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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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30 views

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/...
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43 views

How to understand frustration phase factor?

For a system with basis $|m\rangle$, where $m=1,2,3...$ The frustration phase factor is defined in any path $C=\{m_1m_2...m_\alpha\}$ as: $$\Phi_C=\arg[(-1)^\alpha H_{m_1m_2} H_{m_2m_3}\dotsb H_{m_\...
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1answer
96 views

Physical Hilbert space of dimension $N$ factorial?

In many-body physics, Hilbert spaces are usually equipped with a tensor structure (ie: $\mathcal{H}=\mathcal{V}^{\otimes N}$). If the dimension of local degrees of freedom is set to be $dim(\mathcal{...
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22 views

what is the relationship between topological charge and chern number in topological materials?

I would like to ask, what is the relationship between topological charge and chern number in topological materials? Why the topological charge of the Dirac cone is $0$?
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12 views

How to differentiate b/w are lowest extended levels and highest extended levels in IQHE?

At low disorder there are three bands. Two side bands have one conducting state and the central band has two conducting state. I want to know that which states are lowest conducting states ?
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38 views

Meaning of complex pairing terms in Kitaev chain

I am studying some properties of the one dimensional Kitaev chain, which has the following form: $ H = -\mu \sum_n c_n^\dagger c_n - t \sum_n (c_{n+1}^\dagger c_n + h.c.) + \Delta \sum_n (c_n c_{n+1} ...
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1answer
98 views

Why Kubo formula can be applied to calculate conductivity?

It seems that Kubo formula is widely adopted to calculate conductivity, or at least Hall conductivity [for example, in the famous paper by TKNN: PRL 49 405-408 (1982)]. However, the derivation of ...
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31 views

What is a non-local particle in condensed matter physics?

What exactly is "non-local" in physics? How can a particle be non-local particle? Are non-local particles and collective modes related with each other? Are solitons local or non-local? (I am asking in ...
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1answer
31 views

Is the Hubbard 2-body potential non diagonal in both direct and momentum space?

I was looking at the following table from these lecture notes: http://www.lassp.cornell.edu/clh/Book-sample/1.1.pdf And was wondering if the 2-body potential is always non-diagonal, or if there is a ...
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15 views

Metal resistivity temperature dependence in free electron model

In the context of the Drude model, I understand why the conductivity of a metal should decrease with increasing temperature (the conductivity scales linearly with scattering time $\tau$, which due to ...
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0answers
59 views

Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?

Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT). Irrational conformal field ...
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62 views

Clarification on DMRG computational complexity

I was reading a paper on the density matrix renormalization group (https://arxiv.org/abs/1008.3477). In DMRG, we gradually grow a chain by inserting a unit cell at the center of the chain (for ...
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1answer
43 views

Prove that group velocity is the velocity of energy transport in wave

Generally, the group velocity $v_g = \dfrac{\partial \omega}{\partial k}$ of a wave is the velocity of energy transport. In "Introduction to Solid State Physics", Kittel following is stated: The ...
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1answer
30 views

Can we measure the angular momentum of a magnetic domain using precession?

The amount of angular momentum of a single iron atom is small, just $\hbar / 2$. In a single magnetic domain, though, all of the iron atoms have their spins aligned. Presumably, it should be possible ...
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23 views

Questions about unitary condensate wave-function and $p_x+ip_y$ superconductor

I read about the unitary and non-unitary order parameter states here https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.657 and https://arxiv.org/abs/1512.01151 The form of the order ...
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39 views

Static Structure Factor

I know that static structure factor can be calculated from molecular simulation or X-ray diffraction. I would like to ask that if there is a way I can also calculate static structure factor given a ...
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1answer
78 views

What are emergent gauge fields in condensed matter physics?

My background: I have a very little knowledge about topological insulators. Medium level knowledge of Quantum mechanics and linear algebra. Almost no knowledge about Field Theories. I have studied ...
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0answers
27 views

Simultanious eigenstate of Hubbard Hamiltonian and Spin operator in two-site model

Known fact If two operators $A$ and $B$ commute, $[A,B]=0$, they have simultaneous eigenstates. That means $A|a,b\rangle=a|a,b\rangle$ and $B|a,b\rangle=b|a,b\rangle$. Hubbard Hamiltonian $H_\text{...
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29 views

Conditions for zero mode edge state to appear

Consider a non-interacting translationally invariant system described by H(k), k is the crystal momentum. The dimensionality of the system is denoted as d. I was thinking about what are the general ...
3
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1answer
61 views

Can we add the resistivity due to different scattering mechanisms?

Suppose there's a metal in which electrons interact with themselves and with the phonons. The hamiltonian might look like this \begin{equation} H= \sum_{k}\epsilon_k c^\dagger_k c_k + \sum_{k}\...
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1answer
72 views

How to obtain time-ordered density correlation function of free Bosonic system via Wick's theorem?

Consider a free Bosonic system. The Hamiltonian is given by $$ H=\sum_k \frac{k^2}{2m}a_k^\dagger a_k. $$ Since the spectrum is gapless, the ground state can be of any particle number (or even ...
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1answer
47 views

Level statistics of many body localization

I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order: $E_1,E_2,E_3...E_N$. The quantity I calculated is r, ...
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1answer
136 views

Gauge transformation for Bloch waves?

I have seen in many places saying a gauge transformation transform the Bloch wave function as $\psi_{nk}\to e^{-i\phi_n(k)}\psi_{nk}$. However I don't quite understand how it is related to the "gauge ...
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2answers
32 views

Number of electrons within Fermi Surface

This question is regarding problem 9.5 in Ashcroft and Mermin where we have to calculate the radius of the Fermi circle in a 2D square lattice with lattice constant $a$ and $m$ electrons per primitive ...
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1answer
43 views

How to get the energy bands of the Haldane model?

I am struggling with how to get the dispersion relationship of the Haldane model and plot it, just like this: And then apply it to graphene nanoribbons (armchair) and plot it like this: Here's a ...
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1answer
62 views

Electrons with disorder & something like AdS/CFT duality

I know that consideration of electrons with disorder can be based on Feynman diagrams with disorder lines. In this approach, only non-crossing diagrams are important and give contribution to self-...
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1answer
36 views

How does the Hubbard hamiltonian change when considering a Peierls distortion (bipartite lattice)?

The following is the Hubbard contribution to the hamiltonian in the Hubbard-Tight Binding model. $$H_{hubbard}=U \sum_i n_{i \uparrow}n_{i\downarrow}$$ where $n_{i \sigma}=c_{i\sigma}^\dagger c_{i\...
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42 views

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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55 views

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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0answers
21 views

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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1answer
37 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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1answer
40 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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1answer
29 views

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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1answer
38 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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0answers
28 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
39 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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0answers
78 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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51 views

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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38 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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0answers
33 views

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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30 views

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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1answer
73 views

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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1answer
26 views

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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18 views

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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0answers
32 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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3answers
62 views

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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0answers
17 views

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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28 views

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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0answers
33 views

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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1answer
78 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=...