Questions tagged [tensor-network]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
17 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
75 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 ...
user avatar
  • 1
0 votes
0 answers
51 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. ...
user avatar
  • 45
0 votes
0 answers
60 views

Tensor contraction in matrix product state

From Matrix product state, the matrix product can be written as $$ |\Psi\rangle = \sum_{\{s\}} \operatorname{Tr}\left[A_1^{(s_1)} A_2^{(s_2)} \cdots A_N^{(s_N)}\right] |s_1 s_2 \ldots s_N\rangle, $$ ...
user avatar
2 votes
0 answers
50 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\...
user avatar
  • 207
1 vote
0 answers
18 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 ...
user avatar
  • 743
1 vote
1 answer
49 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 $\{\phi_1,...,\phi_m\}$, ...
user avatar
  • 207
1 vote
1 answer
49 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 ...
user avatar
  • 45
0 votes
0 answers
54 views

Can a classical approximation of a quantum model give smaller energy?

I'm analyzing phase transitions of the XXZ model on a honeycomb lattice. The fully quantum Hamiltonian can be written as follows $$ H = - \bigg( J \sum_{<i, i'>, i<i'} \bar{S}_i \cdot \bar{S}...
user avatar
1 vote
1 answer
52 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 ...
user avatar
  • 11
0 votes
1 answer
81 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: ...
user avatar
  • 11
2 votes
1 answer
67 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 ...
user avatar
  • 133
1 vote
1 answer
76 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.
user avatar
2 votes
1 answer
55 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 ...
user avatar
0 votes
1 answer
58 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^...
user avatar
0 votes
1 answer
98 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. ...
user avatar
1 vote
0 answers
119 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 ...
user avatar
3 votes
2 answers
216 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 "...
user avatar
  • 518
3 votes
0 answers
101 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-...
user avatar
  • 743
0 votes
1 answer
49 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=...
user avatar
  • 743
2 votes
1 answer
85 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 ...
user avatar
  • 743
0 votes
1 answer
87 views

Truncation Problem of Density Matrix Renormalisation Group (DMRG)

I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site ...
user avatar
2 votes
1 answer
129 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 ?
user avatar
  • 528
1 vote
0 answers
23 views

Thermodynamic Limit of Entanglement-Entropy like quantities

Suppose i have, in one spatial dimension, a unique ground state $\Omega$ of a local, gapped, translational invariant Hamiltonian. Denote by $\sigma_s$ the density matrix of $\Omega$ on lattice sites $\...
user avatar
  • 1,389
1 vote
0 answers
49 views

Is there any study about using DMRG to simulate two spin chains coupled at only several sites on each chain?

Is there any study about the DMRG simulation of such kind of systems? or Each blue site is a spin, for example. Only one or several spins on each chain are coupled.
user avatar
  • 204
4 votes
0 answers
143 views

Is the only difference between tDMRG and TEBD the way the central sites are shifted?

I have been reading up on time evolution methods using matrix product states. Reading from Schollwoeck's notes on the density matrix renormalization group, (https://arxiv.org/abs/1008.3477), I looked ...
user avatar
4 votes
0 answers
103 views

Hopf algebras vs Fusion categories for topological order

Disclaimer: Before I begin with the question I want to warn that some people would argue that it is a math question and not a physics question. However, it finds it origins in the study of topological ...
user avatar
  • 1,276
1 vote
1 answer
326 views

Matrix product state (MPS): Creating and understanding a specific 2-site Ising ground state?

I've been trying to better understand matrix product states (in order to implement them in code in the near future), so I'm considering small examples. I was wondering if I could get some ...
user avatar
  • 349
0 votes
1 answer
103 views

Tensor Network/MPS Code examples for simple condensed matter systems?

I've been recently learning about numerical methods in physics, and have come across matrix product states and tensor networks. This is definitely a vague question, but I was wondering if anyone knew ...
user avatar
  • 349
1 vote
0 answers
69 views

Optimizing MERA disentanglers to represent a specific state

I've read multiple papers (e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.144108) on the multiscale entanglement renormalization ansatz (MERA) where algorithms are given for how to ...
user avatar
  • 134
1 vote
0 answers
33 views

AdS/CFT Correspondence With Discrete Bulk Geometry

I am looking for an answer from AdS/CFT perspective in 2+1D. If there is a discrete bulk geometry rather than continuous, is it possible to have CFT on boundary with discrete symmetries? Can we have ...
user avatar
  • 11
2 votes
0 answers
89 views

How to decompose Hamiltonian into a MPO in DMRG

I would like to write a python script for performing DMRG. I'm following the code here, but I do not understand the second part of the code where the $XX$ Hamiltonian is decomposed into a matrix ...
user avatar
  • 517
1 vote
0 answers
75 views

How should I self-study condensed matter in many-body quantum systems? [closed]

I am a computer scientist that has been doing research on quantum computing and tensor networks for a couple of years. I have a strong understanding of the math and multilinear algebra underlying ...
1 vote
0 answers
368 views

Schmidt decomposition for Matrix Product State in canonical form

During a lecture on comp. Quantum Phyiscs the concept of Matrix Product States (MPS) (with open boundry conditions) was introduced in the form $$\vert\psi\rangle = \sum_{i_1,\dots,i_n}\psi_{i_1\dots ...
user avatar
  • 1,079
0 votes
0 answers
114 views

Why is tensor networks applicable only to ground states?

When one uses tensor network as a wave function ansatz for a variational method, we usually use this scheme to find a ground state. Why can’t we apply the tensor network formalism to find any excited ...
user avatar
13 votes
2 answers
614 views

What is meant exactly by "renormalization" in condensed matter physics, specifically in density matrix renormalization group (DMRG)?

I first encountered the concept of renormalization in the context of statistical physics. Here, the renormalization "group" is a set of transformations of the system such that the Hamiltonian $H(J,\...
user avatar
  • 4,366
2 votes
0 answers
204 views

Partial trace of matrix product state

I have come accross a formula that puzzles me a bit in the proof of lemma 23 (page 32) of this paper. The authors start from a (translationally-invariant) matrix product state: $$\lvert\psi\rangle := ...
user avatar
-1 votes
1 answer
356 views

How to left-normalize a Matrix Product State

If you are reading this, you should probably have some background in Tensor Networks or Matrix Products States or this will be insufficient information. So when putting a MPS into left (or right) ...
user avatar
-1 votes
1 answer
129 views

Can a random product state be expressed as a MPS (Matrix product state)?

$ |\psi\rangle = \prod_{i=1}^{N}|s_{i}\rangle $ where, $|s_{i}\rangle = \cos\left (\frac{\theta_{i}}{2}\right )|\uparrow_{i}\rangle + \exp{(i\phi_{i})}\sin\left (\frac{\theta_{i}}{2}\right )|\...
user avatar
0 votes
0 answers
111 views

Reduction from PEPS to MERA possible?

Multi-scale entanglement renormalization ansatz (MERA) includes two kinds of isometric tensors, disentanglers and isometries. Thus tensors in MERA are by definition composed of isometries. Meanwhile ...
user avatar
0 votes
0 answers
135 views

Finding eigenvalue and eigenvector of non-Hermitian matrix product operator

Suppose we have a matrix product operator (MPO) $X$ with a periodic boundary, which is not necessarily Hermitian. That is, $$X^{s_1\cdots s_n}_{s^{\prime}_1\cdots s^{\prime}_n}:=\mathrm{Tr}(G_1[s_1,...
user avatar
5 votes
2 answers
397 views

Is HaPPY code a certain type of MERA?

Pastawski, Yoshida, Harlow, and Preskill introduced the HaPPY code in their (now famous) paper, arXiv:1503.06237, as a way to model the AdS/CFT correspondence as a quantum error-correcting code. ...
user avatar
  • 175
2 votes
0 answers
65 views

All infinite volume matrix product states are in different super-selection sectors?

Consider two matrix product states $\Psi_1,\Psi_2$, i.e. let them be described (schematically) by $$ \Psi_\alpha = \sum_{...i_n ... } \left(\ell_{\alpha}, \left[\prod_{i \in \mathbb{Z}} E_\alpha(i) \...
user avatar
  • 1,389
5 votes
0 answers
259 views

Does a gapped, local and non-frustration-free 1D Hamiltonian have an exact MPS groundstate?

(Fact 1) It is known that any arbitrary matrix product state (MPS) is a unique groundstate of a gapped, local, and frustration-free parent Hamiltonian (Perez-Garcia et al. 2007). It is by Fact 1, that ...
user avatar
  • 147
3 votes
1 answer
117 views

Why do matrix product states work at critical point?

Matrix product states satisfy the entanglement area law, which should be a property of gapped states. But usually, MPS work well in 1D quantum phase transition problems. As far as I know, ...
user avatar
3 votes
0 answers
54 views

Can we define a parent Hamiltonian for a given Multiscale Entanglement Renormalization Ansatz (MERA) state?

Given a state represented by a MERA (Multiscale Entanglement Renormalization Ansatz), can we define a local Hamiltonian such that the MERA is the exact ground state of such a Hamiltonian? If this is ...
user avatar
0 votes
1 answer
186 views

Can any 1D critical state be represented by a MERA tensor network?

My understanding of the Multiscale Entanglement Renormalisation Ansatz (MERA) is that it is designed to represent highly entangled, but low complexity states. Is MERA capable of representing high ...
user avatar
1 vote
0 answers
149 views

Tensor networks and construction of PEPO

I have a basic understanding of how to construct the tensors of an MPO (matrix product operator), based on, in part, on PhysRevA.81.062337 (arXiv version), see their equations 5 and 6. I am looking ...
5 votes
1 answer
201 views

Nature of the $W$-state in the thermodynamic limit

Consider a matrix product state on $\mathbb{C}^{d N}$: $$ \Psi = \sum_{\sigma_1,...\sigma_N} A_1(\sigma_1) ... A_N(\sigma_N) |\sigma_1 ... \sigma_N \rangle \quad \quad (\text{OBC MPS}) $$ with some ...
user avatar
  • 1,389
3 votes
1 answer
177 views

Doing addition and subtraction with tensor diagrams?

Tensor diagrams are a beautiful and useful tool for making calculations with tensors, up until you need to contract with the sum or difference of two tensors, at which point it seems to become awful. ...
user avatar