# Questions tagged [tensor-network]

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### DMRG for anyons

I want to do some DMRG calculations for anyons. For example, consider the golden chain model for fibonacci anyons. https://arxiv.org/pdf/cond-mat/0612341 I have two anyon types: $1, \tau$. However, ...
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1 vote
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### Example of an injective matrix product state (MPS)

I am struggling to understand what is an injective matrix product state (MPS). From the definition, it is said that an injective MPS $|M(A)\rangle$is one where the tensor $A$ has a projector $P(A)$ ...
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### Why are PEPS more frequently used when simulatind 2D systems rather than branching MERA?

From what I've read it seems that PEPS is a go-to method while simulating 2D quantum systems. Why is it the preferred method rather than branching MERA? The contraction of PEPS is a #P-complete ...
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• 409
1 vote
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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, ...
• 193
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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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### What are the advantages of tensor network algorithms over monte-carlo simulations in terms of time-evolution?

I understand that tensor networks and monte carlo simulations are based on completely different principles. However, to my knowledge both are used to simulate the time evolution of a system. Is there ...
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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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### How to find canonical form of three site MPS?

I am trying to implement the iTEBD algorithm for a certain model, where the hamiltonian acts on three successive sites. This means that my time-evolution operator is a rank 6 tensor, acting on a rank ...
• 193
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### Physical meaning of Schmidt states

Given a bipartite system AB (where A and B are the subsystems), a generic pure quantum state $|\psi\rangle$ on AB can be Schmidt-decomposed into: |\psi\rangle = \sum_\alpha^{r}s_\...
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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....
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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 ...
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### Why Matrix Product State (MPS) representation provide fast computation?

I am interested in tensor networks and I am trying to understand why MPS (for example) provide an efficient representation of a quantum state. In order to transform the quantum state in MPS ...
1 vote
153 views

### 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 ...
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### Reshaping $U$ and $V^\dagger$ matrices resulting from an SVD into rank-3 tensors

Let's say, that we have a $6 \times 6$ matrix $M$. By conducting an SVD of $M$ we obtain $USV^\dagger$ matrices, where $U$ is of size $6 \times 6$ and is left-normalized, $S$ is diagonal with 6 ...
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1 vote
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### Resource recommendation for time-dependent DMRG

I am looking for any references (journal article/ review /tutorial) to understand the TEBD (Time-evolution by block decimation) algorithm and code it up for a simple 1D model system. Broadly, I am ...
260 views

### Particle number conservation in matrix product state

I've been trying to understand how particle number conservation is enforced in matrix product state algorithms. As far as I understand, if the Hamiltonian commutes with the number operator, you can ...
317 views

### Overlap of Matrix Product States (Python)

I'd like to implement the TEBD (finite, real time evolution) by hand (in python) and want to compute the overlap of a reference MPS with the time evolved MPS. I want to regard a simple Ising Chain. ...
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### Tensor contraction in matrix product state

From Matrix product state, the matrix product can be written as $$|\Psi\rangle = \sum_{\{s\}} \operatorname{Tr}\left[A_1^{(s_1)} A_2^{(s_2)} \cdots A_N^{(s_N)}\right] |s_1 s_2 \ldots s_N\rangle,$$ ...
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### Projected Entangled Pair States (PEPS) and classical statistical physics

In the paper arXiv:quant-ph/0601075 the authors introduce an interesting correspondence between Projected Entangled Pair States (PEPS) and classical statistical physics. Basically, for any locally-...
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