# Exact holographic tensor networks for the Motzkin spin chain

@article{Alexander2021ExactHT, title={Exact holographic tensor networks for the Motzkin spin chain}, author={Rafael N. Alexander and Glen Evenbly and Israel Klich}, journal={Quantum}, year={2021}, volume={5}, pages={546} }

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network's utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works…

## 6 Citations

### Highly Entangled Spin Chains and 2D Quantum Gravity

- PhysicsSymmetry
- 2020

Large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams, are introduced to study of Motzkin and Fredkin spin chains from a different viewpoint.

### Tensor Networks for Language Modeling

- Computer ScienceArXiv
- 2020

A uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data that has the ability to condition or marginalize sampling on characters at arbitrary locations within a sequence, with no need for approximate sampling methods.

### The spin-one Motzkin chain is gapped for any area weight $t<1$

- Mathematics
- 2022

We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-1 Motzkin chain is gapped for any area weight t < 1. Existence of a ﬁnite spectral gap is necessary for the Motzkin Hamiltonian to…

### Tensor Networks for Probabilistic Sequence Modeling

- Computer ScienceAISTATS
- 2021

A novel generative algorithm is introduced giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression, which permits the generation of richly structured text in a manner that has no direct analogue in current generative models.

### Number-State Preserving Tensor Networks as Classifiers for Supervised Learning

- Computer ScienceArXiv
- 2019

A restricted class of tensor network state, built from number-state preserving tensors, is proposed, argued to be a natural choice for classifiers and to be as powerful as generic (unrestricted) tensor networks in this task.

### Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol

- PhysicsPhysical Review X
- 2022

Thomas Schuster,1, ∗ Bryce Kobrin,1, 2, ∗ Ping Gao,3 Iris Cong,4 Emil T. Khabiboulline,4 Norbert M. Linke,5 Mikhail D. Lukin,4 Christopher Monroe,5 Beni Yoshida,6 and Norman Y. Yao1, 2 Department of…

## References

SHOWING 1-10 OF 48 REFERENCES

### Exact rainbow tensor networks for the colorful Motzkin and Fredkin spin chains

- PhysicsPhysical Review B
- 2019

We present bulk tensor networks that exactly represent the ground states of a continuous family of one-dimensional frustration-free Hamiltonians. These states, which are known as area-deformed…

### Gapless quantum spin chains: multiple dynamics and conformal wavefunctions

- Physics
- 2017

We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the…

### Finitely correlated states on quantum spin chains

- Mathematics
- 1992

We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a…

### Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks

- Physics
- 2016

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important…

### Criticality without frustration for quantum spin-1 chains.

- PhysicsPhysical review letters
- 2012

This work proposes the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior.

### Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

- PhysicsProceedings of the National Academy of Sciences
- 2016

This work suggests that simple quantum matter is richer and can provide much more quantum resources than expected, and introduces a class of exactly solvable one-dimensional physical models which can prove violate the area law by a square root, i.e., exponentially more than the logarithm.

### Novel quantum phase transition from bounded to extensive entanglement

- PhysicsProceedings of the National Academy of Sciences
- 2017

This work has uncovered a unique, physically transparent quantum phase transition in a spin chain where entanglement entropy itself jumps from low scaling, most typical for gapped models and short-range correlations, to a critical phase where the scaling exhibits an extraordinary amount ofEntanglement.

### Matrix product state renormalization

- Physics
- 2016

The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization…

### Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants

- Mathematics
- 2017

Matrix product vectors form the appropriate framework to study and classify one-dimensional quantum systems. In this work, we develop the structure theory of matrix product unitary operators (MPUs)…

### Fourier transform for fermionic systems and the spectral tensor network.

- Computer SciencePhysical review letters
- 2014

A new class of tensor network is proposed that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law and can be used as generic structures to variationally describe more complicated systems, such as interacting fermions.