All Questions
Tagged with spin-chains ising-model
27
questions
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36
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Why is the excitation energy of antiferro 1/2 spin XXZ chain associated with the $\psi_{n+2}$ and $\psi_{n-2}$
I do not understand the equation on page 5 of nagaoso's book "quantum field theory in strongly correlated electronic systems".
The Hamiltonian is shown in this form
$H=\frac{J_\bot}{2}\sum_{...
- 11
1
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0
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37
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Parity of a 1d Ising model, and with higher order terms
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\...
- 368
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1
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Coupling two Ising chains via an energy-energy interaction
Consider the transverse-field Ising model on a chain with periodic boundary conditions:
$$ H = -\sum_{i=1}^{L} \sigma_{i}^z \sigma_{i+1}^z + h \sigma_{i}^x$$
There's a phase transition at $h=1$, which ...
- 2,292
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2
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169
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Mapping a 1D quantum Ising chain to a 2-dimensional classical Ising system
Going through Ref. 1 (I'll stick with the book's equation numbering), I'm learning about the mapping of quantum systems into classical systems. First of all let me briefly recap notation and some ...
- 1,989
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Tunneling lowers the energy of a ground state superposition of spins up and down in the quantum Ising model
Considering an Ising model in the quantum scenario in quantum spatial dimension d=1 (that corresponds to classical D=2=d+1 dimension). Starting with the Ising model hamiltonian under the approximation ...
- 310
2
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1
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676
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Transverse-field Ising model in the presence of a longitudinal field - ferromagnetic phase diagram
I am wondering what is the phase diagram of the transverse-field Ising model in the presence of a longitudinal field, in particular, a one-dimensional spin-1/2 chain with ferromagnetic interactions. ...
- 21
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155
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How to take into account finite temperature in transverse Ising chain?
A similar question has already been asked here
What I'm wondering is how to take into account finite temperature in the transverse Ising chain and see how that affects the magnetization. The reason ...
- 741
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178
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Bosonization of critical theories without $U(1)$ symmetry?
When studying lattice models using bosonization, we expect the total charge is conserved so that the elementary excitation is particle-hole-like bosonic degrees of freedom. How about models without $U(...
- 356
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474
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1D transverse-field Ising model - what is the difference between its classical and quantum treatment?
The 1D transverse field Ising model:
$$ H(\sigma)=-J\sum_{i\in Z} \sigma^x_i \sigma^x_{i+1} -h \sum_{i \in Z} \sigma^z_i$$
is usually solved in quantum way, but we can also solve it classically - ...
- 960
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380
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Magnetization ($z$-basis) of a 1D Transverse Ising Model
I'm trying to find the magnetization $\langle\sigma_{z} \rangle$ of a 1D transverse Ising chain and plot it as a function of the transverse field $\lambda$. More specifically, I want to plot this for ...
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2
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What is the ground state wavefunction of $\hat{H}=-J\sum\limits_{\langle i,j\rangle}\hat{S}_i^z\hat{S}_j^z,~~ (J>0)$?
The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-...
- 26.8k
1
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1
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431
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1D Ising Model with magnetic field on even sites: Transfer Matrices
I have been trying to work out a practice problem after reading about Transfer Matrices method for solving 1D Ising Model. Please, if you are able to, tell me whether the way I introduced transfer ...
- 61
3
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1
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549
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(Transverse) Ising Model Higher Than Four Dimensions
First question:
Wiki says Ising Model higher than four dimensions can be described by mean field theory. What is the reason for this? Does this mean there is no phase transition for higher dimensions ...
- 470
13
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Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation
In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in ...
- 988
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Generalised Ising models?
Are there generalised Ising models:
The underslying mesh/connectivity is completely arbitrary - non rectangular, 3D...ND, complete connectivity should be possible
The interaction potential is ...
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