All Questions
Tagged with spin-chains quantum-information
24
questions
2
votes
0
answers
96
views
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
0
votes
1
answer
287
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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
2
votes
0
answers
53
views
"Entropy" of a set of correlators in a quantum system
Please forgive the ill-posedness of this question; I am hoping someone can help me formulate what I am asking more clearly.
Consider the ground state of a one-dimensional quantum spin chain on $N$ ...
- 472
7
votes
0
answers
127
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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
3
votes
0
answers
144
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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
1
vote
0
answers
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
1
vote
1
answer
311
views
Can bond dimension vary from bond to bond?
Consider a bipartite system composed of subsystems $A$ and $B$, with corresponding Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, spanned by $\{\chi_1,...,\chi_n\}$ and $\{\phi_1,...,\phi_m\}$, ...
- 327
1
vote
1
answer
671
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How to add two Matrix Product States of different bond dimensions?
If I have the MPS representation of two quantum states, how do I add them? Note that the bond -dimensions need not be the same for the two MPSs.
- 11
0
votes
1
answer
112
views
Relationship between Hartley entropy and local dimension
I am recently reading a paper about entanglement entropy. It mentions that if we consider a 1D spin chain and write a pure state in the matrix product state:
\begin{align}
|\psi\rangle = A^{\sigma_1}A^...
- 1
3
votes
2
answers
1k
views
How to translate from a state/density matrix formalism to matrix product state representation?
From what I understand, MPS is just a simpler way to write out a state, compared to the density matrix. But how do I get those $A_i$ matrices? From all the examples I read, people just somehow "...
- 700
0
votes
1
answer
129
views
Matrix product state representation for the "infinitely repulsive hardcore boson" state
Consider a one-dimensional spin-1/2 chain with $N$ spins, and let $|\psi\rangle$ be the equal weight superposition of all states with no adjacent spin-ups, e.g.
for $N=3$ with open-boundary, $|\psi_{N=...
- 883
4
votes
0
answers
399
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Is it possible to diagonalize a Hamiltonian with both quadratic and linear terms in the fermi operators?
A quadratic Hamiltonian in the fermi operators is exactly diagonalizable. The most convenient way of describing these Hamiltonians is of the form:
$$\mathcal{H}=\displaystyle \sum_{j,k}(\alpha_{jk}a_{...
- 558
3
votes
1
answer
293
views
The dominant eigenvalue of the transfer matrix of a matrix product state
Consider a translation-invariant matrix product state
\begin{equation}
|\psi_L\rangle= \mathrm{Tr}[A(s_1)A(s_2)\ldots A(s_L)]|s_1 s_2\ldots s_L\rangle.
\end{equation}
I'm interested in the ...
- 883
2
votes
1
answer
333
views
Efficient MPS Description of a given quantum state
If we know the amplitudes of a (pure) quantum state wrt some basis, is there an algorithmic procedure to ensure an efficient MPS description (one with the lowest bond dimension) of the state ?
- 558
1
vote
1
answer
162
views
Correlation Functions: How can I prove this simple equation [closed]
The correlation functions of the Transverse Ising Model is beautifully explained in "Quantum Ising Phases and Transitions in Transverse Ising Models" Quantum Ising Phases and Transitions in ...
- 233