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Pinch points in fidelity per site (quantum phase transitions)

In Sachdev's Quantum Phase Transitions he defines a quantum phase transition in an infinite lattice as the point in which the ground energy as a function of the parameters of the system becomes non-...
2
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1answer
171 views

Why do we use matrix product states?

Given a many body $\vert\psi\rangle$, we can express it in terms of a matrix product state. That is, $\vert\psi\rangle = \sum_{i,j..k}\psi_{i,j..k}\vert i,j..k\rangle$ can be rewritten as $\vert\...
1
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1answer
56 views

Reduced density matrix of the edge spin-1/2 in AKLT spin chain

I am trying to understand the paper titled, "Entanglement in a Valence-Bond-Solid State" by Fan, Korepin, and Roychowdhury (https://arxiv.org/abs/quant-ph/0406067). I was able to understand the ...
1
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0answers
68 views

How does one bound the growth of the support of local operators in the Transverse-Field Ising Chain?

Consider the transverse-field Ising chain (TFIC) in a transverse-field $B$: $$H_{TFIC}(B)\equiv -\sum_{j=1}^{N-1} \sigma^x_j\sigma^x_{j+1}+B\sum_{j=1}^N \sigma^z$$ At $B=0$, we have the classical ...
0
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1answer
113 views

ground state of spin chain with $Z_i X_{i+1} Z_{i+2}$ interaction

the problem comes from transverse field Ising model, with an extra 3-spin interaction term $$H=H_0+H_1+H_2=-h\sum_{i=1}^{N}X_i -\lambda_1 \sum_{i=1}^{N-1}Z_i Z_{i+1}-\lambda_2 \sum_{i=1}^{N-2}Z_i X_{i+...
3
votes
2answers
302 views

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 ...