All Questions
Tagged with hamiltonian condensed-matter
115
questions
3
votes
2
answers
203
views
Form of the Hamiltonian at Half-filling
I am trying to understand why chemical potential $= U/2$ is considered to be at half-filling in the case of the Hubbard Model Hamiltonian. So when I substitute this in its Hamiltonian, this is the ...
- 53
0
votes
1
answer
50
views
Obtaining Eigenvalue Expression
Say we have an excitonic system with a creation operator operator:
$$ |\Psi_{ex}\rangle=\sum_{\vec{k}} \phi(\vec{k})c^\dagger_{\vec{k}+\vec{Q}}b_{\vec{k}}|GS\rangle$$
And the Hamiltonian of the system ...
- 155
2
votes
1
answer
95
views
Is the Hamiltonian for the transverse field Ising model Hermitian?
I'm watching these lectures in Condensed Matter Physics. At Lec. 13, the lecturer introduces the transverse field Ising model with the Hamiltonian
$$H = - J \sum_i \sigma_i^x \sigma_{i+1}^x - h \sum_i ...
- 22.1k
0
votes
0
answers
52
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Sign of momentum doesn't affect Bogoliubov coefficients in Bogoliubov transformation for BEC
I'm running into some issues with the deriving Bogoliubov transformation. Specifically, in order to diagonalize the Hamiltonian
$$\begin{align}H = \sum_p \frac{p^2}{2m} \hat a^\dagger_p \hat a_p + \...
- 319
3
votes
1
answer
76
views
$\mathbf k\cdot\mathbf p$ Hamiltonian
I am looking into the $k\cdot p$ Hamiltonian approach to describe a semiconductor system. The simplest system appears to be the 2x2 system which can be visualised as: \begin{pmatrix}
\epsilon(k) &&...
- 155
1
vote
0
answers
77
views
Renormalization of two-sublattice tight-binding Hamiltonian
I have a generic tight-binding Hamiltonian of the form
$$H=\sum_n A c_n^\dagger d_n+Bd_n^\dagger c_n +C c_{n+1}^\dagger d_n + D d_n^\dagger c_{n+1}$$
where $A,B,C,D$ are parameters (hopping amplitudes)...
- 105
2
votes
0
answers
90
views
Effective Hamiltonian for twisted bilayer graphene
I'm trying to follow along with this paper, which reviews the Bistrizer--MacDonald model of twisted bilayer graphene. I'm particular, I'm struggling to derive their Eq. (100). Starting from the ...
- 349
1
vote
1
answer
80
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:
$$ \widehat{H} = -NJ\hbar^2s^2 + J\hbar^2s \...
- 237
2
votes
0
answers
62
views
$\vec{k}\cdot\vec{p}$ Hamiltonian approach
I am new to reading into the $\vec{k}\cdot\vec{p}$ approach.
Where for a periodic function $u_{\vec{k}}$, which satisfies the Schrodinger equation:
$$
H_\vec{k}u_{\vec{k}}=E_{\vec{k}}u_{\vec{k}}
$$
...
- 31
1
vote
1
answer
218
views
Diagonalize a many-body Hamiltonian
Assume we start with a generic many-body Hamiltonian:
$$
H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k.
$$
Now if there is only the one-body part, which ...
- 11
1
vote
1
answer
44
views
Non-Hermitian PT-symmetric Interacting Hamiltonian with Real Spectra
The following hamiltonian is $\mathcal{PT}$-symmetric $$\mathcal{H} = -J \sum_{j = 1}^{2N} [ 1 + (-1)^j \delta ] [ c^{\dagger}_{j} c_{j+1} + h.c. ] + \imath \gamma \sum_{j = 1}^{2N} (-1)^j c^{\dagger}...
- 199
0
votes
1
answer
81
views
How to evaluate interaction term in Hamiltonian?
If one has an interaction term in the Hamiltonian of a system as follows:$$
\sum_{\vec{q}}V(\vec{q}) \psi(\vec{k}-\vec{q})
$$
where $\psi(\vec{k}-\vec{q})$ and $V(\vec{q})$ is the wave function and ...
- 155
3
votes
0
answers
55
views
What is the ground state of a Hamiltonian in $k$-space after Bogoliubov transformation? [duplicate]
Consider the following Hamiltonian in $k$-space, quadratic in terms of the $\gamma$ operators:
\begin{equation}
\hat{H}_2=\frac{1}{2}\sum_k
\begin{pmatrix}
\gamma_k^\dagger & \gamma_{-...
3
votes
0
answers
72
views
Why must a Hamiltonian be gapped to have "local" excitations?
On page 4 of Kitaev's "Anyons in an Exactly Solved Model and Beyond" he states
The notion of anyons assumes that the underlying state has an energy gap (at least for topologically ...
- 93
1
vote
0
answers
35
views
Is there any method for folding a Hamiltonian matrix to lower dimension?
I want to solve a tight-binding Hamiltonian which is $6\times6$. I'm only interested in two of the six bands which lie near zero energy at $\vec{k}=(0,\frac{4\pi}{3\sqrt{3}a})$. Is there any way to ...
- 75