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

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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 ...
2
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1answer
143 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 ...
9
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1answer
610 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
53 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 ...
18
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1answer
661 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
464 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 ...
3
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0answers
108 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 ...
2
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2answers
101 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
380 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
352 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
92 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
248 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 ...
3
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1answer
381 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 ...
3
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0answers
72 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
501 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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0answers
398 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
162 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. ...
3
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0answers
136 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 ...
4
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1answer
286 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
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1answer
200 views

Bose-Einstein condensate and nonlinear waves

Can Bose-Einstein condensate be written as non-linear wave equation (in terms of mean field approximation theory)? the equation is: source: http://xxx.tau.ac.il/abs/1308.2288 What I do ...
2
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1answer
343 views

A naive question on the $U(1)$ gauge transformation of electromagnetic field?

For simplicity, in the following we set the electric charge $e=1$ and consider a lattice spinless free electron system in an external static magnetic field $\mathbf{B}=\nabla\times\mathbf{A}$ ...
4
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0answers
256 views

Some ambiguous points on Spontaneous Symmetry Breaking (SSB)?

Almost in every textbook of condensed matter physics, the standard description of SSB could be formulated as follows: Consider the lattice Heisenberg model in an external magnetic field ...
3
votes
2answers
277 views

Dehn twists and topological order

I am trying to understand notion of a "Dehn twist" and how it relates to topological order. In particular refering to http://arxiv.org/abs/1208.4834 it is stated that Xiao Gang Wen's paper on ...
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0answers
354 views

Mean-field approximation of the disordered state of Heisenberg model

Consider a 1D ferromagnetic Heisenberg model with the Hamiltonian $$\mathcal H=-J\sum_i \vec S_i\cdot \vec S_{i+1}.$$ For $|\vec S|=\frac{1}{2}$, we have the usual fermionic representation $\vec ...
3
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1answer
634 views

Hubbard-Stratonovich transformation and mean-field approximation

For an interacting quantum system, Hubbard-Stratonovich transformation and mean-field field approximation are methods often used to decouple interaction terms in the Hamiltonian. In the first method, ...
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2answers
573 views

Is the thickness of a sample related to the intensity of x-ray diffraction?

I understand that in general if we're adding more planes of atoms (increasing thickness of sample) then the intensity would increase because we have more constructive interference. But isn't there a ...
4
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1answer
279 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
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1answer
151 views

Non-abelian behavior of vortices in p-wave superconductors

I am trying to understand why vortices in p-wave superconductors are actually non-abelian anyons and how this relates to Majorana modes. However I am having a hard time finding proper resources (in ...
2
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1answer
91 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
2
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1answer
306 views

Connecting Fermi levels and band diagrams to potential diagrams?

I'm trying to make sense of how you can find the potential diagram given the band diagrams of a few adjacent materials. As a simple example, in semiconducting heterostructures, if you have sandwich ...
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1answer
120 views

Spinor and Scalar Bose-Einstein condensate

I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that ...
3
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1answer
337 views

Symmetry breaking in Bose-Hubbard model

According to Landau's symmetry breaking theory, there is a symmetry breaking when phase transition occurs. What is the symmetry breaking of superfluid-Mott insulator transition in Bose-Hubbard ...
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1answer
166 views

By saying a physical state has some 'symmetry', what do we really mean?

Here our arguments are restricted to the realm of the Projective Symmetry Group(PSG) proposed by Prof. Wen, Quantum Orders and Symmetric Spin Liquids. Xiao-Gang Wen. Phys. Rev. B 65 no. 16, 165113 ...
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1answer
116 views

Does Ising model belong to the field of strongly correlated systems?

How to make a judgement that whether a problem is within the field of strongly correlated systems? Do classical problems (not quantum mechanical) belong to this field?
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393 views

Two puzzles on the Projective Symmetry Group(PSG)?

Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's paper. To present the questions clearly, imagine that we use the Shwinger-fermion ...
3
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1answer
127 views

Are the symmetry operators well defined in the context of Projective Symmetry Group(PSG)?

Consider the Schwinger-fermion approach $\mathbf{S}_i=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$ to spin-$\frac{1}{2}$ system on 2D lattices. Just as Prof.Wen said in his seminal paper on PSG, the ...
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0answers
44 views

Ergodicity Breaking in Supercooled Liquids

What is a ergodic system? What is Onset temperature of ergodicity breaking in super cooled liquids when we go towards lower temperature?
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0answers
65 views

generation / destruction of fermions by phonons

my Hamiltonian consists of 1D free fermions coupled to a bosonic bath. The interaction is dictated both by scattering terms $H^{scatt}=\sum_{kq}\alpha^S_{kq}c^\dagger_kc_{k+q}X_q+h.c.$ as well as ...
2
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2answers
646 views

Anticommutatorrelation in Bogoliubov-de Gennes Hamiltonian

I almost solved the problem Equivalence of Bogoliubov-de Gennes Hamiltonian for nanowire. In the next steps I used the notation by arXiv:0707.1692: $$ \Psi^{\dagger} = ...
2
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1answer
546 views

Path integral & Gaussian integration

The following is from Ref. 1. Given the (Euclidean) action for a particle ($q$) coupled to a bath of harmonic oscillators $q_\alpha$. Goal is to find an effective action for the particle, e.g ...
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1answer
206 views

Different invariant gauge groups (IGG) on different lattices with the same form mean-filed Hamiltonian?

Suppose that we use the Schwinger-fermion ($\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$) mean-field theory to study the Heisenberg model on 2D lattices, and now we arrive at the mean-field ...
9
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1answer
2k 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, ...
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1answer
430 views

Energy band diagram for solid state: what is the meaning of $k$?

I am having trouble with the meaning of the $k$ vectors in an energy diagram. If I want to populate some band, let say using a laser, what will be the significance of $k$? Does it correspond to the ...
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0answers
640 views

how to determine the parity eigenvalues of time-reversal invariant momenta point from first principle calculation when we judge topological insulator?

This is a question of topological insulator. Liang Fu and C. L. Kane proposed a method to judge whether an inversion symmetric insulator is a topological insulator or not in their article(L. Fu and ...
2
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1answer
197 views

Can spin liquids without spin-rotation and time-reversal symmetries possess nonzero Spin Density Wave (SDW) order parameters?

For those spin liquids with SU(2) spin-rotation symmetry or time-reversal(TR) symmetry , the Spin Density Wave (SDW) order parameters are always zero, say $\left \langle \mathbf{S}_i \right ...
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0answers
83 views

Can classical orders coexist with quantum orders?

For example, the ground state of the antiferromagnetic(AFM) Heisenberg model $H=J\sum_{<ij>}\mathbf{S}_i \cdot \mathbf{S}_j(J>0)$ on a 2D square lattice is a Neel state, which is a classical ...
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2answers
353 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
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1answer
1k views

Difference between gapless excitations and Goldstone bosons in Condensed matter physics

I have been looking around on the web and in books to clarify this, but can't find a good explanation describing relationship/difference between gapless modes/excitations and Goldsone modes/bosons in ...
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0answers
156 views

A simple question on the projected wave function?

For example, consider a spin-1/2 AFM Heisenberg Hamiltonian $H=\sum_{<ij>}\mathbf{S}_i\cdot\mathbf{S}_j$, and we perform a ...
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1answer
96 views

What crystal structure have electrons in Wigner crystal?

If electrons form a crystal in the Wigner crystal what is the structure of that crystal? cubic, bcc, fcc,...?