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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, ...
Souroy's user avatar
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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 $P(A)$ ...
Kim Dong's user avatar
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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 ...
brzepkowski's user avatar
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1 answer
88 views

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 = \...
Yoav Zack's user avatar
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127 views

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&...
QBHS's user avatar
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1 answer
199 views

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 ...
quics-ilver's user avatar
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52 views

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: ...
Luc4aa's user avatar
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88 views

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 ...
mavzolej's user avatar
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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 ...
Alex's user avatar
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285 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 ...
lgotta's user avatar
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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 ...
Suppenkasper's user avatar
3 votes
0 answers
137 views

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}}(\...
VaibhavK's user avatar
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151 views

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 ...
squareroottwo's user avatar
6 votes
2 answers
511 views

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 ...
Cha's user avatar
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1 answer
142 views

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 ...
CrisPhy's user avatar
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1 answer
572 views

$G$-injective MPS and symmetry-broken phases

First, a little bit of motivation. I was reading the paper "Matrix Product States and Projected Entangled Pair States" to try to learn more about MPS representations of symmetry broken ...
user196574's user avatar
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63 views

iTEBD\iDMRG for gapless systems

I have learned that the Matrix Product State (MPS) formulation can only handle systems where the entropy scales up to logarithmically. For gapped systems, as the entanglement entropy is constant, a ...
Souroy's user avatar
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0 answers
164 views

Intuitive understanding of bond dimensions

I am trying to understand what is bond dimension in tensor network more intuitively, by meaning of bond dimension I meant the tensor dimension that connects between tensors (in the example below the ...
Tomer's user avatar
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0 answers
142 views

Eigenvectors of Matrix Product Operator (MPO)

I am starting to work with tensor network and I wanted to know how to get the eigenvectors of a Matrix Product Operator (MPO). As far as I know when one is trying to diagonalize his Hamiltonian he ...
Tomer's user avatar
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1 answer
219 views

How to solve the eigenvalue problem of Matrix product operator (MPO) using Tensor network method?

I am new to the Tensor network approach. I need to solve the eigenvalue problem for a Matrix product Operator (MPO). What are some techniques, resources, softwares or packages available to do it? I am ...
Prem's user avatar
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1 vote
0 answers
68 views

How to obtain the goal function of DMRG by Lagrange multiplier method?

The goal of DMRG is to minimize the expectation value of energy, which can be written as $$ \frac{d}{d |\psi \rangle} \frac{\langle \psi | \hat{H} | \psi \rangle}{\langle \psi | \psi \rangle} = 0. \...
brzepkowski's user avatar
1 vote
0 answers
101 views

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, ...
Souroy's user avatar
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0 answers
133 views

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 ...
Souroy's user avatar
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0 answers
119 views

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 ...
Souroy's user avatar
  • 193
0 votes
1 answer
144 views

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 ...
Souroy's user avatar
  • 193
0 votes
1 answer
89 views

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 ...
Souroy's user avatar
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2 votes
0 answers
90 views

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: \begin{equation} |\psi\rangle = \sum_\alpha^{r}s_\...
Karim Chahine's user avatar
7 votes
0 answers
127 views

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....
brzepkowski's user avatar
3 votes
2 answers
349 views

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 ...
user196574's user avatar
  • 2,292
2 votes
1 answer
182 views

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 ...
raf_quantum's user avatar
1 vote
0 answers
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 ...
user333905's user avatar
0 votes
1 answer
94 views

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 ...
brzepkowski's user avatar
1 vote
0 answers
92 views

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 ...
0 votes
1 answer
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 ...
KyVinE's user avatar
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0 votes
0 answers
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. ...
Juri V's user avatar
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0 answers
106 views

Tensor contraction in matrix product state

From Matrix product state, the matrix product can be written as $$ |\Psi\rangle = \sum_{\{s\}} \operatorname{Tr}\left[A_1^{(s_1)} A_2^{(s_2)} \cdots A_N^{(s_N)}\right] |s_1 s_2 \ldots s_N\rangle, $$ ...
Lancashire3000's user avatar
2 votes
0 answers
171 views

Mutual information of a tensor network

Suppose I've got a tensor network (TN) representing some bipartite quantum state, $|\Psi\rangle$. Using the Schmidt decomposition, I can write $|\Psi\rangle = \sum_{k=1}^r \sqrt{\lambda_k}|\chi_k\...
redfive's user avatar
  • 327
2 votes
0 answers
34 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 ...
Lagrenge's user avatar
  • 883
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 $\{\phi_1,...,\phi_m\}$, ...
redfive's user avatar
  • 327
1 vote
1 answer
105 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 ...
Kitchen's user avatar
  • 165
-1 votes
1 answer
220 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 ...
bidon's user avatar
  • 17
1 vote
1 answer
308 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: ...
bidon's user avatar
  • 17
2 votes
1 answer
120 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 ...
jackaraz's user avatar
  • 133
1 vote
1 answer
671 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.
Asir Abrar's user avatar
3 votes
1 answer
335 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 ...
Ricky Pang's user avatar
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^...
jisutich's user avatar
0 votes
1 answer
372 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. ...
Ricky Pang's user avatar
1 vote
0 answers
365 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 ...
ricci_flow's user avatar
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 "...
Kim Dong's user avatar
  • 700
3 votes
0 answers
248 views

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-...
Lagrenge's user avatar
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