Questions tagged [condensed-matter]

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

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On the Bogoliubov transformation in the BCS

I have a question regarding the diagonalization of the BCS-Hamiltonian using the Bogoliubov-DeGennes-transformation. I hope someone can help me, so I start with the following Hamiltonian, it is ...
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25 views

Numerical Calculation of Berry Curvature

I am trying to calculate some berry curvature (BC) in a 2D lattice and I have some things I am getting lost with. In the 2D lattice, we set up the eigenvalue problem $H|u_1\rangle = \epsilon_i|u_i\...
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36 views

What is difference between $U(1)$ symmetry and $U(1)$ gauge invariance

According to Wen's description if two states $|a\rangle$ and $|b\rangle$ with $\langle a|b\rangle=0$ have same physical properties, they are symmetric. On the the other hand if we label same ...
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1answer
152 views

Many-body states that do not belong to Fock space?

This question may be related with other phys. stackexchange questions: (q1) and (q2). Fock space is a direct sum of antisymmetrized tensor products of single-particle Hilbert space. In other words, ...
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36 views

Distance $E_F-E_i$ in a compensated semiconductor

Given two energy level diagrams for a compensated conductor: At $0~\text{K}$ At $500~\text{K}$ I want to determine for which diagram is the Fermi level closest/farthest from $E_i$. It's a ...
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18 views

Realtivistic interaction in graphene

Near the Dirac points, Graphene can be described by the Lagrangian equivalent to free massless Weyl spinors: $$ L_0 = \overline{\Psi}\gamma^\mu\partial_\mu\Psi \quad. $$ From the theoretical point of ...
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2answers
117 views

Exciton in semi-conductor

I don't understand why an exciton describes only the interaction between an electron hole and an electron in the conduction band? How is this interaction different from the interaction between an ...
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1answer
44 views

References and papers to distinguish between the Heisenberg and Ising Model

Does anybody have any good papers or references to explain the differences between the Heisenberg model and Ising model? To the best of my knowledge, I am aware that the Hamiltonians are similar, ...
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19 views

Harper-Hofstadter model in symmetric gauge

If I have l a square lattice, with the total flux = $\pi$, I can work in the symmetric gauge, which will have my vector potential be $A = \frac{\pi}{2}(-y,x)$. In a tight-binding model with Peirels ...
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8 views

What are possible causes that can lead a self consistent calculation to diverge in DFT?

I am extending a code written to do self consistent Density Functional Theory calculations to the case of spin polarized systems. Due to the modifications, the calculations are leading to diverging ...
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131 views

Fermion creation operator in boson basis

I've been reading Giamarchi, Quantum Physics in One Dimension, Chapter 2 on 1d bosonization, and in appendix B.1, he derives equation B.2, which represents the fermion creation operator $\psi_r (x)$ ...
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20 views

Projection into Lowest Landau Level and Fourier transform

I am studying Quantum Hall and therefore Laughlin wave functions and the Lowest Landau Level. States in the Lowest Landau Level have the form: $\phi_m(z,\bar{z}) \propto z^m exp( - z \bar{z} / 4 l^...
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1answer
120 views

Diatomic chain and speed of sound

I have been unable to obtain the speed of sound in a one dimensional diatomic chain. Suppose you have a diatomic chain with particles of mass $M$ and others of mass $m$. The particles of the same type ...
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11 views

How are the two Stacking Faults namely intrinsic(formed by vacancy agglomeration) and extrinsic(formed by interstitial agglomeration) different?

Stacking Faults and its association with partial dislocations seem to bother me day in and day out.With regard to this I do not understand how Partial dislocations lead to stacking faults and not the ...
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31 views

Help with understanding Pauli matrices in specific Hamiltonian

I am trying to explicitly write out using matrices a Hamiltonian given in this condensed matter paper. In eq (3) of the paper, we have: $$ \hat{H} = a t (\tau k_x \hat{\sigma_x} + k_y \hat{\sigma_y} ) ...
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38 views

How can a metal be magnetic in this way?

I am reading a book about Skyrmions (Skyrmions in Condensed Matter, by Jung Hoon Han), and while reading about the interaction of Skyrmions with electrons (Chapter 5), the following statement was made:...
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Certain doubts in Lomer Cottrell dislocation

With regard to this particular phenomenon that occurs there are a couple of things that need to be addressed.Firstly,Why do I have a region of stacking fault in that particular junction. I mean why is ...
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1answer
101 views

Deriving classical Hall effect from quantum Hall effect

I'm interested in the derivation of the classical Hall effect coefficient, given in cgs by $$R_{H}=-\frac{1}{nec},$$ where $n$ is the electron number density, $-e<0$ is the electron charge,and $c$ ...
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41 views

All infinite volume matrix product states are in different super-selection sectors?

Consider two matrix product states $\Psi_1,\Psi_2$, i.e. let them be described (schematically) by $$ \Psi_\alpha = \sum_{...i_n ... } \left(\ell_{\alpha}, \left[\prod_{i \in \mathbb{Z}} E_\alpha(i) \...
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Is there any qualitative difference between the WZW $SO(2)_1$ and the WZW $SU(2)_1$ CFT?

Consider the anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_{n=1}^N S^x_n S^x_{n+1}+S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ which for $\Delta = 0$ realizes the Wess-Zumino-Witten (WZW) $...
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1answer
120 views

Parity of Bloch states at TRIM points

There is an argument presented in Fu and Kane's paper on inversion symmetric topological insulator which I have not yet convinced myself. Just below Eq.(3.6), the authors said that because of ...
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1answer
119 views

Is an Ewald Sphere's centre always on Brillouin zone (BZ) boundary?

I am trying to understand diffraction a little better and eventually Kikuchi lines. I am confused about something -- namely the difference between the Ewald sphere and the so-called sphere of ...
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How is Meissner effect explained by BCS theory?

Someone says we can derive the GL equations from BCS theory, which can explain Meissner effect, but I want a more clear physical picture of this phenomena.
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2answers
90 views

Why is effective mass a tensor?

So I came across the effective mass concept for solids the other day. It was mentioned that the effective mass is a tensor and may have different values in different directions. However, this is stark ...
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27 views

Tight Binding Hamiltonian for graphene

The TB Hamiltonian for the tetragonal lattice is $ \hat H_0 = -J\sum_{m,n} (\hat a_{m+1,n}^\dagger \hat a_{m,n}+\hat a_{m,n}^\dagger \hat a_{m,n+1}+h.c.) $ How can this be derived for the hexagonal ...
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29 views

Does pseudospin break the crystal symmetry?

Pseudospin is a concept to describe a superposition of two quantum states. Sometimes, I see a pseudospin texture in the momentum space which breaks a crystal symmetry. A simple example is the ...
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19 views

Is there a theoretical ground for ionic superconductivity?

I've been wondering for a while if there's a possible theoretical ground for ionic superconductivity, or whether it is at all possible from a thermodynamic and condensed matter physics standpoint. ...
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1answer
124 views

Left and Right Eigenvectors of Transfer Matrix in Matrix Product States (MPS)

Let $$\lvert{\psi}\rangle=\sum_{i_1i_2...i_n}Tr(A^{[1]}_{i_1}A^{[2]}_{i_2}...A^{[n]}_{i_n})\lvert{i_1 i_2...i_n}\rangle$$ be a MPS, where $i_k=1,2...d$ and $A^{[k]}_{i_k}$ are $D\times D$ matrices ...
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342 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 $H=\sum_{ij}...
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202 views

Elastic properties of materials at low temperature

It is common knowledge that materials are more brittle at low temperature. But does it apply also on elastic deformations or is it just matter of plastic deformations? Practically: Is it possible to ...
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For what choice of the basis atoms origin the Structure Factor is real?

I have a Cuprite Structure: Now, given that I described this structure as a Simple Cubic lattice with a 6 atoms basis, I have to choose the origin for these basis atoms such that the structure ...
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3answers
162 views

Different energies for the same $k$-vector for free electrons in a solid

when we use the nearly free electron approximations for electrons in a solid and get them as plane waves the energy becomes $E=\frac{\hbar^2k^2}{2m}$, which gives us a parabola. but when we see the ...
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1answer
52 views

What is the physical meaning of the Kondo Temperature?

From my understanding, in a Kondo lattice, the Kondo temperature is where the resistivity dramatically drops. I've also read that the Kondo temperature is the only real "scale" in the physics, with ...
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26 views

Kosterlitz-Thouless transition and renormalisation group theory

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
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60 views

Band Structure for free electrons

Consider a BCC lattice. How can I explicitly calculate the expression of the n$^{th}$-energy band $E_n(k)$ with $n=1,2,3,4$ for free electrons from $\Gamma$ to $N=\frac{2\pi}{a}(1/2, 1/2, 0)$ as a ...
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1answer
151 views

In what condensed matter systems (without chiral anomaly) do we need two $U(1)$ gauge fields?

In condensed matter systems, we use a $U(1)$ gauge field to describe the electric current by charge carriers. If there is a chiral anomaly, there will be a vector $U(1)$ and an axial $U(1)$. Suppose ...
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Why the geometrical frustration (spin ice model) has never been studied in superparamagnetic size range?

I'm trying to understand the effect of geometrical frustration in assembly of superparamagnetic nanoparticles but I can't find any reference. Does anyone know how magnetism can be affected by ...
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1answer
176 views

Which Chern-Simons TQFTs are spin?

Refs.1&2 prove several level/rank dualities among different 3d Chern-Simons theories. An important point is that some dualities involve, on one side, a theory that depends on the spin structure, ...
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1answer
123 views

Laughlin wave function and CFT

I have a question regarding Eq. (3.5) in Moore & Read's paper. They said \begin{equation} \Psi_{\text{Laughlin}}=\left\langle\prod_{i=1}^{N}e^{i\sqrt{q}\phi(z_i)}\exp\left[-i\int \mathrm d^2z^{\...
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218 views

Nature of metallic bonding in solid state

What is the reason behind attraction of metal kernels & free electrons in electron sea model?
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Does an insulator always contain the Fermi surface in the 1st BZ

I'm looking for a clarification about the classification of metals and insulators; is it correct to state that if the Fermi surface is contained into the first BZ, then the material is an insulator, ...
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43 views

How to know which topological invariant is in play?

I'm currently working on the Haldane model where I've worked through the math to find that when the condition $$ \frac{M}{t_2} = 3 \sqrt{3} sin (\phi) $$ is satisfied the gap closes, meaning there ...
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62 views

Wavefunction of Cooper Pairs

I tried to solve the wave-function of cooper pairs but i am stuck in an integral equation and have no idea how to solve for the wave-function. Before, i tell you how i got the integral in brief. ...
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1answer
158 views

Quantum ising/heisenberg model, states representation

I am working with a hamiltonian which looks like this (Heisenberg model) I have made a program which computes this hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor ...
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2answers
72 views

Creating a spatial variation of phase in a given superconducting sample

Blundell's book on Magnetism, talks about the generalized rigidities as a general consequence of spontaneously broken symmetries. In this context, it mentions that in a superconductor the phase of the ...
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Vertex function and bounded state

I would like to understand how to see superconductivity phenomena from the two particle Green function. To do it, I try convince myself that bounded state appears as the pole of two particle Green ...
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14 views

Magnetization of spin system

suppose we have 3 spin particle system, with a given Hamiltonian we allow our system to evolve. after some time t suppose we perform measurement on identically prepared (evolved for t time) 1024 ...
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125 views

What is the meaning of the diamagnetic current in linear response theory?

When we consider the response of a quantum lattice model with Hamiltonian $H=H_{kin}+H_{int}$ to an applied vector potential $\mathbf{A}(\mathbf{r},t)$ we obtain the current operator $\mathbf{j}(\...
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Metal-Insulator from number of atoms in the basis

I have an issue understanding what A&M means while saying this in chapter 12: It is a reassuring exercise to go through the periodic table looking up the crystal structure of all insulating ...