[La loi de Fourier et les systèmes quantiques à n corps]
Cet article porte sur les propriétés de transport de chaînes quantiques à n corps en s'accompagnant de simulations de type « groupe de renormalisation de matrice de densité » du modèle de Bose–Hubbard. Pour dresser une vue d'ensemble, nous présentons d'abord une très brève introduction à la théorie quantique à n corps et aux approximations des réseaux de tenseurs. Les propriétés de transport sont étudiées à l'aide de fonctions dynamiques de corrélation de densité, en suivant la théorie de la réponse linéaire. Nous observons un comportement diffusif à « température infinie » . Enfin, nous mentionnons d'autres approches permettant d'étudier le transport, par exemple en imposant explicitement un gradient de température via des réservoirs thermiques aux bords.
The topic of this article are transport properties of many-body quantum chains accompanying DMRG-type simulations of the Bose–Hubbard model. To set the stage, we first provide a very brief introduction to many-body quantum theory and tensor network approximations. Transport properties are studied via dynamical density correlation functions, in line with linear response theory. We observe diffusive behavior at “infinite temperature” . Finally, we mention other approaches to study transport, e.g., explicitly imposing a temperature gradient via thermal reservoirs at the boundary.
Mot clés : Chaînes quantiques à n corps, Transport diffusif, Fonctions de corrélation dynamiques, GRMD / réseaux de tenseurs
@article{CRPHYS_2019__20_5_442_0,
author = {Christian B. Mendl},
title = {Fourier's law and many-body quantum systems},
journal = {Comptes Rendus. Physique},
pages = {442--448},
publisher = {Elsevier},
volume = {20},
number = {5},
year = {2019},
doi = {10.1016/j.crhy.2019.08.006},
language = {en},
}
Christian B. Mendl. Fourier's law and many-body quantum systems. Comptes Rendus. Physique, Volume 20 (2019) no. 5, pp. 442-448. doi : 10.1016/j.crhy.2019.08.006. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.08.006/
[1] Modern Quantum Mechanics, Cambridge University Press, 2017
[2] Introduction to Quantum Mechanics, Pearson Prentice Hall, 2004
[3] Many-Body Quantum Theory in Condensed Matter Physics: An Introduction, Oxford Graduate Texts, Oxford University Press, 2004
[4] Mathematische Grundlagen der Quantenmechanik, Springer, 1932
[5] Markoff random processes and the statistical mechanics of time-dependent phenomena, II: irreversible processes in fluids, J. Chem. Phys., Volume 22 (1954) no. 3, pp. 398-413
[6] Statistical-mechanical theory of irreversible processes, I: general theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn., Volume 12 (1957), pp. 570-586
[7] Computational Many-Particle Physics, Springer-Verlag, Berlin–Heidelberg, 2008
[8] Strongly Correlated Systems – Numerical Methods, Springer-Verlag, Berlin–Heidelberg, 2013
[9] Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett., Volume 69 (1992), pp. 2863-2866
[10] Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B, Volume 48 (1993), pp. 10345-10356
[11] The density-matrix renormalization group, Rev. Mod. Phys., Volume 77 (2005), pp. 259-315
[12] The density-matrix renormalization group in the age of matrix product states, Ann. Phys., Volume 326 (2011), pp. 96-192
[13] Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Adv. Phys., Volume 57 (2008), pp. 143-224
[14] Tensor Spaces and Numerical Tensor Calculus, Springer Series in Computational Mathematics, Springer-Verlag, Berlin–Heidelberg, 2012
[15] Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett., Volume 91 (2003)
[16] Class of quantum many-body states that can be efficiently simulated, Phys. Rev. Lett., Volume 101 (2008)
[17] Minimally entangled typical thermal state algorithms, New J. Phys., Volume 12 (2010)
[18] Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes, New J. Phys., Volume 15 (2013)
[19] Area laws for the entanglement entropy, Rev. Mod. Phys., Volume 82 (2010), pp. 277-306
[20] Generic construction of efficient matrix product operators, Phys. Rev. B, Volume 95 (2017)
[21] Unifying time evolution and optimization with matrix product states, Phys. Rev. B, Volume 94 (2016)
[22] Scrambling and thermalization in a diffusive quantum many-body system, New J. Phys., Volume 19 (2017)
[23] Fundamentals of Carrier Transport, Cambridge University Press, 2009
[24] The quantum Boltzmann equation in semiconductor physics, Ann. Phys., Volume 523 (2011), pp. 87-100
[25] Matrix-valued Boltzmann equation for the Hubbard chain, Phys. Rev. E, Volume 86 (2012)
[26] On the generators of quantum dynamical semigroups, Commun. Math. Phys., Volume 48 (1976), pp. 119-130
[27] Exact nonequilibrium steady state of a strongly driven open XXZ chain, Phys. Rev. Lett., Volume 107 (2011)
[28] Exact nonequilibrium steady state of an open Hubbard chain, Phys. Rev. Lett., Volume 112 (2014)
[29] Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system, Phys. Rev. Lett., Volume 117 (2016)
[30] Energy flow in quantum critical systems far from equilibrium, Nat. Phys., Volume 11 (2015), pp. 509-514
Cité par Sources :
Commentaires - Politique