Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
4,711
questions
0
votes
0
answers
50
views
Where can I read about Valleytronics?
Where can I read about Valleytronics? Are there any good books or review papers on this topic? And which are the most influential papers?
0
votes
1
answer
44
views
Brillouin Zone Summation
If one has the following summation:
$$\frac{1}{A}\sum_{\vec{k}} F(\vec{k})$$
which is taken over all k-space and $A$ is the area of the unit cell from the system itself. I want to them limit this to ...
- 75
-1
votes
0
answers
25
views
spin operator in fermion creation and annihilation operators
There's a site (quantum well, atomic orbit, etc) that can host a pair of electrons, with corresponding creation and annihilation operators:
$c^\dagger_\uparrow,c_\uparrow,c^\dagger_\downarrow,c_\...
- 311
1
vote
0
answers
50
views
Quantum pressure of a Bose gas in a harmonic trap: Why is the result divergent?
The quantum pressure of a Bose gas in the Thomas Fermi limit with contact interactions in a symmetric harmonic trap is determined by (Pitaevskij & Stringari, 2016):
$E_{K}=\int d\mathbf{r}\frac{\...
- 619
5
votes
0
answers
37
views
Question about the duality between 2+1 d transverse-field Ising model (TFIM) and $\mathbb{Z}_2$ gauge theory
I was reading McGreevy's Lecture notes Where do QFTs come from?
, and on chapter 5 he talks about a duality between the $2+1d$ transverse-field Ising model (TFIM) and the $\mathbb{Z}_2$ gauge theory, ...
- 421
-1
votes
0
answers
18
views
Tight binding hamiltonian graphene [duplicate]
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
0
votes
1
answer
33
views
Identity of bosonic coherent states
I have a short question about the meaning of the identity of the bosonic coherent states.
Before I ask the question I will explain some background.
The eigenstate of the bosonic annihilation operator $...
- 217
2
votes
0
answers
27
views
Expansion of interaction potential in terms of spherical harmonics in unconventional superconductivity
I am currently reading the book Introduction to Unconventional Superconductivity by V. P. Mineev and K. V. Samokhin. In Equation (1.6), the interaction potential $V$ is expanded in terms of spherical ...
- 21
2
votes
1
answer
37
views
Non-Saturation in Interacting Bose Gas Integral
I am independently working through some problems on Bose-Einstein condensation. In particular, I am trying to show that—in the Hartree-Fock mean-field approximation—for a Bose gas with contact ...
- 63
0
votes
0
answers
41
views
Berry curvature and eigenvalues [closed]
I have a simple question. I have 4 Berry curvatures corresponding to the band structure described by the eigenvalues. How can I verify from which eigenvalue is the specific berry curvature?
- 105
0
votes
0
answers
37
views
Electron in magnetic field and slowly varying potential $V(x)$
What are the approximation methods for the spectrum and wavefunctions of a 2D electron in a perpendicular magnetic field $B$ and a scalar potential $V(x)$ which is slowly varying on the scale of the ...
- 1,932
1
vote
0
answers
13
views
Leading thermal corrections to Lindhard susceptibility
I am interested in deriving the leading temperature-dependent correction to the zero-temperature static Lindhard susceptibility of a homogeneous free electron gas. My starting point is the following ...
- 963
-3
votes
0
answers
89
views
Tight-Binding Hamiltonian Graphene
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
0
votes
0
answers
18
views
Symmetries near the K/K' points in graphene
I am trying to understand one paper and I have a problem with symmetries.
The authors introduce the 2x2 Bloch Hamiltonian as
$$
\mathcal{H}(\textbf{k}) = \textbf{h}(\textbf{k}) \cdot \sigma,
$$
where $...
- 105
1
vote
1
answer
35
views
How does one produce a condensate?
In physics textbooks, one learns about Bose-Einstein condensate and it is all about taking thermodynamic limits. Of course, in real life, infinite systems do not exist. So, picture the following ...
- 825
0
votes
0
answers
49
views
Retarded green function of tight-binding Hamiltonian [closed]
I want to compute the retarded Green function of a one-dimensional tight-binding model on $N$ sites with periodic-boundary conditions.
The Hamiltonian is:
$$
H_0=\sum_k \epsilon_k c_k^\dagger c_k
$$
...
- 109
0
votes
0
answers
19
views
Continuum formulation of the Kitaev chain
In Kitaev's seminal paper (https://arxiv.org/abs/cond-mat/0010440), the Kitaev chain is described in a lattice formulation. On the other hand, many of the original papers on the the related ...
1
vote
1
answer
60
views
Hall Conductivity of Maxwell Action [closed]
I am currently reading David Tong's notes on Chern-Simon's theory and below equation (5.5), he makes the statement:
"The action (5.5) has no Hall conductivity because this is ruled out in d = 3+...
- 23
1
vote
0
answers
33
views
What's physical meaning of 2-point correlation function in holographic condensed matter?
Background: In AdS/CFT, we can do calculations in AdS spacetime, and get the result in CFT. When we consider RN-AdS black hole/brane, 2-point correlation functions in CFT can be obtained, which are ...
- 11
0
votes
0
answers
23
views
Examples of operators like multi body fermions in finite potential well with total energy being sum of energies, and not entirely homogeneous
I'm looking for examples of systems with operators like the 2 fermion system in finite potential well where the total energy
$\lambda(k) = \lambda_1(k) + \lambda_2(k)$
where $k$ is the depth of the ...
- 455
1
vote
1
answer
38
views
Fourier transform of the Heisenberg antiferromagnetic model
I have a short question about the Fourier transform of the antiferromagnetic Heisenberg model.
The Hamiltonian, written in terms of bosonic operators, is:
$$ \widehat{H} = -NJ\hbar^2s^2 + J\hbar^2s \...
- 217
3
votes
4
answers
117
views
Meaning of the momentum vectors $\mathbf{k}$ in electronic band structure
In solid-state physics, I struggle to understand momentum vectors $\mathbf{k}$ in reciprocal space. We usually draw a picture of a Brillouin zone as follows (hexagonal in this case):
And we can then ...
- 45
1
vote
1
answer
47
views
Fractional filling of Laughlin wavefunction
I am not clear about the following argument why Laughlin wavefunctions have $1/m$ filling.
The single-electron wavefunction in the zeroth Landau level is
\begin{equation}
\psi_{m}(z)\sim z^m e^{-|z|...
- 88
1
vote
0
answers
47
views
Quantum phase transition in condensed matter
I want to know that, for any spin-chains in condensed matter Physics like X-Y spin model, Kitaev model 1-D only in which degenerate point is critical point. Is it necessary that the critical points ...
- 11
0
votes
1
answer
55
views
Why does flowing current break time reversal symmetry?
I am reading about the Quantum Hall Effect. In a course, they wrote that
How does one get a Hall effect? The key is to break time-reversal symmetry. A flowing current breaks time-reversal symmetry, ...
- 105
0
votes
0
answers
63
views
Why does mirror/inversion symmetry exclude nearest-neighbor spin-orbit coupling in the Kane-Mele model?
I've been reading about the Kane-Mele model and noticed that it does not include nearest-neighbor spin-orbit coupling, with explanations often pointing to mirror symmetry as the reason. Could someone ...
- 336
2
votes
1
answer
53
views
Quasiparticle Density of States
In this paper we have the following:
The corresponding quasiparticle density is given by the equation
$$n_{qp} = 4N_0 \int_\Delta ^\infty dE \frac{E}{\sqrt{E^2 - \Delta^2}} f(E),$$
where $N_0$ is the ...
- 2,194
4
votes
1
answer
460
views
Tricky Integral: Evaluating Renormalized Ultraviolet "Divergent" Integral
I am trying to rederive the results presented in the paper, in particular equation (30). That is, I am trying to compute the correction to the ground-state energy of a dipolar condensate due to beyond-...
- 63
1
vote
0
answers
31
views
Quantum master equation for light in medium with dissipation
The effective theory of photons in medium is usually obtained by inserting the electric susceptibility $\chi$ (linear or nonlinear) into $\int \mathrm{d}{\mathbf{D}} \cdot \mathbf{E}$ and complete the ...
- 351
-1
votes
0
answers
12
views
Cuprate Superconductors parameters
What are the parameters for cuprate superconductors, is it the same with normal superconductors? Because I was wondering if the high temp and low temp makes the difference.
8
votes
2
answers
2k
views
What is Robert B. Laughlin saying about quantum field theory?
Robert B. Laughlin, A Different Universe states the following concerning the relationship between superconductivity and quantum field theory. I do not understand why he says "the microscopic ...
- 941
3
votes
0
answers
32
views
Discretising Hexgonal Brillouin Zone
I am looking at a system at which I have a 2D Hexagonal Brillouin Zone (BZ). The aim is to take the following type of procedure:
$$
\frac{A}{(2\pi)^2}\int_{BZ} F(\vec{k}) d\vec{k} \hspace{5pt} \...
- 75
5
votes
2
answers
26k
views
Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?
I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
- 88
0
votes
0
answers
16
views
How to know the relationship among the superconducitng phase , the gap, and the gapless edge states?
I feel puzzled about how to decide whether a material is in the superconducting phase, whether the gap can decide the superconducting phase, and whether there exists the gapless edge states.
- 1
3
votes
0
answers
26
views
Spectral function of superconductor in the BEC regime: how does Higgs mechanism affect the spectrum?
Consider the standard BCS theory but assume that the interaction energy $U$ that enters the definition of gap parameter (i.e. $\Delta = (U/N)\sum_k \langle c_{-k\downarrow} c_{k\uparrow} \rangle$, ...
- 2,674
0
votes
1
answer
39
views
Position-dependent Fermi velocity
In models of strained graphene one seems to obtain a position-dependent Fermi velocity. By this I mean that if the original Dirac operator is
$$ H = v_0(\sigma_1 p_1 + \sigma_2 p_2),$$
with constant ...
1
vote
1
answer
61
views
Obtaining the Ising and XY model from the XYZ $O(3)$ model
I have the classical XYZ model Hamiltonian $\mathcal{H}$ with a magnetic field $\vec{H}$ given as
\begin{equation}
\mathcal{H} =
-\sum_{i< j} J^x_{ij}S_i^xS_{j}^x + J^y_{ij}i^yS_{j}^y+ J^z_{ij}S_z^...
- 673
2
votes
0
answers
56
views
$\vec{k}\cdot\vec{p}$ Hamiltonian approach
I am new to reading into the $\vec{k}\cdot\vec{p}$ approach.
Where for a periodic function $u_{\vec{k}}$, which satisfies the Schrodinger equation:
$$
H_\vec{k}u_{\vec{k}}=E_{\vec{k}}u_{\vec{k}}
$$
...
- 21
1
vote
1
answer
53
views
CDW correlation function for 1D Dirac fermion in condensed matter
I am following Shankar's lecture notes on bosonization, specifically the theory of left-/right-moving fields for a low-energy 1D fermionic chain. For now, I ignore the Heisenberg time dependence of ...
- 55
1
vote
1
answer
147
views
Diagonalize a many-body Hamiltonian
Assume we start with a generic many-body Hamiltonian:
$$
H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k.
$$
Now if there is only the one-body part, which ...
- 11
0
votes
0
answers
17
views
The total energy of an atomic supercell with a local dipole moment in an external electric field
How to define the total energy of an atomic supercell with a local dipole moment in an external electric field?
The figure below illustrates the two cases of the local dipole moment within an atomic ...
- 343
1
vote
0
answers
26
views
Particle density and current in terms of Green function
Consider a non-relativistic free-fermion system. I am wondering how to calculate observables like average particle density and average current in terms of momentum-space Green functions. I know that ...
- 21
1
vote
0
answers
19
views
How to calculate the Green function of 1D Kitaev chain?
After performing Jordan-Wigner transformation, a uniform transverse Ising model becomes a 1D Kitaev chain as
$\hat{H}_{p=0,1} = -J\sum_{j=1}^{L}{(\hat{c}_{j}^{\dagger}\hat{c}_{j+1}+\hat{c}_{j}^{\...
- 11
2
votes
1
answer
31
views
Why does the energy gap of sublattice-symmetric systems never close?
I am studying from this famous site some symmetries useful for topological quantum matter.
At some point, talking about the particle-hole symmetry, it states:
You can however notice that, unlike in ...
- 21
1
vote
0
answers
67
views
Expectation value of non-interacting groundstate
Assume that I have a tight binding model given in second quantized form as follows;
\begin{equation}
H = \sum_i f_i^{\dagger}f_i + t \sum_{i,j} f_i^{\dagger}f_j
\end{equation}
In real space, ...
- 11
1
vote
0
answers
39
views
Finite temperature Greens function simplification
I am currently studying topological insulators using Topological insulators and superconductors by Bernevig. In chapter 3, section 3.2.2, he has derived the finite temperature Green's function using ...
- 147
2
votes
0
answers
50
views
Do the fractional electric charges in FQHE violate the Dirac quantization relation?
Dirac quantization relation says that the electric charge must be quantized if there is a magnetic monopole in our universe. But the fractional quasi-particles and quasi-holes in FQHE have fractional ...
- 534
0
votes
1
answer
53
views
Real part of Raman response function in linear response theory?
When we calculate the Raman scattering, we usually derive the imaginary part of the Raman response function. The general formula of the imaginary part is given by
\begin{align}
\text{Im}[I(\omega)] \...
- 1
0
votes
0
answers
13
views
Is the flat band of zigzag ribbon topological or just a state of topological origin?
In my understanding, an edge state has topological origin if its existence is bound to a nontrivial topological invariant. An edge state is topological if it has topological origin.
The flat bands of ...
- 327
0
votes
0
answers
32
views
Programming a self-consistent hamiltonian in the momentum space
I would like to know what the procedure should be to determine the orbitals of a periodic lattice considering a Hamiltonian in the momentum space. For example, I think the most general expression for ...
- 113