All Questions
Tagged with spin-chains quantum-entanglement
18
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What is the appropriate 'Page Value' for entanglement entropy in a symmetry sector, say for example with a $U(1)$ symmetry?
Don Page derived the formula for the average entropy of a subsystem of a quantum system (assumed to be in a pure state), if the system is partitioned into two subsystems of dimensions $m$ and $n$, ...
- 43
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88
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How non-local can the interactions be for Density Matrix Renormalization Group (DMRG) to still work?
I know that Density Matrix Renormalization Group (DMRG) / Tensor Networks (TN) work well for local Hamiltonians, where on each site I have a fermion or boson, which only have nearest-neighbor ...
- 2,921
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96
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Obtaining a Matrix Product State (MPS) using Schmidt Decomposition for a Tripartite State
I understand that one method to derive an MPS representation of a quantum state involves applying the Schmidt decomposition $ N−1$ times. While I'm familiar with the diagrammatic notation, I wanted to ...
- 1,198
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MPS canonical form
If I express a MPS in its (left, right or anything else) canonical form, does this representation encode all Schmidt decompositions between a subsystem and its complement,rather than only the Schmidt ...
- 325
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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 ...
- 53
3
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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 ...
- 2,292
2
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387
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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 $L$ ...
- 2,292
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153
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How does the proof for the area law for 1D systems work?
I am currently reading this paper in order to understand the proof of the area law for one dimensional, low energy systems such as 1D spin chains. The main area law theorem is given on page 13 and is ...
- 129
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Uniqueness of AKLT Ground State vs. SU(2) symmetry and Lieb-Schultz-Mattis theorem
I have a question in my mind regarding the uniqueness of AKLT ground state. Currently I am watching a video clip of MPS and I am curious why the AKLT ground state model is unique gapped ground state. ...
- 413
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$S^+$ acting on a spin chain raises the entropy by at most $\ln(2)$
Consider the operator $S^+ = \sum_{i=1}^L S^+_i$ acting on a spin-chain of spin-1/2 particles.
Denote the half-chain Von Neumann entanglement entropy of a state $|\psi\rangle$ by $\mathbb{S}[|\psi\...
- 2,292
5
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846
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How can you (computationally) calculate the halfchain entanglement entropy of a spinchain?
I am simulating a (small) spinchain with exact diagonalization and dynamics. I would like to track the entanglement entropy of half the chain with the other part of the chain.
I have the vectors of ...
- 548
3
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169
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Why do matrix product states work at critical point?
Matrix product states satisfy the entanglement area law, which should be a property of gapped states.
But usually, MPS work well in 1D quantum phase transition problems.
As far as I know, ...
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4
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164
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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, ...
- 1,469
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Physical Interpretation of the Spectrum of MPS Transfer Matrices
Take an injective, translation invariant MPS with transfer matrix $E = \sum_\sigma \overline{A^\sigma} \otimes A^\sigma$ (i am using the terminology of https://arxiv.org/abs/quant-ph/0410227 , eq. (6))...
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