In solid-state physics, a description of the physics of interacting spinless bosons on a lattice.
Questions tagged [bose-hubbard-model]
46 questions
9
votes
1 answer
Superfluid Stiffness Definition
I am currently reading S. Sachdevs Book on Quantum Phase Transitions focusing on the Bose-Hubbard Model (Chapter 9) and especially the Dilute-Boson Field Theory (Chapter 16).
When describing the fluid phase of the one dimensional model Sachdev says…
jan0155
- 647
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5
votes
2 answers
Why is there a chemical potential term in the Bose-Hubbard Hamiltonian?
When looking at the Bose-Hubbard Hamiltonian
$$H_{BH}=-t\sum_{\langle i,j\rangle}a^\dagger_ia_j+\frac{U}{2}\sum_ia^\dagger_ia_i(a_i^\dagger a_i-1)-\mu\sum_ia_i^\dagger a_i,$$ I'm wondering why there is the chemical potential term. In my…
Simon
- 149
4
votes
1 answer
Is Bose-Einstein condensate in the optical lattice a single mode condensate?
I recently read about BEC loaded into the optical lattice p.200
Looking at a condensate released from a lattice after a
time of flight typically on the order of a few milliseconds
amounts to observing its momentum
distribution. A harmonically…
WoofDoggy
- 2,190
3
votes
0 answers
Bogoliubov spectrum: fermions vs bosons
I am trying to understand the difference in the Bogoliubov spectrum for superconductors and superfluids. In the context of superconductivity, the spectrum of the low-energy excitations is given…
redfive
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3
votes
1 answer
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
$$
H = \sum_{\text{nearest neighbors } ij \text{ and spin } \sigma} a^\dagger_{i\sigma} a_{j\sigma} + U \sum_i \hat{n}_{i\uparrow}…
3
votes
2 answers
Which experiments can offer insights about Hubbard $U$ parameter?
When considering $\mathrm{DFT}+U$ calculations, people either go with (1) first-principles approach: calculating the $U$ parameter using linear response theory, $\mathrm{DFPT}$, $\mathrm{ACBN0}$, etc., or (2) empirical approach: tuning the U…
AbdulMuhaymin
- 223
3
votes
2 answers
Form of the Hamiltonian at Half-filling
I am trying to understand why chemical potential $= U/2$ is considered to be at half-filling in the case of the Hubbard Model Hamiltonian. So when I substitute this in its Hamiltonian, this is the equation I am getting $$ H = K.E-\frac{U}{2}\Sigma…
CuriousMind
- 75
2
votes
0 answers
Heisenberg and Dyzaloskinkii Moriya Interaction
The Heisenberg hamiltonian is $H= J\vec{S_i}\cdot\vec{S_j}$ whilst the Dzyaloshinkii Moriya Interaction is $H=\vec D\cdot\left(\vec{S_i}\times\vec{S_j}\right)$. But how do these equations come about? How are they derived? How is that one is a dot…
Tanuz
- 53
2
votes
0 answers
Integrable Lattice Lieb Liniger Model
Is there a model of the 1D Bose gas (aka the Lieb Liniger Model) on a lattice that retains integrability? As a naive guess, I had thought that the Bose Hubbard model would fit this criterion, since the Fermi Hubbard model is integrable (although I…
Primo-uomo
- 143
2
votes
1 answer
Ground state of composite and non-interacting bosons on a lattice
Background
Consider a lattice system described by the Hamiltonian
$$
H = - J \sum_{\left\langle ij \right\rangle} \left( \Delta^{\dagger}_i \Delta_j + \mathrm{h.c.} \right)
$$
where $\Delta_i$, $\Delta^{\dagger}_i$ destroy and create a particle on…
Matteo
- 3,261
2
votes
1 answer
Origin of Hubbard sub-bands
I would like to know the origin of the sub-bands in the non degenerate Hubbard model. Most of the texts consider the Hubbard model at half-filling. Is the emergence of the sub-band specific to the half-filling condition or is it also seen for…
AlphaBaal
- 420
2
votes
2 answers
Lattice vs Superlattice
What is the difference between lattice and superlattice ? Can anyone describe with a schematic figure? I have encountered superlattice in the context of bose hubbard model. Also what are the advantages or disadvantages in superlattice compared to…
1
vote
0 answers
How can we interpret long-range entanglement in the context of the Hubbard model?
How can we interpret long-range entanglement in the context of the Hubbard model, particularly with respect to its implications for quantum phases like superconductivity and other strongly correlated states?
I’m exploring the role of long-range…
Amirhoseyn
- 228
1
vote
0 answers
Two species of bosons
Consider the Bose-Hubbard model for a single species of boson in a square lattice,
\begin{equation}
H_{a}=-t\sum_{} a^{\dagger}_{i}a_{j}+U \sum_{i}a^{\dagger}_{i}a^{\dagger}_{i}a_{i}a_{i}-\mu\sum_{i}a^{\dagger}_{i}a_{i}
\end{equation}
This model…
Santanu Singh
- 335
1
vote
0 answers
Simplest quantum Monte-Carlo method for the Bose-Hubbard model
I want to use quantum Monte-Carlo results to benchmark an algorithm for the Bose-Hubbard model. There are so many QMC methods in the market, so which one is the simplest one? I want the ground state energy, some simple correlation functions. I…
poisson
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