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Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum.
An extension of kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras
Donald Bures · 1969
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Black holes and entropy
Jacob D Bekenstein · 1973
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Gravitation
Charles W Misner, Kip S Thorne, John Archibald Wheeler, et al · 1973
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Particle creation by black holes
Stephen W Hawking · 1975
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Thermodynamics: A riemannian geometric model
George Ruppeiner · 1979
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Riemannian structure on manifolds of quantum states
JP Provost and G Vallee · 1980
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Quantized hall conductance in a two-dimensional periodic potential
David J Thouless, Mahito Kohmoto, M Peter Nightingale, and Marcel den Nijs · 1982
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Quantal phase factors accompanying adiabatic changes
Michael Victor Berry · 1984
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Model for a quantum hall effect without landau levels: Condensed-matter realization of the” parity anomaly”
F Duncan M Haldane · 1988
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Towards a quantum pump of electric charges
Q Niu · 1990
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Geometry of quantum evolution
J Anandan and Yakir Aharonov · 1990
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On the riemannian geometry of finite dimensional mixed states
Jochen Dittmann · 1993
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Gauge fields, knots and gravity , volume 4
John C Baez and Javier P Muniain · 1994
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Thermodynamics of spacetime: the einstein equation of state
Ted Jacobson · 1995
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Berry phase, hyperorbits, and the hofstadter spectrum: Semiclassical dynamics in magnetic bloch bands
Ming-Che Chang and Qian Niu · 1996
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Maximally localized generalized wannier functions for composite energy bands
Nicola Marzari and David Vanderbilt · 1997
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Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and berry-phase effects
Ganesh Sundaram and Qian Niu · 1999
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Explicit formulae for the bures metric
J Dittmann · 1999
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The anomalous hall effect and magnetic monopoles in momentum space
Zhong Fang, Naoto Nagaosa, Kei S Takahashi, Atsushi Asamitsu, Roland Mathieu, Takeshi Ogasawara, Hiroyuki Yamada, Masashi Kawasaki, Yoshinori Tokura, and Kiyoyuki Terakura · 2003
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Quantum spin hall effect in graphene
Charles L Kane and Eugene J Mele · 2005
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Berry phase correction to electron density of states in solids
Di Xiao, Junren Shi, and Qian Niu · 2005
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Orbital magnetization in periodic insulators
Timo Thonhauser, Davide Ceresoli, David Vanderbilt, and Raffaele Resta · 2005
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Quantum theory of orbital magnetization and its generalization to interacting systems
Junren Shi, Giovanni Vignale, Di Xiao, and Qian Niu · 2007
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Information-theoretic differential geometry of quantum phase transitions
Paolo Zanardi, Paolo Giorda, and Marco Cozzini · 2007
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Lectures on Kähler geometry , volume 69
Andrei Moroianu · 2007
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Einstein manifolds
Arthur L Besse · 2007
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Topological field theory of time-reversal invariant insulators
Xiao-Liang Qi, Taylor L Hughes, and Shou-Cheng Zhang · 2008
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Quantum criticality as a resource for quantum estimation
Paolo Zanardi, Matteo GA Paris, and Lorenzo Campos Venuti · 2008
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Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields
Ming-Che Chang and Qian Niu · 2008
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Berry phase effects on electronic properties
Di Xiao, Ming-Che Chang, and Qian Niu · 2010
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Abelian and non-abelian quantum geometric tensor
Yu-Quan Ma, Shu Chen, Heng Fan, Wu-Ming Liu, et al · 2010
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Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
Ali T Rezakhani, Damian F Abasto, Daniel A Lidar, and Paolo Zanardi · 2010
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Thermodynamical aspects of gravity: new insights
Thanu Padmanabhan · 2010
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Geometric orbital susceptibility: Quantum metric without berry curvature
Frédéric Piéchon, Arnaud Raoux, Jean-Noël Fuchs, and Gilles Montambaux · 2016
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Spectral sum rules and magneto-roton as emergent graviton in fractional quantum hall effect
Siavash Golkar, Dung X. Nguyen, and Dam T. Son · 2016
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Band geometry, berry curvature, and superfluid weight
Long Liang, Tuomas I Vanhala, Sebastiano Peotta, Topi Siro, Ari Harju, and Päivi Törmä · 2017
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Quantum metric and effective mass of a two-body bound state in a flat band
Päivi Törmä, Long Liang, and Sebastiano Peotta · 2018
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Momentum-space cigar geometry in topological phases
Giandomenico Palumbo · 2018
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Extracting the quantum metric tensor through periodic driving
Tomoki Ozawa and Nathan Goldman · 2018
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Building up spacetime with quantum entanglement
Mark Van Raamsdonk · 2010
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Momentum space metric, nonlocal operator, and topological insulators
Shunji Matsuura and Shinsei Ryu · 2010
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The insulating state of matter: a geometrical theory
Raffaele Resta · 2011
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Geometrical description of the fractional quantum hall effect
FDM Haldane · 2011
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On the origin of gravity and the laws of newton
Erik Verlinde · 2011
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Maximally localized wannier functions: Theory and applications
Nicola Marzari, Arash A Mostofi, Jonathan R Yates, Ivo Souza, and David Vanderbilt · 2012
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Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
Yuan Cao, Valla Fatemi, Ahmet Demir, Shiang Fang, Spencer L Tomarken, Jason Y Luo, Javier D Sanchez-Yamagishi, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, et al · 2018
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Ultraflatbands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides
Mit H Naik and Manish Jain · 2018
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Maximally localized wannier orbitals and the extended hubbard model for twisted bilayer graphene
Mikito Koshino, Noah F. Q. Yuan, Takashi Koretsune, Masayuki Ochi, Kazuhiko Kuroki, and Liang Fu · 2018
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Nonreciprocal directional dichroism induced by the quantum metric dipole
Yang Gao and Di Xiao · 2019
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Spacetime and geometry
Sean M Carroll · 2019
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Quantum distance and anomalous landau levels of flat bands
Jun-Won Rhim, Kyoo Kim, and Bohm-Jung Yang · 2020
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Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
Grazia Salerno, Nathan Goldman, and Giandomenico Palumbo · 2020
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Measurement of the quantum geometric tensor and of the anomalous hall drift
A Gianfrate, O Bleu, L Dominici, V Ardizzone, M De Giorgi, D Ballarini, G Lerario, KW West, LN Pfeiffer, DD Solnyshkov, et al · 2020
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Analogue spacetimes from nonrelativistic goldstone modes in spinor condensates
Justin H. Wilson, Jonathan B. Curtis, and Victor M. Galitski · 2020
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High-order nonlinear optical response of a twisted bilayer graphene
Tatsuhiko N Ikeda · 2020
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Quantum geometry and stability of moiré flatband ferromagnetism
Fengcheng Wu and S Das Sarma · 2020
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Excitations of a bose-einstein condensate and the quantum geometry of a flat band
Aleksi Julku, Georg M Bruun, and Päivi Törmä · 2021
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Swati Chaudhary, Cyprian Lewandowski, and Gil Refael · 2021
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Quantum metric and correlated states in two-dimensional systems
Enrico Rossi · 2021
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Topology and symmetry of quantum materials via nonlinear optical responses
J Orenstein, JE Moore, T Morimoto, DH Torchinsky, JW Harter, and D Hsieh · 2021
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Geometric photon-drag effect and nonlinear shift current in centrosymmetric crystals
Li-kun Shi, Dong Zhang, Kai Chang, and Justin CW Song · 2021
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Intrinsic anomalous hall conductivity in a nonuniform electric field
Vladyslav Kozii, Alexander Avdoshkin, Shudan Zhong, and Joel E Moore · 2021
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Riemannian geometry of resonant optical responses
Junyeong Ahn, Guang-Yu Guo, Naoto Nagaosa, and Ashvin Vishwanath · 2021
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Light-matter coupling and quantum geometry in moir \ \backslash ’e materials
Gabriel E Topp, Christian J Eckhardt, Dante M Kennes, Michael A Sentef, and Päivi Törmä · 2021
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Seth M. Davis and Matthew S. Foster · 2021
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Realizing fractional-quantum-hall gravitons on quantum computers
Ammar Kirmani, Kieran Bull, Chang-Yu Hou, Zlatko Papić, Armin Rahmani, and Pouyan Ghaemi · 2021
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