Questions tagged [condensed-matter]

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

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Finding eigenvalue and eigenvector of non-Hermitian matrix product operator

Suppose we have a matrix product operator (MPO) $X$ with a periodic boundary, which is not necessarily Hermitian. That is, $$X^{s_1\cdots s_n}_{s^{\prime}_1\cdots s^{\prime}_n}:=\mathrm{Tr}(G_1[s_1,...
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Constraints in path integral and the Lagrange multiplier

I was reading some references on the slave-particle approach to the Kondo problem and Anderson model. It is known that the slave-particle is introduced in the large Hubbard $U$ limit of the system so ...
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How to calculate optical conductivity from numerical eigenstates of tight-binding model?

Let's say we have a 1D spatially inhomogeneous tight-binding model that does not have momentum as a good quantum number. We can numerically diagonalize it to get the spectrum and eigenstates. But how ...
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30 views

Some confusion in Drude theory of metals

Discussion on the drude theory of metal usually begin with the case of zero magnetic field so that the force acting on the electrons is just the one from the electric field. But then, this electric ...
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37 views

Getting the Bose-Hubbard Hamiltonian from cold atoms

In the famous paper by Dieter Jaksch, it is shown that the usual Hamiltonian for cold bosonic atoms interacting by s-wave scattering (Equation (1) in the paper): $$ \hat{H}=\int d^3 x\hat{\psi}^\...
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Representation of spin-$1/2$ operators in terms of Majorana fermions

I am reading Quantum Field Theory in Condensed Matter Physics by A.M. Tsvelik. In Chapter 20, it is claimed that introducing three Majorana fermions $\gamma^\mu_i$ on each site $i$ of the lattice (...
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29 views

Why do we have to introduce quasiparticles in the Fermi liquid theory

Why is it necessary in Fermi liquid theory to introduce quasiparticles? I understand the notion of system where someone can turn on the interactions slowly (i.e., adiabatically), but I do not ...
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15 views

Magnetoresistance

Why free electron theory could not explain magnetoresistance, but the two0band model could. I need the physics behind the explaination. A lot of theory have been provided, but how to physically ...
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1answer
38 views

Maximum metallic resistivity: dependence of resistivity on temperature

The electrical resistivity of metals usually increases with temperature. For a metal like copper at room temperature it increases almost linearly with temperature. At melting point we see a jump in ...
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54 views

Thermal average of fermionic operators in QFT

Consider the following expression of a thermal average involving fermionic operators \begin{equation} \sum_{\nu, \nu', \sigma, \sigma'}\langle c_{\nu,\sigma}^{\dagger}(t)c_{\nu',\sigma'}\rangle, \end{...
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High Temperature Expansions and Cumulants

In this paper the authors perform a high-temperature expansion of the correlation functions for a Heisenberg model on a lattice. Starting from $$\left<\mathbf{S}_i\cdot\mathbf{S}_j\right>_\beta ...
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Vacuum restructuring for superconductivity

I have posted several questions about superconductivity recently and all of them are related to vertex function but these questions were incorrect. I have found the following statement in book ...
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34 views

Connection between Matsubara frequencies and Landau Quasiparticle Interpretation

In a zero-temperature Fermi liquid, I understand that Landau quasiparticles correspond to poles in the interacting retarded Green's function, with the quasiparticle weight given by the residue of said ...
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Number of edge states as Topological Invariant

Can anyone please direct me to some sources which provide some definite rigorous proofs for the fact that the number of edge states ($N_A-N_B$ in case of SSH Model) is a topological invariant
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How does this quantity transform under time reversal and inversion operation respectively?

Suppose $\psi_{nk}=e^{ikr}u_{nk}$ is the Bloch function of a periodic Hamiltonian $H(r)=H(r+R)$, where $H(r)\psi_{nk}=\varepsilon_{nk}\psi_{nk}$ and $H(k)=e^{-ikr}H(r)e^{ikr}$. What would the ...
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How imaginary part of susceptibility is measure of dissipation?

In linear response theory, we focus only imaginary part of the generalized susceptibility and consider it a measure of dissipation in the system. Can someone throw some light at it that what is meant ...
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Fourier Transform from lattice site into $k$-space in Hubbard-Holstein model

Say I have a one dimensional lattice with lattice constant $a$. With next nearest neighbor hopping (NNN) included, the hopping term that describe such system would be $$H_{hop} = -t\sum_j(\hat c_{j+1}...
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Auger electron spectroscopy

I am doing Auger electron spectroscopy on a sample. I found the differential spectra is not symmetrical. For example, oxygen peak in as received sample looks symmetrical but that for carbon is not ...
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29 views

Polarization operator of fermi system

I misunderstand the following derivation. The polarization operator is given by the integral: $$\Pi(\omega,{\bf k})=-2i\int\frac{d\epsilon}{2\pi}\frac{d^3p}{(2\pi)^3}G(\epsilon_+,{\bf p}_{+})G(\...
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Understanding the Born-Mayer binding potential for ionic crystals

what was supposed to be a simple question, turned out to be a conundrum. I am asked to plot the Born-Mayer potential energy for a single pair of positive and negative ions. The potential energy is ...
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Diamagnetic current in the BdG superconductor

Recently, I am following the paper arXiv:1610.01803 to study superfluid weight. In this paper the diamagnetic current is given by: $j^D_{\mu}(\vec{q})=\sum_{\vec{k},\sigma}\partial_{\mu}\partial_{\...
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How to know the symmetry (point group) of crystal field in a material?

As an example, Let's consider a material $Ba_{2}YMoO_{6}$,(ref:PRB 81,224409), the space group of this material is Fm3m, the crystal structure is shown below (https://journals.aps.org/prb/abstract/...
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Why are we even assuming $\alpha Gb^2$+$\alpha Gb^2$ on one case and again $\alpha G(2b)^2$ on the other case?

My point of interest is to know where the energy of two edge dislocation system comes from ($\alpha Gb^2$+$\alpha Gb^2$).It not really the formula that I am looking for but essentially why are we ...
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70 views

Solution Cahn-Hilliard 1d for a domain of finite size

I'm trying to get the solution of the Cahn-Hilliard equation in 1d with a certain mass $C$. We have two components, and let's assume we have the relation $c_1+c_2=1$.Hence we take only the variable $c=...
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28 views

How to derive the macroscopic dielectric function?

I'm following Matteo Gatti's slides to repeat the derivation of macroscopic dielectric function $\epsilon_M$: $$\epsilon_M=\dfrac{1}{\epsilon^{-1}_{\vec{G}=0,\vec{G}'=0}(\vec{q},\omega)}.$$ On page ...
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Is there a commonly accepted definition of a quantum phase definition for a finite lattice/set of particles?

As noted by Sachev, and in a previous question, https://www.physicsoverflow.org/41602/, there cannot be quantum phase transitions for finite systems (with bounded local Hilbert space dimension). The ...
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38 views

What magnetic interaction makes spin not conserved?

If $[S_i,H]\neq0$ or $[S^2,H]\neq0$, we might say spin is not a good quantum number in the system. But is there any more practical or detailed criterion? Or certain families of magnetic interaction ...
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51 views

BCS theory and Cooper pairs

I'm studying superconductivity and BCS theory. Looking at the BCS ground state construction, I see two things that seem conflicting Occupation of Cooper pairs in BCS ground state (look at the figure ...
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1answer
21 views

A question on the transition matrix. (algebraic derivation)

I am trying to follow the derivation of the following identity: $$[\epsilon -H_0+i\eta]^{-1}T = [\epsilon - H +i\eta]^{-1}U$$ where $T$ is the transition matrix and $U$ is the potential caused by ...
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Effective action for 1D anti-ferromagnet

I'm following Fradkin's (p. 204) derivation of the effective action for a 1D anti-ferromagnet. He splits the spin field $\vec{n}$ into two pieces - a slowly varying $\vec{m}(j)$ which is the order ...
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How to include the possiblity of Umklapp Scattering into transport calculations

I'm trying to calculate transport properties of a certain model with a Hamiltonian that has electron-electron interactions. I know that, in order to use the Boltzmann equation \begin{equation} 0=\...
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40 views

Modifying the Hamiltonian when there is a presence of the Coulomb interaction

Referring to the Hamiltonian of a system of free electrons, $$ H_0= \sum_{\sigma} \int d^3rd^3r' \psi_{\sigma}^{\dagger}(\mathbf{r})\left(- \frac{\hbar^2}{2m}\nabla^2\right)\delta(\mathbf{r}-\mathbf{...
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44 views

What is the meaning of $\tau$=$Gb/l$

What is the physical meaning or intuition of the Shear Stress vs Shear Modulus and Burger Vector over length relation($\tau$=$Gb/l$). I have seen this formula being used to determine length in case ...
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44 views

Spectrum of the momentum operator for free Dirac fermions on a lattice

I am studying lattice field theory and would like to understand the momentum operator for free Dirac fermions on a square lattice. In this case one needs to discretize the momentum operator (which ...
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1answer
29 views

Why are the autocorrelations larger for the energy at the critical temperature?

Considering a simulation with the Swendsen-Wang algorithm for the 3-D cubic lattice I wanted to have a look at the auto-correlations, and expecting it to be quite small considering Swendsen-Wang is a ...
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1answer
47 views

How do LCDs vary light intensity?

What exactly happens when an electric field is applied? Say we're dealing with a TN LCD, in a 'normally white' mode. With no voltage applied, the orthogonal grated plates cause the director of the LC ...
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1answer
43 views

How can we see the microstructure of steel samples at room temperature?

When we intend to see the microstructure of a steel sample at a temperature say 950 $^\circ$C they say we quench it in order to freeze the microstructure. However, if we quench it are we not going to ...
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75 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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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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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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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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28 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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1answer
55 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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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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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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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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37 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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43 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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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. ...