Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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iTEBD real time evolution for 3-body time evolution operator
I am trying to implement the iTEBD algorithm for real-time evolution of the PXP model. Here, $P$ is the projector onto the ground state, and $X$ is the Pauli spin matrices.
I know for the 2-body case, ...
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CFT description of polynomially degenerate, critical spin-chain
For length $L$ spin chains described by conformal field theories, there's a nice a way to extract the central charge via fitting the following ansatz for the entanglement entropy of the ground state:
$...
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What is $v$ in conformal field theory?
In reading about conformal field theory applied to spin chains of length $N$, I've seen the following expression several times, describing how the central charge $c$ can be extracted from the ground ...
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Normalization in tensor networks [closed]
I am trying to implement the iTEBD algorithm for the $PXP$ model, i.e, the hamiltonian is
$$H = \sum_iP_{i-1}X_iP_{i+1}.$$
Here $P$ is the projector onto the ground state and $X$ is the usual pauli x ...
- 193
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How do you calculate the entanglement entropy of a tensor network?
I found that the entanglement entropy can be calculated using the Schmidt coefficients of the state, using
$S = -\sum_i|\alpha_i|^2\log(|\alpha_i|^2)$
In the case of tensor networks, does this simply ...
- 193
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Why the ground-state energy of S-1/2 Anti-Ferromagnetic Heisenberg Chain is not$-\frac{N}{4}J$
The Hamiltonian of traditional Heisenberg model is
$$\hat H = J\sum_{<i,j>}\vec{S_i}\cdot\vec{S_j}=J\sum_{<i,j>}\left(S_i^zS_j^z+\frac{1}{2}\left(S_i^+S_j^-+S_i^-S_j^+\right)\right)$$
if J ...
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Magnons and creation and annihilation operators
I am trying to obtain the spin waves (or magnons) arising from a 1D Heisenberg spin-chain, namely
\begin{equation}
{\cal H}=-J\sum_{i=1}^N \mathbf{S}_i\cdot \mathbf{S}_{i+1}
\end{equation}
After ...
- 137
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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. ...
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How to handle Dzyaloshinkii-Moriya imaginary terms in Heisenberg chain?
The DM interaction has three coordinate-specific terms when splitting it up. Two of these, the DM-x and DM-z terms, are imaginary when we transform them into series of raising and lowering operators. ...
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How to efficiently get the largest probabilities / amplitudes of a quantum state stored as an MPS?
Let's say, that we have the following pure, superposition state
$$ |\psi \rangle = \frac{1}{\sqrt{2}}|000001 \rangle + \frac{1}{2}|101101 \rangle + \frac{1}{2}|100100 \rangle $$
stored in the MPS form....
- 409
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Is there a relationship between spin correlation and entanglement entropy?
Can someone explain whether there is a connection between spin correlation in say a 1D Heisenberg chain and its entanglement entropy? I'd say, albeit naively, that there is just from their concepts. ...
- 11
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Writing the Random Matrix model corresponding to any physical hamitonian model
I am an amateur in Random Matrix Theory (RMT). In RMT, we start with ensemble of a random matrices of a certain symmetry classes (GOE, GUE..) to find the various distribution of our interest, e.g.- ...
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Is there a zero correlation length spin-$1$ chain in the Haldane phase?
The ground state of the spin-$1$ AKLT model gives an example of a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological (SPT) phase, the Haldane phase. This state is a nice example of the ...
- 2,292
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Calculating entanglement negativity without constructing density matrix
There are two procedures that I know of for finding the von Neumann entanglement entropy of a bipartite system split between $A$ and $B$ - a bad way and a better way. I have in mind computationally ...
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How can I actually get to the AKLT state from a product state in finite depth?
I'm currently learning about symmetry-protected topological phases in one dimension. The ground state of the AKLT model provides one such example. In particular, the AKLT state for any length $L$ ...
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