Questions tagged [bose-hubbard-model]
In solid-state physics, a description of the physics of interacting spinless bosons on a lattice.
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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 \...
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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.,...
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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 ...
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Two species of bosons [closed]
Consider the Bose-Hubbard model for a single species of boson in a square lattice,
\begin{equation}
H_{a}=-t\sum_{<ij>} a^{\dagger}_{i}a_{j}+U \sum_{i}a^{\dagger}_{i}a^{\dagger}_{i}a_{i}a_{i}-\...
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Average Energy and Magnetization of One Site Hubbard Model
I have been trying to implement the exercises from Section 2 part B (for which $t = 0$, and only considering the effects of U) given in this set of lecture notes - Numerical Studies of Disordered ...
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Fourier transform of spinless $t$-$V$ model for $t=0$
I am trying to compute the Fourier transform of the 2D $t$-$V$ model for the case $t=0$.
\begin{equation}
\hat H = -t \displaystyle \sum_{\langle i,j\rangle} ( \hat c_i^{\dagger} \hat c_j + \hat c_j^{...
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How to Calculate the Case of $t=0$ in the $t$-$V$ Model?
In the $t$-$V$ model, the Hamiltonian is defined as:
\begin{equation}
\hat H = -t \displaystyle \sum_{\langle i,j\rangle} ( \hat c_i^{\dagger} \hat c_j + \hat c_j^{\dagger} \hat c_i) + V \sum_{\langle ...
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What is the significance of these lines in the explicit Bose-Hubbard Hamiltonian?
I was doing some 2nd quantization computational physics and as my first system i decided to build up a Bose-Hubbard Hamiltonian
$$
H = \sum_{k} \left\{ \tau_k(a^\dagger_{k} a_{k+1} + a_{k} a^\dagger_{...
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What's the matrix representation of Slave-Boson operators?
$\newcommand{\ket}[1]{\left|#1\right>}$
I think I'm not understanding the construction of the slave-particle operators.
In the Bose-Hubbard model, the slave-boson approach attempts to alter the ...
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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 ...
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Do Hubbard parameters depend on the localisation of Wannier orbitals?
Wannier orbitals are not unique and depend on a choice of phase of the Bloch wave functions. This typically leads to people attempting to define Wannier functions such that they are "maximally ...
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What is particle-hole symmetry for Bose-Hubbard model (if there is)?
When people talking about particle-hole symmetry on Bose-Hubbard model, one always considers single particle and single hole excitations on Mott-insulator phase:
$$
E_{\mathbf{q}}^{\pm}=\pm \omega_{\...
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How is volume of quantum harmonic oscillator related to the trapping frequency in BEC?
For a ideal Bose gas in harmonic trap, the total particle number can be written as,
,
and is fugacity.
Now I want to find the expression for particle density for excited states. In case of Bose gas ...
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Bose Hubbard Model Phase Transitions
I am studying the Bose Hubbard model by reading this paper. I have three questions:
(1) The sides of the Mott lobes are symmetry-breaking phase transitions (second order). What is the corresponding ...
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Three-site Bose Hubbard Model Equations of Motion
I was wondering for the three-site Bose Hubbard model how we can get the equations of motion out of the following hamiltonian:
$$ \hat{H} = \hbar \chi \sum_{j} \hat{\alpha}_{j}^{\dagger} \hat{\alpha}_{...
