Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
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What is the energy associated with the degrees of freedom of a nucleus?
I am following Martin in his book on electronic structure. On page 11 he explains that we discriminate between properties of matter due to the electric ground state, and excited states. He writes
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S-W correlation plot from positron annihilation Doppler broadening spectroscopy
From Doppler broadening spectroscopy, we get the S-parameter and W-parameter. I found a S-W correlation plot in many research papers. What information does this plot provide?
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How to discretize a Hamiltonian?
In the famous article Physical Review B 92, 064520 (2015), a theoretical model was proposed to realize the chiral Majorana zero mode.
$$H_{\mathrm{BdG}}=\left(\begin{array}{cc}{H_{0}(\mathbf{k})-\mu} ...
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Why is contact resistance proportional to $\frac{1}{\sqrt{F}}$ not $\frac{1}{F}$?
See pages 13-15 in "Electrical Contacts: Principles and Applications" for reference.
Imagine the following system:
Two flat, but rough, surfaces of the same finite area $A$ being brought together.
...
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Can there be quantum spin liquids in 1D?
It seems like everyone studies quantum spin liquids in either 2D or 3D. Can not there be quantum spin liquids in 1D?
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Reason for Kitaev chain Pfaffian being calculated in momentum space
In Kitaev's paper where Kitaev defines his toy model for observation of Majorana fermions (MFs), he suggests a method of determining whether a system contain MFs at it ends. This method is to ...
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How to understand long-range propagate without decay in time and space?
Assume there is a Green function:
$$G=\frac{1}{(p^2+r)-\sum-\omega^2}$$
where $\sum$ is self-energy. We know that if the self-energy vanishes, the quasi-particle is well-define, and it can propagate ...
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Master Thesis in Theoretical Condensed Matter Physics [on hold]
I will start planning my master thesis in theoretical physics next semester and my supervisor wants me to come up with suggestions. I am working at the center of condensed matter theory and he wants ...
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Superfluid Vortex Lines Bifurcation and Winding Numbers
Vortex lines in superfluids are characterized by their quantised circulation: $k = \frac{h}{m}\times n$, where $n$ is the winding number in the sense of a topological winding number. Now, most vortex ...
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What are the properties and codomain of the spin $\alpha$, $\beta$?
I am following Mike Finnis on interatomic forces in condensed matter. I believe he uses the letter $s_i$ to denote spin number $\pm 1/2$ for fermions for example. But he has two functions $\alpha,\...
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(Transverse) Ising Model Higher Than Four Dimensions
First question:
Wiki says Ising Model higher than four dimensions can be described by mean field theory. What is the reason for this? Does this mean there is no phase transition for higher dimensions ...
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Deriving the expression for one body density
My textbook (Richard M. Martin - Electronic structure) has the following equation for the one body density of a system of $N$ electrons:
$$
\langle \Psi | \Psi \rangle n(r) = \langle \Psi | \hat n(r) |...
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67 views
How can you know that 2 photons are occupying the same location?
Someone told me once that a photon can be in the same exact location of another photon. Because they are bosons and have spin 1 you can have billions of photons occupy the same location.
I was ...
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How to derive the nearest neighbor Rashba spin-orbit coupling term?
I know that Rashba SOC can be written in the form of $(\mathbf{s} \times \mathbf{p}) \cdot \hat{z}$, but how can I get the Rashba SOC in tight-binding model :$i \lambda_{R} \sum_{\langle i j\rangle} ...
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80 views
Fermi level and chemical potential in doped and pure semiconductors
Recently I was studying about band theory of semiconductors and I have some questions.
I found two definitions of Fermi level
$1)$ The quantum state which has a probability of occupancy of $0.5$
(...
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The Gell-Mann and Low theorem and the expansion of the Green function
If we have a system with Hamiltonian $H = H_{0} + V$, with $| \Phi_{0} \rangle$ being the ground state of the system without the interaction, the Gell-Mann and Low theorem say that the quantite
$$ |\...
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Mathematical definition of a Wigner–Seitz cell
Let $\mathfrak{A}$ be a Bravais lattice generated by the primitive vectors $a_1,a_2,a_3$. We know that the Wigner–Seitz cell of a lattice point is the region of space that is closer to that point than ...
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50 views
Does the air conduct electricity?
If the air is compressed at high pressure in a container, then the volume of the air is less, therefore the air molecules are close to each other.
If electricity is passed through the container, do ...
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Sensitivity of electron tunneling on cross section of particles
In the industry of nanocomposite materials, electron transport through the system is governed by electron tunneling. Often, in such materials, with the right amount (to form a percolative network) of ...
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2answers
51 views
Treatment of electrons and phonons in condensed matter physics
I was watching the lectures by steve simon(oxford) on solid-state physics. In the course, he derived the dispersion relation for phonons(assuming spring between atoms) and dispersion relation for ...
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Which is the difference between Josephson and Rabi oscillations?
Consider a bosonic Josephson junction, such as a Bose-Einstein condensate trapped in a double-well potential. What are Josephson oscillations and what are Rabi oscillations? In what do they differ?
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Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation
In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in ...
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Feynman diagrams in quantum transport theory
I'm looking to find references that describe the role that Feynman diagrams play in quantum transport theory.
I have heard discussions where it is possible to just insert a self-energy loop into an ...
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1answer
49 views
Renormalization when there is spontaneous symmetry breaking
Standard quantum field theory textbooks discuss spontaneous symmetry breaking with the following Lagrangian:
$$L=\frac{1}{2}\partial_{\mu}\vec{\phi} \cdot \partial^\mu \vec{\phi}+m^2\vec{\phi}\cdot \...
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X-ray diffraction by Debye-Scherrer Method
I was watching lectures by Dr. Steve Simon(Oxford) at Stanford. He said that in a Debye-Scherrer Method for measuring X-ray diffraction, you should calculate d(spacing between lattice planes) by $$d=\...
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23 views
How to relate Green's function at finite temperature with thermodynamic magnitudes
I obtained the Green function at finite temperature for a given system using a simulation. This means I have a list of numbers that represent G(t). Now I would like to use this information to compute ...
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Difference in energy between fine grain and large grain
Whenever there is a question of grain growth there are two things that simultaneous are asked.Whether the grain growth should take place should be governed by two things the volume factor(whether the ...
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10 views
Characteristic energy quantum fluctuations as opposed to Boltzmann thermal energy
Heretofore, I was browsing a Wikipedia article on quantum critical points, and I came across the statement that the characteristic energy of quantum fluctuations is always smaller than characteristic ...
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1answer
29 views
Derivation of density of states (free electrons)
I am reading Condensed matter physics from M.Marder.
This is the derivation for the density of states for free electrons.
$\begin{aligned} D(\mathcal{E}) &=\int[d \vec{k}] \delta\left(\mathcal{E}...
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“Imaginary-time” argument in high energy physics
In many-body physics, there are many "imaginary-time" techniques, such as Matsubara Green's function, imaginary-time path integral and others. It seems that these concepts are frequently used in ...
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Speed of sound in Aluminum given the debye temperature
I am trying to calculate the speed of sound in aluminum given the Debye temperature $\theta_D=428 \;\mathrm{K}$, the mass density of Al is $\rho = 2.7 \cdot 10^3 \;\mathrm{kg}\cdot \mathrm{m}^{-3}$, ...
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Is there a general behavior of energy gap under renormalization?
Perform real space renormalization on a discrete lattice model with a finite energy gap. Is it always true that under the flow of coarse-graining, the energy gap will only increase?
I think the ...
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1answer
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Deriving the Heat capacity from Fermi-Dirac statistics
I was watching the lectures on Solid state physics by Steve Simon (Oxford). He was explaining how to find Heat capacity of metal due to electrons from Fermi-Dirac statistics. You can write the total ...
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How to derive the $t$-$J$ model from the Hubbard model in the $U \gg t$ limit
Assa Auerbach derives the $t$-$J$ model starting with the zeroth-order Hamiltonian $\mathscr{U} = U \sum n_{i\uparrow} n_{i\downarrow}$ and then includes the hopping term $\mathscr{T}=-\sum t_{ij} c_{...
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Calculating a correlator
Consider a system of a quantum dot coupled to a metal (tunneling Hamiltonian approach). Creating and destroying electrons in the dot is done with the operators $c_{d\sigma}$ and $c^{\dagger}_{d\sigma}$...
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Difference between electrical conductivity and optical conductivity
Is there any difference between electrical conductivity and optical conductivity? How to explain it physically and is there any method available to connect them mathematically?
If I calculate carrier ...
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1answer
81 views
First-order Contribution to the Self-energy Operator
In Altand and Simons' book 'Condensed Matter Field Theory,' on page 225 they claim that the first-order contribution to the self-energy (effective mass) operator reads
$$\big[\Sigma_p^{(1)}\big]^{ab} =...
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Strange symmetry of Haldane model edge
In the Haldane model we break both the inversion symmetry and time reversal symmetry, as a consequence I didn't not have any expectations when it comes to symmetry of the energy bands. However, to my ...
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quantum order in a (generalized) thermal steady state
It is known that starting from an initial product state, non-integrable systems will thermalize and eventually local observables can be described by a Gibbs ensemble. It has also been argued that a ...
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Does flat band imply localization?
Consider the Kitaev chain, whose Hamiltonian is as follows:
$$ H = -\mu \sum_n c_n^\dagger c_n -t\sum_n (c_n^\dagger c_{n+1} + \mathrm{h.c.}) +\Delta \sum_n (c_n c_{n+1} + \mathrm{h.c.}) $$
I have ...
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What is the best numerical way of solving this Schwinger-Dyson equations?
I have to solve these equations numerically
\begin{equation}
\begin{cases}
G(\omega)=\frac{1}{-i\omega-\Sigma(\omega)} \\ \Sigma(\tau)=J^2G(\tau)^2G(-\tau)
\end{cases}
\end{equation}
These are the ...
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63 views
About symmetry constraints in momentum space
When people study symmetry protected topological phases, certain symmetry constraints are enforced on the Hamiltonian. Specifically, for non-interacting fermionic systems, we could focus on the ...
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Nielsen-Ninomiya Theorem on a 2+1 lattice
(a) In the paper on the proof of the Nielsen-Ninomiya theorem, it is shown for 1+1 and 3+1 lattices. Does the proof hold on lattices with even number of spatial dimensions (e.g 2 spatial + 1 time)? If ...
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1answer
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What are $U(n)$ or $\mathbb{Z}_2$ quantum spin liquids?
Quantum spin liquid is a state of matter in which spins are correlated and fluctuate even at zero temperature.
My question is about these terms in general. When we say that a state or a quasi-...
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Transition Dipole Moments and Quantum Yield
I'm using some DFT calculations to compute Transition Dipole Moments between the HOMO and LUMO of a molecule in different geometries. Intuitively, this is closely related to the relative probability (...
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2answers
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Tight binding model contradiction
I have been studying recently the tight binding model and there is a point I cannot understand. First, it starts from the idea that the electrons belong to the atom more than to the crystal, so they ...
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1answer
60 views
What is a rigid wave function?
The London equations prior to BCS that describe superconductivity require assuming the wavefunction describing the superconducting pair of electrons to be rigid. I've been looking all over trying to ...
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Reduction from PEPS to MERA possible?
Multi-scale entanglement renormalization ansatz (MERA) includes two kinds of isometric tensors, disentanglers and isometries. Thus tensors in MERA are by definition composed of isometries. Meanwhile ...
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1answer
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When are the off-diagonal terms of magnetic susceptibility tensor non-zero?
The susceptibility tensor is defined as
$$
\bf{M}_i = \chi_{ij} \bf{H}_j.
$$
From looking at a material's geometry and crystalographic properties, is it possible to say whether the off-diagonal ...
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1answer
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Related to error propagation in crystallite size calculation from Scherrer formula
I am trying to calculate the error in crystallite size calculation from Scherrer formula $ t=kλ/β\cos\theta $ and I have calculated error propagation using the formula $\Delta t/t = \sqrt((\Delta\beta/...
