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

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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 ...
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196 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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194 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 ...
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1answer
380 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
261 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 ...
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1answer
195 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
107 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
85 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 ...
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1answer
206 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
99 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
221 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
147 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
108 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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238 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
108 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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35 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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62 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 ...
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2answers
328 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
333 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
167 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 ...
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1answer
694 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
240 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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385 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 ...
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1answer
137 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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72 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
296 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 ...
5
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1answer
436 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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137 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
73 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,...?
6
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1answer
131 views

Material implementations of the holographic principle

I'm afraid this question is a little too open-ended, but bear with me while I find a better formulation. carbon allotropes (like fullerenes and graphene) are regular patterned. Conduction bands of ...
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1answer
155 views

Developement of modern condensed matter physics [closed]

Do you know any resources describing historical aspects of developments of modern condensed matter physics (many body physics etc)? Thanks.
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1answer
326 views

Parity of the ground state of a Majorana chain

I work on the Kitaev toy model for Majorana fermions. He writes that in Majorana basis the Hamiltonian becomes in general $$ H = \frac{i}{4} \sum_{l,m} A_{l,m}\gamma_{l}\gamma_{m} $$ where $\gamma$ ...
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1answer
561 views

What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade ...
6
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0answers
138 views

Finding difficulties in taking continuum limit in nonlinear sigma model

I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
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2answers
5k views

Why don't FCC metals have a brittle-to-ductile temperature transition?

I initially thought that it had something to do with the number of slip systems in FCC vs. BCC, but they're both the same.
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Definition of 'Majorana Number' in the Kitaev Chain

I have some questions about the Kitaev toy model for Majorana fermions (arXiv:cond-mat/0010440). First of all, his proof for the definition of the 'Majorana number' is not so clear to me. $$P(H(L_{1} ...
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59 views

Wavefuntion for Wigner Crystal

Quantum wavefunctions of infinite variables can be written that describe certain Fractional Quantum Halls states, such as the Laughlin family of wavefucntions $ \Pi_{i<j} (z_i-z_j)^k $ that ...
8
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1answer
404 views

Nambu-Goldstone bosons from a quantum anomaly symmetry breaking?

We know that: Nambu-Goldstone bosons come from Goldstone theorem: a spontaneous (continuous)-symmetry breaking of the system leads to massless scalar modes. quantum anomaly: is the anomalous ...
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1answer
337 views

Interpretation of the off-diagonal terms of the conductivity tensor

Say we have the electrical conductivity tensor expressed as a 3x3 matrix. I've seen that if it's cubic material then the conductivity tensor reduces to just the diagonal terms and these are equal, ...
6
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1answer
132 views

Does the Fermi surface make sense for “Fermi liquids” with non-uniform charge density?

For a Fermi liquid, the Fermi momentum is determined by the singularity of the Green's function at $\omega=0$, i.e., $G(\omega=0,{\bf k}={\bf k}_F)\to\infty$. Suppose due to an external field or ...
4
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2answers
458 views

topological entanglement entropy for a punctured torus and sphere

Topological entanglement entropy (http://arxiv.org/pdf/cond-mat/0510613.pdf, http://arxiv.org/abs/hep-th/0510092) is usually calculated for surfaces with boundary. How would it look like for compact ...
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1answer
88 views

If I take an XRD image of a single cubic unit cell, would the diffraction pattern simply be its reciprocal lattice?

I've seen the rings from powder diffraction images, and I read that each line is made up of a lot of dots, I was wondering if these dots are reciprocal lattice points of the structure. And if we ...
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117 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
2
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1answer
108 views

What is the broken-sublattice-symmetry phase in an intermediate temperature of the three-state antiferromagnetic Potts model?

I have just read one paper ( Phys. Rev. E 54, R5885 (1996) ) where it was mentioned that the broken-sublattice-symmetry (BSS) phase was stable in the whole low-temperature region. The BSS phase at ...
6
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1answer
1k views

Graphene's Tight Binding Hamiltonian

Graphene has two atoms in its primitive unit cell. This makes it intuitive to see that the tight binding Hamiltonian can be constructed as a $ 2 \times 2 $ matrix $H$ acting on a spinor $S$ that ...
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1answer
96 views

Is diffraction through an aperture similar to diffraction by a plane of atoms?

I'm asking because I have a problem asking me what the diffraction pattern would be if instead of spherical atoms I'd have triangular atoms. I can't find anything about this in my X-ray diffraction ...
4
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1answer
189 views

Fractionalization and the structure of spin rotation group?

As we know, the phenomena of fractionalizations in condensed matter physics is fantastic, like fractional spin, fractional charge , fractional statistics, .... And one key point is that the ...
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1answer
337 views

Diagonalization of a hamiltonian for a quantum wire with proximity-induced superconductivity

I'm trying to diagonalize the Hamiltonian for a 1D wire with proximity-induced superconductivity. In the case without a superconductor it's all fine. However, with a superconductor I don't get the ...
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2answers
971 views

Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? ...
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221 views

Are there solid materials with controllable porosity?

In analogy to piezoelectric materials, where the application of an electrical field creates mechanical deformation in the material, I have the following question. Are there solid materials whose ...