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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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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Where is the orthogonality center of the AKLT ground state matrix product state?
It is a known fact that the ground state of the 1D Affleck-Kennedy-Lieb-Tasaki model (AKLT) can be represented as a matrix product state (MPS) of the following form:
$$
\left|{\psi}\right\rangle = \...
- 167
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What is the computational complexity of adding two matrix product states?
I am relatively new to matrix product states (MPS) and I'm interested in the computational complexity of performing an operation of the form A|a> + B|b> where A, B are scalar coefficients and |a&...
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Understanding the left-canonical matrix product state
I am trying to understand how to represent any quantum state as an MPS while working through this review by Schollwöck. My goal is to take any random $2^N$ dimensional vector and construct its MPS ...
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Generating Matrix Product States from a (random) vector
I try to decomposite an arbitrary quantum state into a matrix product state. For this i follow this paper by U. Schollwöck where especially section 4.1.3 is relevant.
So far I did the following:
...
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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 ...
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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 ...
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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 ...
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What is a parent Hamiltonian? [closed]
The term is used throughout the literature but I was not able to find a definition or even a paper properly introducing the term. What does a Hamiltonian have to satisfy to be a parent Hamiltonian?
An ...
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Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula and tensor networks
While working with AdS/CFT, I am trying to look at the nature of the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula in AdS/CFT, which is the statement that $S(\rho _{A}|\sigma _{A})=S_{\text{bulk}}(\...
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Construct an operator using outer product of two MPS using TeNPy
I am fairly new to Matrix Product State (MPS) formalism, but I've used Density Matrix Renormalisation Group (DMRG) techniques before. I'm learning to use TeNPy, and a particular problem I am trying to ...
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Is there Difference Between 1D and 2D in Spin model?
The Motivation is That:In the Tensor Network method, they say 'time evolution MPS(Matrix Product State) work quite well in 1 Dimension'.
but as I think any 2D could be expressed by 1D
for example in ...
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Question about the 'reduced basis transformation'
I' ve been reading the review Ulrich Schollwöck: The density-matrix renormalization group in the age of
matrix product states (arXiv link)
and encountered with a question about the so called 'reduced ...
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