Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
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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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What does a correlation function measure and how does it do this mathematically?
I would really appreciate if someone could explain.
What does a correlation function like a density-density correlation function
$$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$
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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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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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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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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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Mean Field Theory on Random Graphs
We traditionally use mean field theory to analyze graphs with some degree of translation invariance. This assumption of translation invariance enables a key algebraic simplification which makes ...
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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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Why do we have overscreening?
In lecture, we discussed electron shielding as an additional influence in the interaction between electrons and ions.
My understanding of shielding is that because of coulomb force, electrons have a ...
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How to construct the matrix of Hamiltonians for a hexagonal lattice?
For part of a project I need to solve the time-independent Schrödinger equation, $\mathbf H\Psi = E\Psi$ (where $\mathbf H$ is the matrix with elements $\langle\Psi_i|H|\Psi_j\rangle$, and $\mathbf S$ ...
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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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Sign in Peierls substitution
A method often used to couple a lattice tight binding model to a magnetic field is the Peierls substitution, whereby one changes all hopping elements (schematically) as $t_{ij}\mapsto t_{ij}\exp(\...
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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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Is the Berry curvature in perfect monolayer graphene zero?
I'm struggling to reconcile two concepts and understand if the Berry curvature in graphene is zero or non-zero. Following the reference here, given a generic two-level Hamiltonian (eqn 1.15)
$$H=\...
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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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$\mathbb{Z}_2$ Symmetry in Water
I have learned that the critical exponents for phase transitions is independent of the microscopic structure of the substance and is dependent on the symmetry. For instance the phase transition for a ...
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Why hexagonal closed packed structure is not a Bravais lattice?
Why is the hexagonal closed packed structure not a Bravais lattice?
How can one readily say that a particular lattice is Bravais lattice or not?
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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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How to determine the peak of the dielectric function represent an exciton?
I am reading a paper about exciton-induced dielectric function peak, but I am not sure how could I determine the peak of dielectric function represent an exciton?
The original paper is on Nature ...
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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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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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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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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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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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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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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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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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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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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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Connection between momentum space derivative and Position operator
The crystal momentum $p_1 =\hbar\cdot k $ and this is defined in the reciprocal momentum, I am guessing this $p_1$ is not a real momentum since the reciprocal space is an imaginary space which we use ...
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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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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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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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Order and Disorder Operators in QFT
On the wikipedia page, the 't Hooft loop operator is called a "disorder parameter," in contrast to the Wilson loop operator, which is an "order parameter." From my limited ...
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Computing the density operator commutation relations (Altland & Simons)
I'm trying to work through Altland and Simons' example of interacting fermions in one dimension. It's in chapter 2, page 70 (you can find it here).
They define fermionic operators
$$
a_{sk}^\dagger
$$...
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Bose-Einstein condensate and one-particle state
I am a little confused about the definition of a Bose-Einstein condensate. It is said that, in such a condensate, a huge number of particles are in the same state of lower energy. The term state of ...
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Normal modes of a circular array of interacting particles
I want to study the normal modes of an array of $N$ identical atoms placed in a circular lattice. The particles interact among them via Yukawa interaction potential,
$$\phi_Y(r)=\frac{A}{r}exp(-r/r_0)....
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