quantum system be approximately unitary?

Considering the physics of an open quantum system described by a Hamiltonian $H=H_S+H_E+H_{SE}$, where the subscript $S$ refers to the system of interest, $E$ to the environment and $SE$ to the ...
2
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0answers
40 views

Does the Fermi sea have plane waves, or wave packets?

Consider a zero-temperature, one-dimensional crystal with allowed electron momenta $k_n = \frac{2\pi n}{L}$. Question: Which is the more correct way to think about the Fermi sea? Sharp plane ...
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0answers
29 views

How to deal with $\vec{j}\cdot\vec{A}$ or $\rho A^2$ interaction when utilizing Kubo formula? Gauge invariance?

If there exist electromagnetic fields in solids, electrons can feel interactions like $\vec{j} \cdot \vec{A}$ or $\rho A^2$ (these are not regarded as perturbations). But these are not gauge ...
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0answers
45 views

Introduction and overview of Condensed Matter Physics [duplicate]

Is there any book that provides an overview of Condensed Matter Physics? I have had a course in QM and statistical physics and some. I dont know anything about this field, so is there a readable ...
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0answers
16 views

Is there a way to quantify how similar a polycrystal should behave to a single crystal?

So in solid state classes we learned about phenomena like band structure and others arising from a periodic potential. Then we get to doing actual experiment and find out that materials being single ...
1
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1answer
59 views

Significance of magnetic translation operator defined in fractional QHE's description

What is the significance of the magnetic translation operator used in describing the Fractional Quantum hall effect? I was following Anthony Leggett's lecture video in which he defines these operators ...
2
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1answer
95 views

Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
4
votes
1answer
75 views

String-net models on non-trivalent lattices

I have just started reading about string net models. The following aspect wasn't entirely clear to me: String net models are most naturally defined on trivalent networks, that is to say networks ...
3
votes
1answer
68 views

Is there a wave function for anyons?

People talk about anyons a lot. But i have never seen an anyon wave function. I suspect that there is no such thing as a wave function for anyons. I mean, anyons are not generalizations of bosons ...
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3answers
120 views

Bogoliubov transformation with a slight twist

Given a Hamiltonian of the form $H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix} \begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} ...
3
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0answers
86 views

Why is there a Majorana zero mode in the $\pi$ flux core of the p+ip superconductor?

In this review paper (http://arxiv.org/pdf/1202.1293.pdf), the author shows that threading a $\pi$ flux through a 2D $p_x+ip_y$ superconductor will trap a Majorana zero mode at the flux center. The ...
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0answers
106 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
3
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1answer
60 views

Superconductivity in graphene with spin orbital coupling, is it proper to let the order parameter on two sub-lattice equal?

I am reading this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. Considering just the first part of the article, where a negative-U Hubbard model with the ...
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0answers
35 views

Fractional quantum number induced in a soliton profile

It has been known there is fractional quantum number induced in a soliton profile, such as this Jeffrey Goldstone and Frank Wilczek paper and many works of Jackiw. For example the electric charge ...
3
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0answers
58 views

1+1D Bosonization on a line segment or a compact ring

I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different - Although I know that Bosonization can rewrite fermions ...