Daguerre, Lucas (2021) Teoría de campos no relativistas: dinámica e irreversibilidad / Non relativistic field theory: dynamics and irreversibility. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
![[img]](/style/images/fileicons/application_pdf.png)
| PDF (Tesis) Español 6Mb |
Resumen en español
Estudiamos distintos aspectos de Teoría Cuántica de Campos a densidad finita usando métodos provenientes de la Teoría de Información Cuántica. Primero, revisitamos el Teorema de Reeh-Schlieder y sus corolarios, tanto en la teoría relativista como no relativista. Discutimos los resultados en base a las nociones de microcausalidad y localizaci ón en ambas teorías. Luego, por simplicidad, en la mayor parte del presente trabajo nos enfocamos en fermiones de Dirac masivos con potencial químico no nulo, y trabajamos en 1 + 1 dimensiones espacio-temporales. Usando la entropía de entrelazamiento en un intervalo, construimos la función c entrópica que es finita. Contrario a lo que ocurre en teorías con invarianza de Lorentz, esta función c exhibe una violaci ón rotunda de la monotonicidad; también codica la creación de entrelazamiento de largo alcance proveniente de la supercie de Fermi. Motivados por trabajos previos de modelos en la red, computamos numéricamente las entropías de Renyi y encontramos oscilaciones de Friedel; estas son entendidas en términos del OPE en defectos. Más aún, consideramos la información mutua como una medida de correlación de funciones entre diferentes regiones. Usando una expansión de distancia grande desarrollada por Cardy, argumentamos que la información mutua detecta las correlaciones inducidas por la supercie de Fermi todavía al orden dominante en la expansión. También analizamos la entropía relativa y sus generalizaciones de Renyi para distinguir estados con diferente carga o masa. En particular, mostramos que estados en diferentes sectores de superselección dan origen a un comportamiento super-extensivo en la entropía relativa. Discutimos posibles extensiones a teorías interactuantes, y argumentamos por la relevancia de algunas de estas medidas para testear líquidos que no son de Fermi. Por otro lado, también damos los primeros resultados preliminares del estudio en 2 + 1 dimensiones espacio-temporales. Finalmente, recalcamos que gran parte de los resultados de esta tesis se encuentran publicados en [1].
Resumen en inglés
We study different aspects of Quantum Field Theory at finite density using methods from Quantum Information Theory. First, we review the Reeh-Schlieder theorem and its corollaries, for both the relativistic and non relativistic theory. We discuss the results based on concepts of microcausality and localization in both theories. Then, for simplicity, we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is nite. Unlike what happens in Lorentzinvariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and nd Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. We discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids. On the other hand, we give preliminary results involving quantum information measures in 2+1 space-time dimensions. Finally, we must point out that the majority of the results in this thesis can be found in English on [1].
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
|---|---|
| Palabras Clave: | Quantum field theory; Teoría del campo cuántico; Quantum information; Información cuántica; Renormalization; Renormalización |
| Referencias: | [1] L. Daguerre, R. Medina, M. Solis, and G. Torroba, \Aspects of quantum information in nite density eld theory," arXiv:2011.01252 [hep-th]. vi, viii, 4 [2] M. Srednicki, \Entropy and area," Phys. Rev. Lett. 71 (1993) 666{669, arXiv:hep-th/9303048 [hep-th]. 1 [3] H. Casini and M. Huerta, \A Finite entanglement entropy and the c-theorem," Phys. Lett. B600 (2004) 142{150, arXiv:hep-th/0405111 [hep-th]. 1, 28, 64 [4] H. Casini and M. Huerta, \On the RG running of the entanglement entropy of a circle," Phys. Rev. D85 (2012) 125016, arXiv:1202.5650 [hep-th]. 28, 57, 58 [5] H. Casini, E. Teste, and G. Torroba, \Markov Property of the Conformal Field Theory Vacuum and the a Theorem," Phys. Rev. Lett. 118 no.~26, (2017) 261602, arXiv:1704.01870 [hep-th]. 1, 28, 51 [6] A. B. Zamolodchikov, \Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory," JETP Lett. 43 (1986) 730{732. [Pisma Zh. Eksp. Teor. Fiz.43,565(1986)]. 1, 64 [7] Z. Komargodski and A. Schwimmer, \On Renormalization Group Flows in Four Dimensions," JHEP 12 (2011) 099, arXiv:1107.3987 [hep-th]. 1 [8] P. Calabrese and J. Cardy, \Entanglement entropy and conformal eld theory," J. Phys. A42 (2009) 504005, arXiv:0905.4013 [cond-mat.stat-mech]. 1, 28, 36, 39, 40 [9] H. Casini and M. Huerta, \Entanglement entropy in free quantum eld theory," J. Phys. A42 (2009) 504007, arXiv:0905.2562 [hep-th]. 1, 2, 22, 27, 28, 35, 36, 58, 76 [10] H. Casini, \Relative entropy and the Bekenstein bound," Class. Quant. Grav. 25 (2008) 205021, arXiv:0804.2182 [hep-th]. 1 [11] A. C. Wall, \A proof of the generalized second law for rapidly changing elds and arbitrary horizon slices," Phys. Rev. D85 (2012) 104049, arXiv:1105.3445 [gr-qc]. [Erratum: Phys. Rev.D87,no.6,069904(2013)]. 1 [12] T. Faulkner, R. G. Leigh, O. Parrikar, and H. Wang, \Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition," JHEP 09 (2016) 038, arXiv:1605.08072 [hep-th]. 1 [13] S. Balakrishnan, T. Faulkner, Z. U. Khandker, and H. Wang, \A General Proof of the Quantum Null Energy Condition," arXiv:1706.09432 [hep-th]. 1 [14] R. Orus, \A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States," Annals Phys. 349 (2014) 117{158, arXiv:1306.2164 [cond-mat.str-el]. 1 [15] S. Ryu and T. Takayanagi, \Holographic derivation of entanglement entropy from AdS/CFT," Phys. Rev. Lett. 96 (2006) 181602, arXiv:hep-th/0603001 [hep-th]. 2 [16] S. Ryu and T. Takayanagi, \Aspects of Holographic Entanglement Entropy," JHEP 08 (2006) 045, arXiv:hep-th/0605073 [hep-th]. 2 [17] B. Swingle, \Entanglement does not generally decrease under renormalization," J. Stat. Mech. 1410 no.~10, (2014) P10041, arXiv:1307.8117 [cond-mat.stat-mech]. 2, 27, 32 [18] N. Ogawa, T. Takayanagi, and T. Ugajin, \Holographic Fermi Surfaces and Entanglement Entropy," JHEP 01 (2012) 125, arXiv:1111.1023 [hep-th]. 2, 30 [19] A. Belin, L.-Y. Hung, A. Maloney, S. Matsuura, R. C. Myers, and T. Sierens, \Holographic Charged Renyi Entropies," JHEP 12 (2013) 059, arXiv:1310.4180 [hep-th]. [20] C. P. Herzog and T. Nishioka, \Entanglement Entropy of a Massive Fermion on a Torus," JHEP 03 (2013) 077, arXiv:1301.0336 [hep-th]. 81 [21] J. Cardy, \Entanglement in CFTs at Finite Chemical Potential." http://www2.yukawa.kyoto-u.ac.jp/~entangle2016/YCardy.pdf, 2016. Presentation at the Yukawa International Seminar \Quantum Matter, Spacetime and Information". 30 [22] B. S. Kim, \Entanglement Entropy, Chemical Potential, Current Source, and Wilson Loop," arXiv:1705.01859 [hep-th]. 30 [23] B. S. Kim, \Entanglement Entropy with Background Gauge Fields," JHEP 08 (2017) 041, arXiv:1706.07110 [hep-th]. 2 [24] E. Fradkin, \Scaling of Entanglement Entropy at 2D quantum Lifshitz xed points and topological uids," J. Phys. A 42 (2009) 504011, arXiv:0906.1569 [cond-mat.str-el]. 2 [25] B. Hsu, M. Mulligan, E. Fradkin, and E.-A. Kim, \Universal entanglement entropy in 2D conformal quantum critical points," Phys. Rev. B 79 (2009) 115421, arXiv:0812.0203 [cond-mat.stat-mech]. [26] T. He, J. M. Magan, and S. Vandoren, \Entanglement Entropy in Lifshitz Theories," SciPost Phys. 3 no.~5, (2017) 034, arXiv:1705.01147 [hep-th]. [27] M. R. Mohammadi Mozaar and A. Mollabashi, \Entanglement in Lifshitz-type Quantum Field Theories," JHEP 07 (2017) 120, arXiv:1705.00483 [hep-th]. 2 [28] P. Calabrese, M. Campostrini, F. Essler, and B. Nienhuis, \Parity eects in the scaling of block entanglement in gapless spin chains.," Physical review letters 104 9 (2010) 095701. 3, 35, 39, 64 [29] B. Swingle, J. McMinis, and N. M. Tubman, \Oscillating terms in the renyi entropy of fermi gases and liquids," Physical Review B 87 no.~23, (Jun, 2013) . http://dx.doi.org/10.1103/PhysRevB.87.235112. 3, 39, 41, 59, 64 [30] J. Cardy, \Some results on the mutual information of disjoint regions in higher dimensions," Journal of Physics A: Mathematical and Theoretical 46 no. 28, (2013) 285402. http://stacks.iop.org/1751-8121/46/i=28/a=285402. 3, 44, 45 [31] M. E. Peskin and D. V. Schroeder, An Introduction to quantum eld theory. Addison-Wesley, Reading, USA, 1995. 5, 9, 20 [32] W. Greiner and J. Reinhardt, Field Quantization. Springer-Verlag Berlin Heidelberg, 1996. 5, 9, 12 [33] D. Tong, Quantum Field Theory. University of Cambridge. Part III. Mathematical Tripos, 2007. 9 [34] R. F. Streater and A. S. Wightman, PCT. Spin and Statistics, and all that. Princeton University Press, 1964. 11, 13, 15 [35] R. Haag and B. Schroer, \Postulates of Quantum Field Theory," Journal of Mathematical Physics 3 no.~2, (Mar, 1962) 248{256. 12 [36] R. Haag, Local quantum physics: Fields, particles, algebras. 1992. 13, 15 [37] E. Witten, \APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum eld theory," Rev. Mod. Phys. 90 no.~4, (2018) 045003, arXiv:1803.04993 [hep-th]. 13, 14, 16, 17, 63 [38] H. Casini, S. Grillo, and D. Pontello, \Relative entropy for coherent states from Araki formula," Phys. Rev. D99 no.~12, (2019) 125020, arXiv:1903.00109 [hep-th]. 15 [39] L. A. Robert, Quantum Field Theory: The Wightman Axioms and the Haag-Kastler axioms. (Notes). 16 [40] I. Hason, \Triviality of Entanglement Entropy in the Galilean Vacuum," Phys. Lett. B 780 (2018) 149{151, arXiv:1708.08303 [hep-th]. 17, 32 [41] A. Abrikosov, Methods of quantum eld theory in statistical physics. 20 [42] I. Peschel, \Calculation of reduced density matrices from correlation functions," Journal of Physics A Mathematical General 36 (Apr., 2003) L205{L208, cond-mat/0212631. 22, 29 [43] H. Casini, C. Fosco, and M. Huerta, \Entanglement and alpha entropies for a massive Dirac eld in two dimensions," J. Stat. Mech. 0507 (2005) P07007, arXiv:cond-mat/0505563. 30, 36, 42, 79 [44] A. Cappelli, D. Friedan, and J. I. Latorre, \C theorem and spectral representation," Nucl. Phys. B352 (1991) 616{670. 33, 64 [45] J. Cardy and P. Calabrese, \Unusual corrections to scaling in entanglement entropy," Journal of Statistical Mechanics: Theory and Experiment 2010 (2010) 04023. 39, 41, 64 [46] J. Cardy, O. Castro-Alvaredo, and B. Doyon, \Form factors of branch-point twist elds in quantum integrable models and entanglement entropy," J. Statist. Phys. 130 (2008) 129{168, arXiv:0706.3384 [hep-th]. 39 [47] O. A. Castro-Alvaredo, B. Doyon, and E. Levi, \Arguments towards a c-theorem from branch-point twist elds," J. Phys. A 44 (2011) 492003, arXiv:1107.4280 [hep-th]. 39 [48] E. Levi, \Composite branch-point twist elds in the Ising model and their expectation values," J. Phys. A 45 (2012) 275401, arXiv:1204.1192 [hep-th]. [49] L. Bianchi, M. Meineri, R. C. Myers, and M. Smolkin, \Renyi entropy and conformal defects," JHEP 07 (2016) 076, arXiv:1511.06713 [hep-th]. [50] M. Billo, V. Goncalves, E. Lauria, and M. Meineri, \Defects in conformal eld theory," JHEP 04 (2016) 091, arXiv:1601.02883 [hep-th]. [51] A. Gadde, \Conformal constraints on defects," JHEP 01 (2020) 038, arXiv:1602.06354 [hep-th]. 39 [52] R. Bousso, H. Casini, Z. Fisher, and J. Maldacena, \Entropy on a null surface for interacting quantum eld theories and the Bousso bound," Phys. Rev. D91 no.~8, (2015) 084030, arXiv:1406.4545 [hep-th]. 39 [53] M. Guimaraes and B. Linet, \Scalar Green's functions in an Euclidean space with a conical-type line singularity," Commun. Math. Phys. 165 (1994) 297{310. 40 [54] H. Casini, \Entropy inequalities from re ection positivity," J. Stat. Mech. 1008 (2010) P08019, arXiv:1004.4599 [quant-ph]. 42 [55] D. N. Aristov and A. Luther, \Correlations in the sine-gordon model with nite soliton density," Physical Review B 65 no.~16, (Apr, 2002) . http://dx.doi.org/10.1103/PhysRevB.65.165412. 42, 80 [56] M. M. Wolf, F. Verstraete, M. B. Hastings, and J. I. Cirac, \Area Laws in Quantum Systems: Mutual Information and Correlations," Phys. Rev. Lett. 100 no.~7, (2008) 070502, arXiv:0704.3906 [quant-ph]. 44 [57] C. Agon and T. Faulkner, \Quantum Corrections to Holographic Mutual Information," JHEP 08 (2016) 118, arXiv:1511.07462 [hep-th]. 46 [58] C. A. Agon, I. Cohen-Abbo, and H. J. Schnitzer, \Large distance expansion of Mutual Information for disjoint disks in a free scalar theory," JHEP 11 (2016) 073, arXiv:1505.03757 [hep-th]. [59] B. Chen, L. Chen, P.-x. Hao, and J. Long, \On the Mutual Information in Conformal Field Theory," JHEP 06 (2017) 096, arXiv:1704.03692 [hep-th]. 46 [60] D. S. Fisher, \Scaling and critical slowing down in random-eld Ising systems," Phys. Rev. Lett. 56 (1986) 416{419. 46, 65 [61] L. Huijse, S. Sachdev, and B. Swingle, \Hidden Fermi surfaces in compressible states of gauge-gravity duality," Phys. Rev. B 85 (2012) 035121, arXiv:1112.0573 [cond-mat.str-el]. [62] X. Dong, S. Harrison, S. Kachru, G. Torroba, and H. Wang, \Aspects of holography for theories with hyperscaling violation," JHEP 06 (2012) 041, arXiv:1201.1905 [hep-th]. 46, 65 [63] B. Swingle, \Renyi entropy, mutual information, and uctuation properties of fermi liquids," Physical Review B 86 no. 4, (2012) 045109. 46, 59 [64] H. Casini, I. S. Landea, and G. Torroba, \The g-theorem and quantum information theory," JHEP 10 (2016) 140, arXiv:1607.00390 [hep-th]. 51, 64 [65] H. Casini, E. Teste, and G. Torroba, \Relative entropy and the RG ow," JHEP 03 (2017) 089, arXiv:1611.00016 [hep-th]. 64 [66] N. Lashkari, \Entanglement at a Scale and Renormalization Monotones," arXiv:1704.05077 [hep-th]. [67] H. Casini, R. Medina, I. S. Landea, and G. Torroba, \Renyi relative entropies and renormalization group ows," Journal of High Energy Physics 2018 no.~9, (Sep, 2018) . http://dx.doi.org/10.1007/JHEP09(2018)166. 51, 54 [68] H. Casini, M. Huerta, and R. C. Myers, \Towards a derivation of holographic entanglement entropy," JHEP 05 (2011) 036, arXiv:1102.0440 [hep-th]. 52 [69] M. Muller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, \On quantum renyi entropies: A new generalization and some properties," Journal of Mathematical Physics 54 no. 12, (2013) 122203. 53 [70] M. M. Wilde, A. Winter, and D. Yang, \Strong converse for the classical capacity of entanglement-breaking and hadamard channels via a sandwiched renyi relative entropy," Communications in Mathematical Physics 331 no. 2, (2014) 593{622. 53 [71] S. Beigi, \Sandwiched renyi divergence satises data processing inequality," Journal of Mathematical Physics 54 no. 12, (2013) 122202. 54 [72] R. L. Frank and E. H. Lieb, \Monotonicity of a relative renyi entropy," Journal of Mathematical Physics 54 no.~12, (2013) 122201, https://doi.org/10.1063/1.4838835. https://doi.org/10.1063/1.4838835. 54 [73] A. Uhlmann, \The \transition probability" in the state space of a-algebra," Reports on Mathematical Physics 9 no. 2, (1976) 273{279. 54 [74] V. Eisler, E. Tonni, and I. Peschel, \On the continuum limit of the entanglement Hamiltonian," J. Stat. Mech. 1907 no.~7, (2019) 073101, arXiv:1902.04474 [cond-mat.stat-mech]. 56 [75] V. Eisler, G. Di Giulio, E. Tonni, and I. Peschel, \Entanglement Hamiltonians for non-critical quantum chains," J. Stat. Mech. 2010 (2020) 103102, arXiv:2007.01804 [cond-mat.stat-mech]. 56 [76] H. Casini and M. Huerta, \Universal terms for the entanglement entropy in dimensions," Nuclear Physics B 764 no.~3, (Mar, 2007) 183{201. http://dx.doi.org/10.1016/j.nuclphysb.2006.12.012. 57, 58, 61 [77] H. Casini, M. Huerta, and L. Leitao, \Entanglement entropy for a dirac fermion in three dimensions: Vertex contribution," Nuclear Physics B 814 no.~3, (Jun, 2009) 594{609. http://dx.doi.org/10.1016/j.nuclphysb.2009.02.003. 58, 60 [78] T. Hirata and T. Takayanagi, \Ads/cft and strong subadditivity of entanglement entropy," Journal of High Energy Physics 2007 no.~02, (Feb, 2007) 042{042. http://dx.doi.org/10.1088/1126-6708/2007/02/042. 58, 59, 60 [79] J. Helmes, L. E. Hayward Sierens, A. Chandran, W. Witczak-Krempa, and R. G. Melko, \Universal corner entanglement of dirac fermions and gapless bosons from the continuum to the lattice," Physical Review B 94 no.~12, (Sep, 2016) . http://dx.doi.org/10.1103/PhysRevB.94.125142. 58 [80] P. Bueno, R. C. Myers, and W. Witczak-Krempa, \Universality of corner entanglement in conformal eld theories," Physical Review Letters 115 no.~2, (Jul, 2015) . http://dx.doi.org/10.1103/PhysRevLett.115.021602. 58 [81] H. Casini and M. Huerta, \Entanglement and alpha entropies for a massive scalar eld in two dimensions," Journal of Statistical Mechanics: Theory and Experiment 2005 no.~12, (Dec, 2005) P12012{P12012. http://dx.doi.org/10.1088/1742-5468/2005/12/P12012. 58 [82] H. Casini, R. C. Huerta, Marina and, and A. Yale, \Mutual information and the F-theorem," JHEP 10 (2015) 003, arXiv:1506.06195 [hep-th]. 59 [83] D. Gioev and I. Klich, \Entanglement entropy of fermions in any dimension and the widom conjecture," Phys. Rev. Lett. 96 (Mar, 2006) 100503. https://link.aps.org/doi/10.1103/PhysRevLett.96.100503. 59 [84] R. Islam, R. Ma, P. M. Preiss, M. E. Tai, A. Lukin, M. Rispoli, and M. Greiner, \Measuring entanglement entropy through the interference of quantum many-body twins," arXiv e-prints (Sept., 2015) arXiv:1509.01160, arXiv:1509.01160 [cond-mat.quant-gas]. 64 [85] J. Li, R. Fan, H. Wang, B. Ye, B. Zeng, H. Zhai, X. Peng, and J. Du, \Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator," Physical Review X 7 no.~3, (July, 2017) 031011, arXiv:1609.01246 [cond-mat.str-el]. 64 [86] M. M. Wolf, \Violation of the entropic area law for fermions," Phys. Rev. Lett. 96 (Jan, 2006) 010404. https://link.aps.org/doi/10.1103/PhysRevLett.96.010404. 65 [87] S. A. Hartnoll, A. Lucas, and S. Sachdev, \Holographic quantum matter," arXiv:1612.07324 [hep-th]. 65 [88] A. Chodos and J. Healy, \Spectral degeneracy of the lattice dirac equation as a function of lattice shape," Nuclear Physics B 127 no.~3, (1977) 426 { 446. http://www.sciencedirect.com/science/article/pii/0550321377904497. 73 [89] A. Chodos and J. B. Healy, \Continuous space-time symmetries of the lattice dirac equation," Phys. Rev. D 16 (Jul, 1977) 387{396. https://link.aps.org/doi/10.1103/PhysRevD.16.387. [90] L. Susskind, \Lattice fermions," Phys. Rev. D 16 (Nov, 1977) 3031{3039. https://link.aps.org/doi/10.1103/PhysRevD.16.3031. 73 [91] E. Fradkin, Field Theories of Condensed Matter Physics. Cambridge University Press, 2 ed., 2013. 80 |
| Materias: | Física > Teoría de campos |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Partículas y campos |
| Código ID: | 939 |
| Depositado Por: | Marisa G. Velazco Aldao |
| Depositado En: | 14 Jul 2021 14:18 |
| Última Modificación: | 14 Jul 2021 14:18 |
Personal del repositorio solamente: página de control del documento
