# Questions tagged [tensor-network]

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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 ...
56 views

### 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 ...
1 vote
184 views

### 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 ...
50 views

1 vote
28 views

### Algorithm that checks if a subspace of states contains a product state

Suppose I have two identical qudits, the full Hilbert space is $\mathcal{H}=(\mathbb{C}^{d})^{\otimes 2}$. Say I'm given a supspace of states $\Lambda\subset \mathcal{H}$. What is the fastest ...
1 vote
232 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 $\{\phi_1,...,\phi_m\}$, ...
1 vote
81 views

### Tensor product operator of 2D ( for Tensor Network)

I have difficulty representing Tensor Product Operators (TPO) of 2D in a concrete form. For example in 1D case, according to the tutorial in ITensor , the TPO of the Hamiltonian for the simple Ising ...
1 vote
157 views

### Tensor Networks with Julia and implementing given Hamiltonian

I have this Hamiltonian: (ref: https://arxiv.org/abs/1302.5843) I want to solve this Hamiltonian by using tensor networks. I wanted to make the implementation with ITensors, Julia. However, I am ...
1 vote
234 views

### Ground State calculation for defined 2D Ising Model with tensor networks

I have a Hamiltonian and 2D spin-lattice system. I am trying to find a ground state configuration. Spin interactions are long-ranged so I am trying to use PEPS to approximate. My question is this: ...
91 views

### Tensor networks and sign problem

I've been wondering about why tensor networks are capable of avoiding MC sign problem (e.g. see arXiv:1611.04791 [hep-lat] and the references therein). I have seen many papers stating that the TNs are ...
1 vote
437 views

### 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.
207 views

### Conserved charge in Density Matrix Renormalization Group (DMRG)

Currently I am facing a problem which relates to the conserved quantities in DMRG. I use old-fashioned DMRG (Steven White approach) to compute the ground state of certain models. However, the ground ...
103 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^...
249 views

### 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. ...
1 vote
297 views

### Rigorous derivation of entanglement entropy bound of MPS

I am working on a summer project and am trying to prove the Von Neumann entropy of an MPS is bounded by a constant to gain some introduction. While this easily follows if we start with the MPS being ...
905 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 "...