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Related papers: Classifying quantum phases using Matrix Product St…

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Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…

Quantum Physics · Physics 2025-05-02 Sebastian Leontica , Andrew G. Green

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…

Strongly Correlated Electrons · Physics 2024-09-11 Jan Naumann , Erik Lennart Weerda , Matteo Rizzi , Jens Eisert , Philipp Schmoll

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…

Quantum Physics · Physics 2025-05-27 Alex Mossi , Bojan Žunkovic , Kyriakos Flouris

Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and…

Quantum Physics · Physics 2021-10-22 Kyrylo Snizhko , Nihal Rao , Parveen Kumar , Yuval Gefen

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…

Quantum Physics · Physics 2021-09-22 Caio B. D. Goes , Askery Canabarro , Eduardo I. Duzzioni , Thiago O. Maciel

We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area law entanglement phase of the steady state. Our primary example is circuits with unitaries…

Statistical Mechanics · Physics 2021-06-22 Shengqi Sang , Timothy H. Hsieh

We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build…

Strongly Correlated Electrons · Physics 2019-02-05 Tyler D. Ellison , Lukasz Fidkowski

We consider Projected Entangled Pair State (PEPS) models with a global $\mathbb Z_N$ symmetry, which are constructed from $\mathbb Z_N$-symmetric tensors and are thus $\mathbb Z_N$-invariant wavefunctions, and study the occurence of…

Statistical Mechanics · Physics 2017-08-15 Manuel Rispler , Kasper Duivenvoorden , Norbert Schuch

The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…

Strongly Correlated Electrons · Physics 2013-05-29 Xie Chen , Bei Zeng , Zheng-Cheng Gu , Isaac L. Chuang , Xiao-Gang Wen

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

Quantum Physics · Physics 2025-10-16 Laurens Lootens , Clement Delcamp , Frank Verstraete

We consider symmetry protected topological (SPT) phases with finite non-invertible symmetry $\mathcal{C}$ in 1+1d. In particular, we investigate interfaces and parameterized families of them within the framework of matrix product states.…

Strongly Correlated Electrons · Physics 2026-02-19 Kansei Inamura , Shuhei Ohyama

Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under…

Quantum Physics · Physics 2025-12-17 Luca Capizzi , Vittorio Vitale

Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question…

Strongly Correlated Electrons · Physics 2018-11-27 Andras Molnar , José Garre-Rubio , David Pérez-García , Norbert Schuch , J. Ignacio Cirac

Recently, it was realized that quantum states of matter can be classified as long-range entangled (LRE) states (i.e. with non-trivial topological order) and short-range entangled (SRE) states (\ie with trivial topological order). We can use…

Strongly Correlated Electrons · Physics 2014-02-05 Xiao-Gang Wen

For the classification of SPT phases, defining an index is a central problem. In the famous paper [PTBO1], Pollmann, Tuner, Berg, and Oshikawa introduced ${\mathbb Z}_2$-indices for injective matrix products states (MPS) which have either…

Mathematical Physics · Physics 2019-04-04 Yoshiko Ogata

The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit an enormously rich…

Quantum Physics · Physics 2007-05-23 F. Verstraete , M. M. Wolf , D. Perez-Garcia , J. I. Cirac

Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential…

Strongly Correlated Electrons · Physics 2025-04-02 R. Flores-Calderón , Elio J. König , Ashley M. Cook

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine…

Quantum Physics · Physics 2015-05-19 Marzieh Asoudeh

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…

Statistical Mechanics · Physics 2009-11-11 Michael M. Wolf , Gerardo Ortiz , Frank Verstraete , J. Ignacio Cirac

Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological…

Quantum Physics · Physics 2023-11-01 Yabo Li , Hiroki Sukeno , Aswin Parayil Mana , Hendrik Poulsen Nautrup , Tzu-Chieh Wei