Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems

Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen

Published Mar 29, 2019• 57 citations
Publisher
DOI
10.1007/978-1-4939-9084-9

Related papers

Aspects of Entanglement in Quantum Many-Body Systems

J. W. Clark, Hessam Habibian, Aikaterini Mandilara +1 more

Foundations of Physics•Jun 9, 2010•4 citations

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

Bei Zeng, Xie Chen, Duan-Lu Zhou +1 more

This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

arXiv:1508.02595•Aug 11, 2015•93 citations

Topological Phases of Matter and Quantum Computation

Paul Bruillard, Carlos Ortiz Marrero, Julia Plavnik

Contemporary mathematics - American Mathematical Society•Mar 27, 2020•6 citations

Diagnosing Topological Quantum Matter via Entanglement Patterns

Konstantinos Meichanetzidis

Quantum matter involves the study of entanglement patterns in the ground states of many-body \nsystems. Of significant interest have recently been topological states of matter, \nwhich exhibit characteristics only described globally. As such they are robust to local deformations. \nIn this thesis, we study inter-correlations of many-body states through the entanglement spectrum, \nobtained by a bipartition of both topological and non-topological systems. \n \nIn particular, we introduce two novel diagnostics which operate on entanglement spectra. \nFor topological phases supporting edge states on open boundaries \nwe take a quantum-information inspired approach by invoking \nthe monogamy relations obeyed by multi-partite systems. \nWithin a strictly single-particle framework, \nwe establish a correspondence between highly entangled mode and the existence of edge states. \nIn the many-body context, we introduce the interaction distance \nof a mixed state. \nExclusively via the entanglement spectrum it \ndetermines how close a free-fermion state lies and what the emergent free quasiparticles are. \n \nWe apply these two measures to diagnose the properties of a variety of free and interacting fermionic topological systems and reinterpret their properties from a fresh point of view. \nOur case studies revolve around Kitaev's honeycomb model, \nwhich supports both short-range and long-range topological order, \nconstituting it thus relevant to both the monogamy qualifier and the interaction distance. \nThe possibility to diagnose whether a model has zero interacting distance or if it supports maximally entangled states provides central and compact information about the behaviour of complex quantum systems.

•Aug 1, 2017•0 citations

Topological Phases of Quantum Matter

Wei-Feng Tsai, Hsin Lin, Arun Bansil

Springer series in solid-state sciences•Jan 1, 2018•1 citation

Polarization and entanglement spectrum in non-Hermitian systems

Carlos Ortega-Taberner, Lukas Rødland, Maria Hermanns

The entanglement spectrum is a useful tool to study topological phases of matter, and contains valuable information about the ground state of the system. Here, we study its properties for free non-Hermitian systems for both point-gapped and line-gapped phases. While the entanglement spectrum only retains part of the topological information in the former case, it is very similar to Hermitian systems in the latter. In particular, it not only mimics the topological edge modes, but also contains all the information about the polarization, even in systems that are not topological. Furthermore, we show that the Wilson loop is equivalent to the many-body polarization and that it reproduces the phase diagram for the system with open boundaries, despite being computed for a periodic system.

arXiv:2111.07788•Physical review. B./Physical review. B•Feb 2, 2022•24 citations
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.
Quantum matter involves the study of entanglement patterns in the ground states of many-body \nsystems. Of significant interest have recently been topological states of matter, \nwhich exhibit characteristics only described globally. As such they are robust to local deformations. \nIn this thesis, we study inter-correlations of many-body states through the entanglement spectrum, \nobtained by a bipartition of both topological and non-topological systems. \n \nIn particular, we introduce two novel diagnostics which operate on entanglement spectra. \nFor topological phases supporting edge states on open boundaries \nwe take a quantum-information inspired approach by invoking \nthe monogamy relations obeyed by multi-partite systems. \nWithin a strictly single-particle framework, \nwe establish a correspondence between highly entangled mode and the existence of edge states. \nIn the many-body context, we introduce the interaction distance \nof a mixed state. \nExclusively via the entanglement spectrum it \ndetermines how close a free-fermion state lies and what the emergent free quasiparticles are. \n \nWe apply these two measures to diagnose the properties of a variety of free and interacting fermionic topological systems and reinterpret their properties from a fresh point of view. \nOur case studies revolve around Kitaev's honeycomb model, \nwhich supports both short-range and long-range topological order, \nconstituting it thus relevant to both the monogamy qualifier and the interaction distance. \nThe possibility to diagnose whether a model has zero interacting distance or if it supports maximally entangled states provides central and compact information about the behaviour of complex quantum systems.
The entanglement spectrum is a useful tool to study topological phases of matter, and contains valuable information about the ground state of the system. Here, we study its properties for free non-Hermitian systems for both point-gapped and line-gapped phases. While the entanglement spectrum only retains part of the topological information in the former case, it is very similar to Hermitian systems in the latter. In particular, it not only mimics the topological edge modes, but also contains all the information about the polarization, even in systems that are not topological. Furthermore, we show that the Wilson loop is equivalent to the many-body polarization and that it reproduces the phase diagram for the system with open boundaries, despite being computed for a periodic system.