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

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More physical explanation of impurity energy levels in a doped semiconductor?

I'm reading about doped semiconductors in Ashcroft and Mermin. They tell you that when donor impurities are added to a semiconductor, their energy level $E_d$ is just slightly below the conduction ...
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1answer
159 views

Why does water ($\mathrm{H_2O}$) only have two distinct fluid phases?

Water (and other substances) can exist in many distinct solid phases (with different crystallic micro-structure), but only in two fluid phases - liquid and gaseous, in which the molecules are oriented ...
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2answers
276 views

Why does the $\pi$-flux state have time-reversal symmetry?

It's known that the $\pi$-flux state of the antiferromagnetic Heisenberg model on the square lattice is an important concept. The $\pi$-flux state is described by the (simplified) mean-field ...
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1answer
297 views

Determining spectra of edge states numerically

Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only. Also in the ...
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1answer
228 views

Difference between primitive unit cell and the associated basis?

As I understand it, the basis is the group of atoms whilst the primitive unit cell is the unit space that fits the total space without any gaps, and only containing one lattice point? How do the two ...
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1answer
165 views

Derive non-linear $\sigma$ model from a theory of SU(2) matirx

It's said in Chapter VI.4 of A. Zee's book Quantum Field Theory in a Nutshell, a theory defined as $L(U(x))=\frac{f^2}{4}Tr(\partial_{\mu}U^{\dagger}\cdot\partial^{\mu}U)$, can be write in the form of ...
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41 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
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44 views

Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
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1answer
155 views

How many kinds of topological degeneracy are there?

Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For ...
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1answer
195 views

A commutation problem in Hubbard model

Does the Hubbard Hamiltonian $$H=-t\sum_{\langle ij\rangle \sigma}c_{i\sigma}^{\dagger}c_{j\sigma}+h.c.+U\sum_{i}n_{i\uparrow}n_{i\downarrow}$$ commute with $\sum_{i}\mathbf{S}_i^2$? where ...
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82 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
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1answer
161 views

What happens to chiral Majorana edge fermions near quantum phase transition in p+ip superconductors?

In the weakly-coupled BCS regime two-dimensional chiral (p+ip) spinless superconductors and superfluids posses a chiral gapless fermionic Majorana state localized near the boundary. This gapless edge ...
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1answer
114 views

Wave vector $\vec{k}$ vs position vector $\vec{x}$

My question is about the $k$-vectors in first Brillouin zone. If I am not misunderstood, the relation k = 2π/(Na) tells that when k goes to zero, we are very very far away from the reference atom and ...
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1answer
235 views

Goldstone mode in O(N) (non-linear $\sigma$ model)

The question is does the Non-linear $\sigma$ model have a Goldstone mode? Consider a $O(N)$ mode for which the Hamiltonian is $H=J\sum_{i,j}\vec{n}_i \cdot \vec{n}_j$, where ...
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122 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. ...
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1answer
1k views

Valence band and conduction band, trying to get a clear picture!

I am trying to get a clear picture of the valence band, conduction band, and the band gap. Now I've been researching it for a little while now and understand most of what's going on. I'm still a ...
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1answer
388 views

Physical Interpretation of Relationship Between Hall Conductivity and Berry Curvature?

Why is the Hall conductivity in a 2D material $$\tag{1} \sigma_{xy}=\frac{e^2}{2\pi h} \int dk_x dk_y F_{xy}(k)$$ where the integral is taken over the Brillouin Zone and $F_{xy}(k)$ is the Berry ...
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0answers
586 views

What is the definition of particle-hole symmetry in condensed matter physics?

People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?
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2answers
439 views

Probability of Different States - Canonical Ensemble - Partition Function

Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the ...
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1answer
160 views

Dopant Charge Transfer and Fermi Level shift

When a system has a dopant, how much does the Fermi level shift? For example, say a finite concentration of substitutional dopants replace some bulk atoms, and each has one extra electron. Ignore any ...
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0answers
164 views

Average number of spin up particles

In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$? You can assume we have the ...
2
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1answer
806 views

Partition Function for Two Level System

I have a system with $N_s$ sites and $N$ particles, such that $N_s >> N >> 1$. If a site has no particle, then there is zero energy associated with that site. The $N$ particles occupy the ...
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1answer
156 views

Is water a gas at critical density, room temperature?

I am quoting Chaikin, Lubensky, Principles of Condensed Matter Physics, p. 4. Now suppose we have a closed container of water vapor at a density of 0.322 g/cc at room temperature. As the ...
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1answer
204 views

Definition for Chiral Spin Liquid

What is the definition of chiral spin liquid? Especially what does chiral mean here? I encounter a lot of terminologies with chiral. It seems they mean differently in different contexts. If you could ...
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3answers
167 views

Holes in a P-type semiconductor under external force E

Basically in almost every semiconductor texts, there will be all these concepts concerning electrons, holes, dopants, fermi-levels. However, I have been always confused about the picture of hole ...
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2answers
164 views

Paramagnetism and large N

In a paramagnetic system, we have: $$N = N_\uparrow + N_\downarrow$$. If we have a large system, with $N >> 1$, is it generally okay to assume $N_\uparrow \approx \frac{N}{2}$ and ...
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3answers
250 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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2answers
794 views

What is a Zero-Phonon Line (ZPL)?

I am trying to understand the electronic structure of the negatively charged NV centre in diamond, where there is a so-called Zero-Phonon Line (ZPL) in the spectrum. Can anybody explain what a ZPL is? ...
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1answer
100 views

How are the finite speed of light and the atomic nature of mater related to the end of Moore's law?

In this article from 2007, Moore talks about the end of his Law. Can someone throw more light as to how the finite speed of light and the atomic nature of mater are related to the end of Moore's law?
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1answer
538 views

Paramagnetism Spin-1/2 Particles - Partition Function

I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = ...
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0answers
55 views

Long range repulsion in anomalous solids

As far as I know things like rocks, walls, rubber balls, polished tables etc. exert a short range repulsive force on other everyday objects that is responsible for hardness, softness, collisions, ...
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2answers
265 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
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1answer
124 views

Ergodicity of the Drude model

The Drude model of electric conduction in solids deals with independent free electrons subject to random collisions with the crystal lattice (the direction where the electrons are scattered after a ...
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0answers
185 views

What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
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1answer
43 views

is it possible to condense an object to a point?

When matter is condensed the mass stays the same and we also know that only the volume and density are the only other two effected variables. But is there a point in which the matter cannot condense ...
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1answer
447 views

Why do quasicrystals have well-defined Fourier transforms?

I was recently reading about quasicrystals, and I was really surprised to learn that even though they do not have a periodic structure, and only have long range order in a very different sense to the ...
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1answer
254 views

Ground State Degeneracy in ferromagnetic Heisenberg model

I am reading the book "Lecture notes on Electron Correlation and Magnetism" by Patrik Fazekas. It says, "The ground state (of Heisenberg FM model) is not unique. We have just found that the system ...
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0answers
78 views

What does the term 'a uniform RVB spin-liquid state' mean?

I encountered this term a uniform RVB spin-liquid state in some articles, for example, see the paragraph under Eq.(29) on page 9 in this paper. What does the word 'uniform ' mean? Simply from the ...
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2answers
77 views

Why do excitonic absorptions have small bandwidth?

Below is an image of the optical density (proportional to the absorption coefficient) of KBr crystal at low temperature. Indicated at 6.6 ev and 7.7 eV are the absorption by excitons. As you can see, ...
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1answer
230 views

Majorana wavefunction

I'm trying to compute the wavefunction for a Majorana state in an nanowire/superconductor hybrid system, like arXiv: Majorana Fermions and a Topological Phase Transition in ...
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1answer
173 views

Anderson localization in 1d, 2d and 3d

Why in 1d and 2d systems, all states will be localized for infinitesimal disorder, but in 3d only states with energy lower below mobility edge will be localized?
4
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1answer
70 views

How to derive the Mott gap mathematically

From the one-band Hubbard model, $H=-t\sum\limits_{<ij>, \sigma}c_{i\sigma}^{\dagger}c_{j\sigma}+U\sum\limits_{i}n_{i\uparrow}n_{i\downarrow}$, we know if $U\gg t$, the energy cost of two ...
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0answers
152 views

Bloch's theorem and Bloch's state

The question is not so much about the theorem, but more about what it means in this context: see this link. So yes, because of Bloch's theorem the Hamiltonian eigenstates in a crystalline system can ...
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1answer
208 views

What determines Phonon - Phonon collisions?

I was in Solid State Physics lecture yesterday and we BRIEFLY went over what causes phonons to collide with one another. Things such as crystal imperfections, boundaries, Temperature, but I was ...
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54 views

Two Photon Absorption dependence on Semiconductor Band Gap

It's well known that Two Photon Absorption coefficient is scaling with $E_g^{-3}$. Does anyone know what is the physical reason for this scaling? What is the physical theory behind this mathematics?
3
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1answer
235 views

What does it mean for a Hamiltonian to be SU(2) invariant?

Can somebody explain what it means when one says a Hamiltonian is SU(2) invariant? I know Heisenberg Hamiltonian is SU(2) invariant but why?
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181 views

Topological disorder in condensed matter?

What is meant by topological disorder in condensed matter (both crystalline and amorphous)? For example, please see the following two papers from arxiv.org http://arxiv.org/pdf/0906.3848.pdf ...
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1answer
108 views

Systems with different particle statistics

Is there a way to describe interactions between systems with particles of different species, that is to say with different statistics? For example: I am placing a boson next to a free fermion gas. ...
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115 views

Is the $SU(2)$ flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?

The $SU(2)$ flux defined in the context of PSG is as follows: Consider the mean-field Hamiltonian $H_{MF}=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ description of a 2D lattice spin-model, the ...
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1answer
208 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 ...