All Questions
Tagged with spin-models lattice-model
30
questions
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144
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Is the definition of gap of a Hamiltonian, i.e. difference between two distinct eigenvalues, restrictive?
The spectral gap of a quantum model or a Hamiltonian, in the context of whether it is a gapped or gapless model, is often defined as the difference between the two lowest distinct eigenvalues of the ...
- 197
4
votes
2
answers
2k
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Kagome Lattice: Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
- 359
2
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170
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$T$-duality symmetry of $SU(2)_1$ WZW model
For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.
- 21
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135
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Massive Thirring model as continuum limit of Heisenberg model
The massive Thirring model
$S = \int d^2 x \left[ \bar{\psi} \gamma^\mu \partial_{\mu} \psi - m \bar{\psi} \psi - \frac{g}{2} \left( \bar{\psi} \gamma_\mu \psi \right) \left(\bar{\psi} \gamma^\mu \...
- 4,251
5
votes
1
answer
1k
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What is breathing Kagome lattice?
I know what kagome lattice is. While reading some article I came to know the term breathing kagome lattice. Looked up the web didn't found any definitions of it.
My suspicion is that when hopping ...
- 988
0
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120
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Quantum Monte Carlo Loop Algorithm for quantum spin: why is the freezing graph present in ferromagnetic Ising model?
I study the loop algorithm (Evertz et al).
I cannot understand, why the freezing graph type where we have to flip all 4 spins together is not present for the quantum-XY model and the anti-/...
- 115
1
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223
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How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?
$\underline{\textbf{Model:}}$
Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
- 1,335
1
vote
1
answer
138
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Constructing PEPS representation of an arbitrary quantum state
Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
- 1,285
1
vote
0
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133
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Correlation between spins using delta function in Potts model
In reading about the Potts model, I found this correlation:
$$\langle s_{i}s_{j} \rangle = \frac{q}{q-1}\frac{1}{N_{p}} \sum_{s_{i},s_{j}} (\delta(s_{i} - s_{j})-\frac{1}{q})$$
with the following text:...
- 11
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117
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References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model
I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
- 1,335
6
votes
1
answer
10k
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Bogoliubov-de-Gennes (BdG) formalism of Hamiltonians
The Bogoliubov-de-Gennes (BdG) formalism of a Hamiltonian reduces the dimension of the Hilbert space we work on. For example, in 1D superconducting Hamiltonians with $N$ lattice sites, the actual ...
- 107
2
votes
2
answers
420
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How to understand a Hamiltonian of the form $c^\dagger \sigma^x c$?
In a 2-dimensional lattice Dirac model (a discretized Hamiltonian on a lattice, the model could be found in this dissertation, equation (2.19)), I found a Hamiltonian with terms like:
$$ H = \sum_{m,n}...
- 706
1
vote
3
answers
297
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What is spin on a lattice site is it electrons or atom as a whole?
Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d?
- 13
2
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475
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Can someone explain to me the Rokhsar-Kivelson Hamiltonian? [closed]
The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2)
http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf
Here are some questions I have.
Why ...
- 244
3
votes
2
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233
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Lattice gauge and spin network
I see the similarity between the Lattice Gauge and Spin Network.
(For example, both theories depict the node part as quantum (the latter is explained as spin).)
Are there any other mathematical, ...
- 301