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Questions tagged [condensed-matter]

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

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Berry phase spherical coordinate calculation [closed]

The following content comes from david tong lecture notes on quantum hall effect, p34-35. My question is, how do we get the last equality $ \mathcal{F}_{ij} (\vec{B}) = -\epsilon_{ijk} \frac{B^k}{2|\...
sett the guy's user avatar
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Symmetry group and dualities

Let's say two quantum models $M_1$ and $M_2$ are dual to each other and let their symmetry groups be $S_1$ and $S_2$ respectively. Is it necessary for $S_1$ to be isomorphic to $S_2$? (I thought so ...
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Why are the number of $k$-points in the Brillouin zone different from the number of lattice sites?

Suppose I am doing some sort of Hartree-Fock/DFT calculation in momentum-space. Let us then consider a system comprised of $N$ lattice sites, with lattice constant a. The allowed $k$-points within the ...
meer23's user avatar
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Physical meaning of Cahn-Hilliard boundary conditions

Consider the 1D Cahn-Hilliard equation for a two-component mixture, on an interval $x\in[a,b]$: $\frac{dc}{dt} = -\frac{d}{dx}j(x)$ where the flux $j(x) = -D\frac{d}{dx}\left(c^3 - c - \gamma\frac{d^...
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Jellium Hamiltonian in the thermodynamic limit

In Fundamentals of Many-body Physics by W. Nolting, 1e, the author arrives at the following formula for the electron-electron contribution to the Hamiltonian of Jellium: $$ \hat{\mathcal{H}}_{ee}=\...
CW279's user avatar
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Non-crossing approximation (NCA) in 'Large-$N$ expansion' (Altland & Simons CMFT)

I have a question about non-crossing approximation (NCA) stated in Condensed Matter Field Theory by Altland & Simons1. It is on page 200-203 for the 3rd edition (on page 223-227 for the 2nd ...
Jinu.P's user avatar
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Why are quantum-many body problems difficult to solve? [duplicate]

I am a little confused about which classes of interacting many-problems are considered intractable. Suppose I have some tight-binding system with some nearest-neighbor density-density interactions, ...
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The criterion about maximally localized Wannier function (WF)?

I heard that as the value of "num_iter(tag in wannier 90)" is higher, spread of Wannier function (=WF) is gradually lower in wannier 90. If so, is this procedure that minimize the spread of ...
Y. S. Lym's user avatar
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Finding the classical antiferromagnetic ground state for the Kagomé lattice

I am attempting to do the following exercise in Altland and Simons Condensed Matter Field Theory: "Show that the classical antiferromagnetic ground state of the Kagomé lattice – a periodic array ...
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$p+ip$ pairing in a spinless fermion system with attractive interaction

In this article (Section III.D), the following model of spinless fermions on the honeycomb lattice is considered: $$ H = -t \sum_{\langle ij \rangle} (c^\dagger_i c_j + h.c.) - V \sum_{\langle ij \...
Zhengyuan Yue's user avatar
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Help in plotting the band structure of a maple leaf lattice

I was trying to plot the band structure of a maple leaf lattice. The Hamiltonian is given by: $H = t_1 \sum_{ij} (c^\dagger_i c_j + c^\dagger_j c_i e^{\phi_{ij}}) + \sum_{ij} \sum^{4}_{n=2} t_n (c^\...
Aaradhya Kulkarni's user avatar
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DMRG for anyons

I want to do some DMRG calculations for anyons. For example, consider the golden chain model for fibonacci anyons. https://arxiv.org/pdf/cond-mat/0612341 I have two anyon types: $1, \tau$. However, ...
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Bloch oscillations and umklapp scattering induced by applied electric field

In Kittel's book chapter 8 there is a statement that says "The electron accelerates from k = 0 toward the zone boundary; when it reaches k = pi/a it reappears (as by an Umklapp process) at the ...
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Permittivity real and imaginary parts with similar value possible?

Here's the context; I'm studying biological tissues that are supposed to behave like dielectrics. Using the modified cole-cole equation for theoretical predictions: $$\tilde{\varepsilon}_r (\omega )= \...
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What are some good references for periodic Hartree-Fock calculations?

I am looking to implement a Hartree-Fock program to study periodic, condensed matter system, however, I literally cannot find a single reference or example anywhere for how to do this. In the past, I ...
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Other than approximating the total energy of the system, what other information does the Hartree-Fock method provide?

In the Hartree-Fock method, one computes the energy of an interacting quantum-many body system, described by $H$, via taking a non-interacting trial ground state, $|\psi_{\mathrm{HF}}\rangle$, and ...
meer23's user avatar
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Can we tune chemical potential by gating in solids? [closed]

Often I heard that chemical potential in solids can be controlled by gating the sample, besides other things such as doping or changing the chemical composition. How feasible is it and if any ...
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Using particle-hole symmetry of the Hubbard model to study the model at different densities

In Condensed Matter Field Theory by Altland and Simons, they state that the Hubbard Hamiltonian $$ H = \sum_{\text{nearest neighbors } ij \text{ and spin } \sigma} a^\dagger_{i\sigma} a_{j\sigma} + U \...
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What is the material with the highest mass enhancement factor?

The electron phonon coupling mass enhancement factor $\lambda$ is a measure of the strength of this coupling. This quantity can be measured experimentally. For instance, Pb has a factor of 1.55 ...
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Mahan's derivation of energy current of a free-particle system

On p.25 of the 3rd Ed. analogously to the polarisation operator $\textbf{P}$ for particle currents $$\textbf{P}=\int\textbf{r}\rho(\textbf{r})d^3r$$ he defines an operator $$\textbf{R}_E=\frac{1}{2}\...
Redcrazyguy's user avatar
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How do you see that the Wannier functions are localized on ion sites?

In Condensed Matter Field Theory by Altland and Simons, when discussing the tight-binding approximation for a lattice system with a periodic potential, they define the Wannier states as follows: $$ |\...
zeroknowledgeprover's user avatar
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Is there a superfluid dual to superinsulators?

It's well known that there are many analogies between Superconductors and Superfluids. The diagram below explains a few: $$ \begin{matrix} \bf{\text{Superconductors}} \\ \text{0 electrical resistance} ...
Sidharth Ghoshal's user avatar
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Derivation of two-body Coulomb interaction in momentum space

$\newcommand{\vec}{\mathbf}$ In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
zeroknowledgeprover's user avatar
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Distribution of states in quasiparticles model and in SYK model

I am currently approaching the SYK model with a little Normal Fermi Liquid background (go easy on me, it's my first time!). I have encountered these slides by Sachdev, where at some point he talks ...
nepero27178's user avatar
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Solid-on-solid models

I'm currently wondering about the so-called Chui-Weeks model 1 2, given by $$ H = J \sum_i |h_i - h_{i+1}| + K\sum_i \delta_{0,h_i}, $$ which is a type of solid-on-solid (SOS) model used to describe ...
Wladislaw Krinitsin's user avatar
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Coordinate transform to account for periodic boundary conditions

I have this nice 2D wave packet that is coherent in both R and K space. I am trying to analyse its dynamics in the presence of a perturbation using semiclassical equations of motion and then compare ...
Abhiram Cherukupalli's user avatar
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Why surface and bulk states of topological insulators (TI) have different topological invariants and how it leads to conductive states?

I am trying to understand how TIs work. Right now, the main thing I understand is that the surface states and bulk states have different topological invariants. This leads to spin orbit coupling being ...
Lynn0903's user avatar
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Could there be states of matter that could avoid "matter decay"?

Regular structures of matter may decay over extremely long periods of time (especially if proton decay occurs, which is not proven but it remains a possibility) Even if that happens, are there any ...
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Calculation of Chern number from non-Abelian Berry connection

Does the calculation of Chern number using the Fukui method (Eq.16 of this paper) consider the non-Abelian Berry connection(i.e. $F = \partial_x A_y - \partial_y A_x + [A_x, A_y]$)? Or Is it simply ...
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Coulomb Blockade for a Quantum Dot

I'm working through sections of the textbook, "Many-Body Quantum Theory in Condensed Matter Physics" by Bruus and Flensberg. I'm specifically interested in transport through quantum dots ...
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Calculation of effective mass of electrons from energy dispersion relation for electrons

Given the energy dispersion relation for electrons, $ \epsilon_{k} = \beta(cosk_{x}a + cosk_ya + cosk_za)$ , I want to find out the effective mass of electrons at the boundary of the first Brilloin ...
Kalyan 's user avatar
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114 views

What is the Haldane gap?

The Haldane Phase is a topological phase of matter in which a Haldane gap opens due to the breaking of either time-reversal symmetry or inversion symmetry. Physically speaking, what is the "...
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DMI as a Superexchange?

Superexchnage interaction is an indirect exchange interaction between two magnetic ions; Anderson proposed a model that says the origin of this type of exchange is due to the arrangement of Molecular ...
Shubhay Dikkar's user avatar
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Equivalence of Wannier Functions and Atomic Orbital Wave Functions in the Tight Binding Approximation

In tight binding approximation, what I've learned is that we can write the wave function of an electron which satisfies Bloch theorem in lattice as $$ \psi(\mathbf{r})=\sum_{\mathbf{R}_s} e^{i\mathbf{...
Gao Minghao's user avatar
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1 answer
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1D Lattice with site dependent magnetic field

An external magnetic field is on a 1D lattice with N sites where each site has a magnetic moment, which can rotate freely. The magnetic field at the $j^{th}$ site is, $$\mathbf{B}_j = B_0 \cos\left(\...
HypnoticZebra's user avatar
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1 answer
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Are superinsulators perfect dielectrics?

In Wikipedia its stated: "The phenomenon of superinsulation can be regarded as an exact dual to superconductivity." I understand that superinsulators are terrible conductors. But its not ...
Sidharth Ghoshal's user avatar
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Is spin relaxation asymmetric in magnetic semiconductors?

I am considering photo-excitation in magnetic semiconductors (e.g. metal organic frameworks). The cartoon picture is like this: where there will be a spin polarization in the conduction band since ...
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Partition function of harmonic oscillator using field integral

I'm currently reading Altland and Simon's Field Theory, and while trying to solve the partition function of the harmonic oscillator I ended up with a question. Using a Hamiltonian of the form $H=\hbar ...
Tiago Pinto's user avatar
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dipole-radiation in semiclassical dynamics solid state

Using the semiclassical dynamics in solid state physics (electrons on a lattice with periodic potential, constrained to a band structure), we usually obtain that in the presence of external fields (...
Noam Ophir's user avatar
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1 answer
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Does there exist a superinsulating dual to quantum flux pinning?

The phenomenon of flux pinning is well documented in popular science. It essentially arises from the fact that a superconductor expels all magnetic fields unless the field travels through a very small ...
Sidharth Ghoshal's user avatar
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Does a superconductor with fewer defects flux pin more strongly?

In Jasper's answer its stated that the energy to move a flux-pinned superconductor goes into re-arranging the flux tubes that are passing through defects. In particular it's stated that it takes ...
Sidharth Ghoshal's user avatar
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99 views

Emergence of Dirac Cones: Triangular Lattice vs. Honeycomb Lattice

I'm reading the paper 'Honeycomb Lattice Potentials and Dirac Points' by Fefferman&Weinstein. To my understanding they claim that the existence of Dirac Cones at K/K' points is entirely determined ...
Julian's user avatar
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Which experiments can offer insights about Hubbard $U$ parameter?

When considering $\mathrm{DFT}+U$ calculations, people either go with (1) first-principles approach: calculating the $U$ parameter using linear response theory, $\mathrm{DFPT}$, $\mathrm{ACBN0}$, etc.,...
Abdul Muhaymin -Free Palestine's user avatar
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Difference between GW gap and BSE gap. How does net charge play a role?

The energy gap from BSE (GW-BSE) is just the lowest optical excitation energy. The energy gap from GW, from what I read, is the electron affinity (energy of adding an electron). I suppose this means ...
Bohan Xu's user avatar
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On the units of NRT-dpa electronic losses formula (Lindhard)

I'm trying to convert the PKA energy into damage energy following equation (5) of the NRT-dpa model article. In Fig. 1 you have an example of what you should get. Let's take $E=40keV$ (PKA), therefore ...
Abel Gutiérrez's user avatar
2 votes
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Quantization into Phonon in a multi-basis crystal

I am quite frustrated in quantizing the vibration of a multi-basis crystal. The specific point that confuses me is the potential term, which hinders me from decoupling the Hamiltonian as the sum of HO-...
Neophyte's user avatar
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What's the relations between Quantum spin liquid and Quantum magnetism? [closed]

I am a fourth years undergraduate student. Recently, I am seeking that my research direction for my upcoming graduate program, and I found that my tutor is working that direction (as shown in the ...
Tierisches Gift's user avatar
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42 views

How can red LEDs still give a faint glow at a voltage of only 1.4V? [duplicate]

How can a red LED work at a voltage of only $1.4{\rm V}$? Red photons have an energy of $1.77{\rm V}$ if we use $\lambda = 0.7\mu\text{m}$ in the relation: $$ E = \hbar \omega = \frac{2\pi\hbar c}{\...
Jos Bergervoet's user avatar
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Why do cryogenic temperatures usually result in higher conductivity, even (sometimes) superconductivity, but otherwise nonconductive Wigner crystals?

Wigner crystals are all the rage in the news, since around the start of the pandemic... But at what temperatures (and pressures?) do these cold materials create a nonconducting 'Wigner crystal' rather ...
Kurt Hikes's user avatar
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Why the coupling constant in context of different approaches has different energy dependence?

I know that in the language of renormalization group, the coupling constant in the Hamiltonian is dependent of energy, for example in condensed matter physics, of band width. So, we can do a 'poor man'...
Houmin Du's user avatar

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