Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
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Question about sign convention in electron hole crystal momentum
I was trying to understand a toy model Raman scattering diagram from a paper on pressure tuned moire phonons, when I realized the standard electron hole pair creation diagram confuses me. By ...
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What is the difference and relation between Hartree-Fock and Hartree-Fock-Bogoliubov?
In nuclear physics literature, both appear very often.
HF is easy. It refers to a variational method with a Slater determinant variational wave function. What is HFB? Does it refer to a similar ...
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What does the mean field approximation mean in the Maier Saupe Model (and the Ising Model)?
I am trying to understand what the mean field approximation means when expressed in tensor notation for the Maier-Saupe Model of nematic liquid crystals. I am following along with Jonathan Selinger's ...
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Orthonormality of Wannier functions [duplicate]
In "Modern Condensed Matter Physics" by Girvin and Yang, a question invites the reader to prove the orthonormality of the Wannier functions. My proof will be complete if
$$
\langle n',0\vert ...
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Where is the kinetic energy functional error in the exchange-correlation functional of DFT?
The Kohn-Sham DFT energy functional is:
$$E[\rho]=T^S[{\varphi_i}]+J[\rho]+M[\rho]+E^{xc}[\rho]$$
with the kinetic energy functional of non-interacting electrons $T^S$, the Hartree functional $J$, the ...
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Searching magnetic materials on the basis of point groups symmetry
Where can I search a list of magnetic materials by just knowing the point group symmetries?
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How to conceptually understand bands in a solid?
I am having some trouble making the jump from single electrons to solids. In David Tong's notes, I have worked through the tight binding model section. Here, we solve for the energy levels that result ...
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What is the correct inversion symmetry in a two-band model
Consider a simple two-band tight-binding model
$$H(k)=\sin{k_x}\,\sigma_x+\sin{k_y}\,\sigma_y + \left(\sum_{i=x,y,z}\cos{k_i}-2\right)\sigma_z.$$
Let's assume $H$ is for real spins. It breaks the time-...
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Explicit construction of integrals of motion in 1d XXZ model for few sites
I was studying the algebraic Bethe ansatz for the spin-1/2 XXZ model. In the end one ends up with $2^L$ integrals of motion $Q_k$ that commute with the Hamiltonian, (https://doi.org/10.1103/...
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Electron momentum in a one-dimensional lattice and conservation issue
A one-dimensional lattice is a periodic array of atoms or ions where any two adjacent ions are separated by a fixed distance, the lattice spacing $a$. The Hamiltonian of an electron moving in this ...
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Why are we allowed to treat the moiré superlattice like a single layer with a different periodicity? [closed]
Is this just an approximation? When does it not work?
For twisted tri-layer graphene for example, where do I imagine the electrons lying in the material? Are they propagating through all 3 layers or ...
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What is the ground state of a Hamiltonian in $k$-space after Bogoliubov transformation? [duplicate]
Consider the following Hamiltonian in $k$-space, quadratic in terms of the $\gamma$ operators:
\begin{equation}
\hat{H}_2=\frac{1}{2}\sum_k
\begin{pmatrix}
\gamma_k^\dagger & \gamma_{-...
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Given a solid, predict the number of filled electronic bands
Suppose I have ZnS that's described via an fcc lattice with basis [$\frac{1}{4}, \frac{1}{4},\frac{1}{4}$], therefore we have 4 Zn and 4 S per unit cell. Zn has 2 valence electrons and S has 6 valence ...
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Calculating Madelung constant via Ewald summation [closed]
I am attempting to calculate the Madelung constant for NaCl using an Ewald sum derived by Nijboer. There are other methods and published codes to do this, but I am specifically interested in working ...
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How can valley coherence be defined if the crystal is initially in a mixed state?
In the field of valleytronics, they refer to valley coherence as: "the phase relationship between a particle in a superposition of two different valleys" [S. Vitale et al., Small 1801483 (...
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Does the number of electrons in a material affect the density of states in this material?
The Fermi-Dirac distribution, given by
$$f(E) = \frac{1}{1 + \exp\left(\frac{E - E_{\text{F}}}{k_{\text{B}} T}\right)}$$
describes the probability that a state with energy $E$ is occupied by an ...
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How to exactly calculate the chemical potential in the density matrix from the expectation value of the conserved quantities?
We know that the equilibrium state of an integrable model can be described by a generalized Gibbs ensemble (GGE). Suppose, we have an integrable model where all the conserved charges are given by $Z_i$...
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How check the c4v symmetry in a hamiltonian?without using geometry
In the 2D square ssh model, how to check that the Hamiltonian does not change under c4v symmetry. Based on the square geometry of this model, it is possible to realize the existence of c4v symmetry, ...
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In solid state physics and Density Functional Theory, how are Van Der Waals forces modelled?
Given a material, I'd like to know how to treat VdW interactions among layers. Specifically I'm using Quantum Espresso, an open-source suite based on Density Functional Theory, and I'd like to know ...
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Can charged boson be emergent?
Dirac's initial interpretation of antimatter is the existence of Dirac Sea. However, it doesn't work for bosons since we can't invoke Fermi's exclusion principle. Goldstone boson can be emergent but ...
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Is there a generic behavior of Spectral Form Factor for Integrable models?
The spectral form factor is defined as (usually taken at $\beta = 0$ by definition along with disorder average)
\begin{equation}\label{eq:SFF1}
g(\beta,t) = \left| \frac{Z(\beta,t)}{Z(\beta)}\...
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Plateaus in Quantum Hall Effect and its Robustness
I was studying Quantum Hall Effect and there I came out with a question that why the plateaus in the plot of Hall Resistivity are robust ?
I know by solving Schrodinger equation and using Landau Gauge ...
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Why is it not Pin(1,3) or Pin(3,1) in condensed matter physics?
In electron systems (or condensed matter physics), it is well known that $T^2=-1$ and $M^2=-1$, where $T$ and $M$ are time reversal and reflection along some axis. But in general, the symmetry of ...
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Does the total Zak phase always sum to zero?
In 2D, the sum of the Chern numbers over all bands is zero. However, this result relies on the ability to define a Berry curvature, which is only possible in $d \geq 2$ dimensions. In 1D it is ...
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Why a crystal lattice with short axes would have a diffraction pattern in which spots would appear far apart using Bragg's law?
With the aid of Bragg's law, explain why a crystal lattice with short axes would have a diffraction pattern in which spots would appear far apart?
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Construct an operator using outer product of two MPS using TeNPy
I am fairly new to MPS formalism, but I've used DMRG techniques before. I'm learning to use TeNPy, and a particular problem I am trying to tackle is given a state $| s \rangle$ as a MPS, is there an ...
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How to compute the Chern number of a quantum dot (zero-dimensional topological insulator) in AI class?
Looking at the periodic table of topological insulators, the AI class (only time reversal symmetry is preserved) has a $\mathbb{Z}$ invariant for zero-dimensional topological insulators. In the review ...
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Help understanding the formation of band gap
I need some help understanding how the energy band gap is formed. Here is my understanding so far:
Starting on the farthest right (largest interatomic spacing), the Si atoms are separate and thus ...
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Berry curvature Weyl and Dirac points
I understand that Berry curvature sinks and sources correspond to Weyl points. However, I'm curious about the identity of points exhibiting a Berry curvature spiral, highlighted by red circles in the ...
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Some references on Dh4 point group ans superconductors
Just wondering if anyone has any lecture notes or books/chapters which cover the representations of Dh4 CLEARLY. In particular, the form factors of superconductors are labeled with the representations ...
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Structural notation for multi-element FCC crystal structures
I was wondering if different compound FCC structures share any kind of indicator or structural notation which I could use to find and categorise them.
To clarify my problem: the FCC L12 structure, ...
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Spectral gap (barrier) under centain symmetry
I have recently been taught the problem of preparing the ground state with an adiabatic process, which requires the instantaneous Hamiltonian to have an energy gap between the ground and the first ...
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Lattice symmetry operations in strongly spin-orbit coupled systems
I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references.
Background
Considering a Hamiltonian defined on a triangular lattice:
\...
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In Cyclical Cosmology (Big Bounce) is it possible the new universe will be different or the same? [closed]
Could it be a universe with similar laws to ours but a different configuration of matter, so there may be another earth like planet in this new universe?
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Continuous wave function and non-continuous probability density. Is this possible?
I'm currently dealing with the 2D Dirac equation with an inhomogeneous mass term ($-M$ for $x<0$ and $+M$ for $x>0$) with an external magnetic field applied.
If I impose continuity at $x=0$ for ...
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Floquet Hilbert Space
Why do we need the extended Floquet Hilbert Space $\mathcal{F}$ to study the Time Periodic Hamiltonian (i.e., $H(t+T)=H(t)$)? What is the problem with the Normal Hilbert Space?
Where we define the ...
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Ambiguities of the Hubbard-Stratonovich decoupling
Consider an interacting fermionic theory on some lattice $\Lambda$ with action
$$
\mathcal{S}[\bar{\psi},\psi] = \int_{0}^{\beta} \mathrm{d}\tau \sum_{i\in \Lambda} \sum_{\sigma = \left\{ \uparrow,\...
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Question about statistical field theory
I am starting to learn statistical field theory. The "infinite number of degrees of freedom" refers to the continuous nature of field variables in field theory, where there are infinitely ...
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What is altermagnetism?
Since 2022, I have come across several papers on Altermagnetism, a novel phase of matter that breaks time reversal, but without a net magnetization. It also has many other interesting properties.
What ...
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Spinon is charge neutral or has a unit charge?
I have studied that spinons are charge neutral particles and have spin 1/2. But in XG Wen’s book (quantum field theory for many body system), it is mentioned that spinon coupled to gauge field carries ...
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Band structure diagrams
In band structure diagrams, usually we show the dispersion relation between energy $E$ and the wave vector $\textbf{k}$.
Consider the band structure of $\alpha$-Polonium. Shown in the graph below.
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What is Helicity in High Harmonic Generation?
The harmonic spectra are calculated as $|FT(\frac{d}{dt}\mathcal{J}(t))|^2$, where $FT$ si the Fourier Transform and $\mathcal{J}(t)$ is the current. We need to identify which multiple of incident ...
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Bose-Einstein condensation explanation
I am reading the introduction of The mathematics of the Bose gas and its condensation by E. Lieb, R. Seiringer, J. Solovej and J. Yngavason. The authors explain how, in the free case, the density in ...
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Sign ambiguity of two diagrams in Mahan's book
In Mahan's book 'Many-particle Physics' 3rd Ed., Eq. (3.213) on page 135 gives a sign rule for Matsubara Green's functions $$(-1)^{m+F}$$ where $F$ is the number of fermion loops and $m$ is the order, ...
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Materials known to have higher density than Osmium at at high pressure and/or low temperature
This question is basically a modification of this.
It's well known that Osmium is the densest material you can find at room temperature and pressure. I am curious at higher pressures (and lower ...
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Impact of labeling in a bloch-crystal with orbital basis
If I'm diagonalizing a hamiltonian of electrons in a crystal that is written in the orbital basis, does it matter whether I calculate the matrix element between one atom and another atom (or the image ...
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Landau levels versus Bloch states
People talk a lot about quantum Hall effects without Landau levels. It seems that there are two kinds of quantum Hall effects, with Landau levels or without Landau levels. In the second case, it is ...
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Why Zeeman coupling can be used in Bogoliubov-De Gennes superconducting Hamiltonian and Josephson junctions model for Majorana?
It is well-known that type-1 superconductivity holds perfect diamagnetism, which means that magnetic field is expelled by the superconductor.
However, there are cases, especially in the topological ...
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Can you evaluate the Berry phase integral? [closed]
This is my first post. Can anyone simplify the integral in eq(8.16) in the picture. How the integral is evaluated ? How the sign function came to the scenarion? The pic taken from the book "...
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Calculate partition function of 1D quantum Heisenberg models?
For the 1D Quantum Heisenberg Spin Model:
$\displaystyle {\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z + h\...
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