Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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Prove that negative absolute temperatures are actually hotter than positive absolute temperatures
Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
user7757
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R-matrix for spin chains
In algebraic Bethe ansatz procedure, one of the central objects is the R-matrix satisfying the Yang-Baxter equation, but all the papers/books give directly its expression without deriving it, so my ...
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Detailed derivation and explanation of the AKLT Hamiltonian
I am trying to read the original paper for the AKLT model,
Rigorous results on valence-bond ground states in antiferromagnets. I Affleck, T Kennedy, RH Lieb and H Tasaki. Phys. Rev. Lett. 59, 799 (...
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To calculate the correlation functions of an XX spin chain, Wick's theorem is used. But is it valid for a chain of any size?
The correlation functions found in Barouch and McCoy's paper (PRA 3, 2137 (1971)) for the XX spin chain use a method which uses Wick's theorem. For the zz correlation function, this gives
$\langle \...
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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 - ...
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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 $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
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Confusion about duality transformation in 1+1D Ising model in a transverse field
In 1+1D Ising model with a transverse field defined by the Hamiltonian
\begin{equation}
H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x
\end{equation}
There is a duality transformation which ...
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Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation
In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in ...
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Parent hamiltonian of AKLT state
Given a translationally invariant Matrix Product State (assuming periodic boundary condition) on $N$ sites of dimension $d$ each, which takes the form
$\sum_{i_1,i_2\ldots i_N=1}^dTr(A_{i_1}A_{i_2}\...
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Is there any relation between density matrix renormalization group (DMRG) and renormalization group (RG)?
Probably I am going to receive many down-votes for this post but I really need to ask this question here.
I am new to statistical mechanics.
I wanted to learn Density Matrix Renormalization Group (...
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Is there any qualitative difference between the WZW $SO(2)_1$ and the WZW $SU(2)_1$ CFT?
Consider the anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_{n=1}^N S^x_n S^x_{n+1}+S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$
which for $\Delta = 0$ realizes the Wess-Zumino-Witten (WZW) $...
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Mathematical meaning for Algebraic Bethe Ansatz
I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is ...
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Differentiating between Tensor Networks
I am trying to study tensor networks and their application to quantum phase transitions. However, I had a question concerning the connection between the projected entangled-pair states (PEPS) and the ...
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Partial Transpose in Gapped Time-reversal Symmetric Spin Chains
Suppose you have a one-dimensional quantum spin system with on-site Hilbert spaces $\mathcal{S}$. Suppose there is an anti-unitary, anti-linear operator $C$ on $\mathcal{S}$ inducing an anti-linear, ...
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How to stack two Haldane chains?
This questions is a follow up to a pervious question of mine:
Inverse of Haldane phase?
Now that I know that Haldane phase is it's own inverse, I am having trouble is visualizing how could we stack ...
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