Quantum entanglement in condensed matter systems

By N. Laflorencie. 2015

540 citations recorded by the source corpus.

This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Renyi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in details. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4309593ed522f39c106202377b040d19223a8b98

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Citations in the corpus

Many-body localization and delocalization in large quantum chains (2018, background): “From the perspective of accuracy of MPS simulations, the worst-case scenario for a local Hamiltonian is realized when the von Neumann entanglement entropy for a bipartition of the chain into two parts grows linearly [39], which is known as volume-law entanglement and should be contrasted to the area”
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “(216) 0(6)4010 ( ) ( ) ∼ α S t t log [3, 102], where α> 1 (recall that α = 1 for an MBL system, see also [119] for a detailed review of the entanglement growth in various disordered systems).”
Entanglement certification from theory to experiment (2018, methodology): “[191] Nicolas Laflorencie, “Quantum entanglement in condensed matter systems,” Phys.”
Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, background): “[5] Nicolas Laflorencie, “Quantum entanglement in condensed matter systems,” Physics Reports 646, 1–59 (2016), arXiv:1512.”
Entanglement entropy: Holography and renormalization group (2018, methodology): “The condensed matter applications of entanglement being a probe of quantum critical phenomena and quantum quench dynamics is elaborated in the reviews (Calabrese and Cardy, 2009, 2016) by means of the CFT methods (see also (Laflorencie, 2016)).”
Many-body localization: An introduction and selected topics (2017, unknown): “Entanglement spectroscopy Besides the scaling of entanglement entropy, and given t e success of this approach r pure any-body problems [137, 138], several works [139, 140, 141, 142, 143, 144, 145] considered the information contained in the entanglement spectrum (ES) {λi} of the reduced density matr”
Symmetry resolved entanglement in free fermionic systems (2019, background): “Nowadays a lot has been understood in the context of low-dimensional many body quantum systems, both from the theoretical side [1–4] and, more recently, also experimentally [5–8].”
Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos (2018, unknown): “In particular, it plays a crucial role in the study of quantummany-body systems out of equilibrium [3,4].”
Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations (2019, background): “[3] N.”