All Questions
Tagged with spin-chains fermions
9
questions
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45
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Transforming spin operators into fermionic operators and finding their anticommutation relations
The Jordan-Wigner transformation (JWT) is a method used in quantum mechanics to map spin operators, which are typically associated with spin-1/2 particles, to fermionic operators, which describe ...
0
votes
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Jordan-Wigner transformation in transverse field Ising model
Jordan-Wigner transformation provides an exact solution for transverse field Ising model in both the ferromagnetic phase and the paramagnetic phase. Yet this seems to imply that in both phases, the ...
2
votes
1
answer
223
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Jordan-Wigner Transformations on fermionic system
I've been trying to use Jordan-Wigner Transformations on a given fermionic Hamiltonian. The given Hamiltonian is: $$ \hat{H}= -\sum_{m=1}^{N}(J_z \hat{S}_{m}^{z} \hat{S}_{m+1}^{z} + \frac{J_{\perp}}{2}...
- 23
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Literature Request: Conformal Field Theory for 1D XXZ Chain
It is known that the Heisenberg XXZ chain in 1D
\begin{equation}
\hat{H} = - J \sum_{i=1}^N \left(S^x_jS^x_{j+1} + S^y_jS^y_{j+1} + \Delta S^z_jS^z_{j+1}\right)
\end{equation}
can be described by the ...
3
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2
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652
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Jordan-Wigner transformation for lattice models without $U(1)$ symmetry
The Jordan-Wigner transformation is a powerful approach to studying one-dimensional spin models. The following dictionary between spin operators and creation/annihilation operators for fermions allows ...
- 759
2
votes
1
answer
732
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Why does a 1D hardcore bosonic chain have different ground state energy in bosonic and spin representations?
Consider a simple periodic 1D chain with four sites with periodic boundary condition. The Hamiltonian reads
$$
H = t c_1^\dagger c_2 + c_2^\dagger c_3 + t c_3^\dagger c_4 + c_4^\dagger c_1 + h.c.
$$
...
- 123
7
votes
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answers
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Jordan-Wigner transformation on a circle and spin structures?
Is there an analog of the Jordan-Wigner transformation between fermion algebra on a circle and a Pauli algebra? For example, the continuum analog of bosonization of "compact boson $\...
- 726
13
votes
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answer
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Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation
In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in ...
- 988
29
votes
2
answers
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$\phi^4$ theory kinks as fermions?
In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
- 8,815