Solís Benites, Mario F. (2024) Aspectos de teoría de campos no-relativista a densidad y temperatura finita: non-fermi liquids e irreversibilidad / Aspects of non-relativist field theory density and finite temperature non--fermi liquids irrersibility. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
La teoría cuántica de campos es una de las herramientas más importantes para entender sistemas cuánticos con muchos grados de libertad. Los modelos más estudiados poseen invariancia de Lorentz y surgen en física de altas energías. Las teorías de campos que aparecen en sistemas de materia condensada son no-relativistas, poseen una densidad finita de materia, y su rica dinámica no ha sido del todo entendida. En esta tesis, tenemos como objetivo avanzar en la compresión de la dinámica de la materia cuántica utilizando el formalismo de la teoría de campos a densidad finita. Para lograr este objetivo, utilizaremos un amplio rango de métodos analíticos y numéricos. Esta tesis, se dividirá en dos partes. La primera parte se enfocará en estudiar un modelo de Non-Fermi Liquids. En la segunda parte, estudiaremos teorías a densidad finita utilizando observables no locales, como las medidas de información cuántica y la función de partición en el toro. En más detalle, en la primera parte de esta tesis estudiaremos los Non-Fermi Liquids en d = 2 dimensiones espaciales. Estos sistemas pueden surgir cuando se acopla una superficie Fermi a un bosón no masivo. Encontramos que a temperatura finita, la descripción perturbativa de la teoría cuántica de campos deja de ser válida debido a las divergencias infrarrojas. Estas son causadas por modos bosónicos virtuales estáticos y afectan tanto a correlaciones fermiónicas como bosónicas. Mostraremos cómo estas divergencias se resuelven mediante una masa térmica autogenerada para los bosones. Encontraremos un nuevo régimen Non-Fermi Liquid térmico, que no satisface el escaleo del punto fijo a temperatura cero. Posteriormente, revisitamos la interacción entre superconductividad y criticalidad cuántica. En la segunda parte, estudiamos diferentes aspectos de la teoría cuántica de campo a densidad finita usando métodos de la teoría información cuántica y efectos a temperatura finita. Por simplicidad, nos enfocamos en fermiones de Dirac masivos con un potencial químico distinto de cero, y trabajamos en 1 + 1 dimensiones espacio-temporales. Usando la entropía de entrelazamiento en un intervalo, construimos una función c en evolución que es finita. A diferencia de lo que sucede en teorías Lorentzinvariantes, esta función c exhibe una fuerte violación de la monotonicidad; también codifica la creación de entrelazamiento a larga distancia debido a la superficie de Fermi. Motivados por trabajos previos en modelos de red, calculamos numéricamente las entropías de Renyi y encontramos oscilaciones de tipo Friedel. Además, consideramos la información mutua como una medida de las funciones de correlación entre diferentes regiones. A temperatura finita, nos enfocamos en teorías sobre un toro euclídeo bidimensional. Usando los desarrollos recientes en formas modulares masivas, obtenemos una representación de la energía libre del toro basada en la transformación de Fourier sobre una condición de contorno torcida. Esta representación dual cumple muchas propiedades análogas a la invariancia modular en CFTs. En particular, usamos este resultado para derivar fórmulas para la densidad de estados en teorías no relativistas, generalizando el resultado de Cardy sobre teorías conformes.
Resumen en inglés
Quantum field theory is one of the most important tools for understanding quantum systems with many degrees of freedom. The most studied models possess Lorentz invariance and arise in high-energy physics. The field theories that appear in condensed matter systems are non-relativistic, possess a finite matter density, and their rich dynamics have not been fully understood. In this thesis, we aim to advance the understanding of the dynamics of quantum matter using the formalism of finite density field theory. To achieve this goal, we will utilize a broad range of analytical and numerical methods. This thesis is divided into two parts. The first part will focus on studying a Non-Fermi Liquid model. In the second part, we will study finite density theories using non-local observables, such as quantum information measures and the partition function on the torus. In more detail, in the first part of this thesis, we will study Non-Fermi Liquids in d = 2 spatial dimensions. These systems can arise when a Fermi surface is coupled to a massless boson. We find that at finite temperature, the perturbative description of quantum field theory breaks down due to infrared divergences. These are caused by static virtual bosonic modes and affect both fermionic and bosonic correlations. We will show how these divergences are resolved by a self-generated thermal mass for the bosons. We will find a new regime, the thermal Non-Fermi Liquid, which does not satisfy the zero-temperature fixed point scaling. Subsequently, we revisit the interaction between superconductivity and quantum criticality. In the second part, we study different aspects of finite density quantum field theory using methods from quantum information theory and finite temperature effects. For simplicity, we focus on massive Dirac fermions with a non-zero chemical potential, and work in 1 + 1 spacetime dimensions. Using the entanglement entropy in an interval, we construct a finite evolving c-function. Unlike in Lorentzinvariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the long-range creation of entanglement due to the Fermi surface. Motivated by previous work on lattice models, we numerically calculate the Renyi entropies and find Friedel-type oscillations; these are understood in terms of an OPE expansion with defects. Additionally, we consider mutual information as a measure of correlation functions between different regions. At finite temperature, we focus on theories on a two-dimensional Euclidean torus. Using recent developments in massive modular forms, we obtain a representation of the free energy of the torus based on the Fourier transformation on a twisted boundary condition. This dual representation satisfies many properties analogous to modular invariance in CFTs. In particular, we use this result to derive formulas for the density of states in non-relativistic theories, generalizing Cardy’s result on conformal theories.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Superconductivity; Superconductividad; [Field theory at finite density; Teoría de campos a densidad finita; Non-fermi liquid; Renormalization group; Grupo de renormalización; Modular invariance; Invariancia modular] |
| Referencias: | [1] Damia, J. A., Solís, M., Torroba, G. How non-Fermi liquids cure their infrared divergences. Phys. Rev. B, 102 (4), 045147, 2020. x, 9, 21, 28, 29, 31, 33, 45, 51, 52, 62, 113 [2] Damia, J. A., Solís, M., Torroba, G. Thermal effects in non-Fermi liquid superconductivity. Phys. Rev. B, 103 (15), 155161, 2021. 9, 21, 28, 29, 31, 49, 68, 113 [3] Shankar, R. Renormalization group approach to interacting fermions. Rev.Mod.Phys., 66, 129– 192, 1994. 9, 22, 26, 27 [4] Polchinski, J. Effective field theory and the Fermi surface, 1992. 9, 26 [5] Landau, L. D. The Theory of a Fermi Liquid. Zh. Eksp. Teor. Fiz., 30 (6), 1058, 1956. 9 [6] Landau, L. D. Oscillations in a Fermi Liquid. Zh. Eksp. Teor. Fiz., 32, 1957. [7] Landau, L. D. On the Theory of the Fermi Liquid. J. Exp. Theor. Phys., 35, 1958. [8] Schofield, A. J. Non-fermi liquids. Contemporary Physics, 40 (2), 95–115, 1999. 9, 12 [9] Pauli Jr, W. Uber gasentartung und paramagnetismus. Zeitschrift fur Physik A Hadrons and nuclei, 41 (2), 81–102, 1927. 10 [10] Sommerfeld, A. Zur elektronentheorie der metalle auf grund der fermischen statistik: i. teil: allgemeines, stromungs-und austrittsvorgange. Zeitschrift fur Physik, 47, 1–32, 1928. 10 [11] Onnes, H. K. The superconductivity of mercury. Comm. Phys. Lab. Univ., Leiden, págs. 122–124, 1911. 10 [12] Cooper, L. N. Bound electron pairs in a degenerate fermi gas. Physical Review, 104 (4), 1189,1956. 11 [13] Bardeen, J., Cooper, L. N., Schrieffer, J. R. Theory of superconductivity. Phys. Rev., 108,1175–1204, Dec 1957. URL https://link.aps.org/doi/10.1103/PhysRev.108.1175. 11 [14] Bednorz, J. G., Muller, K. A. Possible high t c superconductivity in the ba- la- cu- o system. Zeitschrift fur Physik B Condensed Matter, 64 (2), 189–193, 1986. 11, 12 [15] Bussmann-Holder, A., Keller, H. High-temperature superconductors: underlying physics and applications. Zeitschrift fur Naturforschung B, 75 (1-2), 3–14, 2020. 11 [16] Meissner, W., Ochsenfeld, R. Ein neuer effekt bei eintritt der supraleitfahigkeit. Naturwissenschaften, 21 (44), 787–788, 1933. 11 [17] Gurvitch, M., Fiory, A. Resistivity of La1,825Sr0,175CuO4 and YBa2Cu3O7 to 1100 k: Absence of saturation and its implications. Physical review letters, 59 (12), 1337, 1987. 12 [18] Broun, D. What lies beneath the dome? Nature Physics, 4 (3), 170–172, 2008. 12 [19] Shibauchi, T., Carrington, A., Matsuda, Y. A quantum critical point lying beneath the superconducting dome in iron pnictides. Annu. Rev. Condens. Matter Phys., 5 (1), 113–135, 2014.12 [20] Dressel, M. Quantum criticality in organic conductors? fermi liquid versus non-fermi-liquid behaviour. Journal of Physics: Condensed Matter, 23 (29), 293201, 2011. 12 [21] Cao, Y., Fatemi, V., Fang, S., Watanabe, K., Taniguchi, T., Kaxiras, E., et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556 (7699), 43–50, 2018. 12 [22] Wilson, K. G. The renormalization group: Critical phenomena and the kondo problem. Reviews of modern physics, 47 (4), 773, 1975. 12 [23] Hertz, J. A. Quantum critical phenomena. En: Basic Notions of Condensed Matter Physics, págs. 525–544. CRC Press, 2018. 12 [24] Vojta, M. Quantum phase transitions. Reports on Progress in Physics, 66 (12), 2069, 2003. 12 [25] Sondhi, S. L., Girvin, S., Carini, J., Shahar, D. Continuous quantum phase transitions. Reviews of modern physics, 69 (1), 315, 1997. [26] Sachdev, S. Quantum Phase Transitions. 2a ed. Cambridge University Press, 2011. 12 [27] Di Castro, C., Metzner, W. Ward identities and the β function in the luttinger liquid. Physical review letters, 67 (27), 3852, 1991. 13 [28] Shankar, R. Renormalization group for interacting fermions in d¿1. Physica A: Statistical Mechanics and its Applications, 177 (1-3), 530–536, 1991. [29] Castellani, C., Di Castro, C., Metzner, W. Instabilities of anisotropic interacting fermi systems. Physical review letters, 69 (11), 1703, 1992. 13 [30] Shankar, R. Renormalization-group approach to interacting fermions. Reviews of Modern Physics, 66 (1), 129, 1994. 13, 15 [31] Polchinski, J. Effective field theory and the fermi surface. arXiv preprint hep-th/9210046, 1992. 13, 15 [32] Son, D. Superconductivity by long-range color magnetic interaction in high-density quark matter. Physical Review D, 59 (9), 094019, 1999. 13, 19 [33] Evans, N., Hsu, S. D., Schwetz, M. An effective field theory approach to color superconductivity at high quark density. Nuclear Physics B, 551 (1-2), 275–289, 1999. [34] Schafer, T., Schwenzer, K. Non-fermi liquid effects in qcd at high density. Physical Review D,70 (5), 054007, 2004. [35] Shovkovy, I. A. Two lectures on color superconductivity. Foundations of Physics, 35 (8), 1309–1358, 2005. [36] Schafer, T. Non-fermi liquid effective field theory of dense qcd matter. arXiv preprint hepph/0608240, 2006. [37] Alford, M. G., Schmitt, A., Rajagopal, K., Schafer, T. Color superconductivity in dense quark matter. Reviews of Modern Physics, 80 (4), 1455, 2008. 13 [38] Tsai, S.-W., Castro Neto, A., Shankar, R., Campbell, D. K. Renormalization-group approach to superconductivity: from weak to strong electron–phonon coupling. Philosophical Magazine, 86 (17-18), 2631–2641, 2006. 13, 16 [39] Tsai, S.-W., Neto, A. C., Shankar, R., Campbell, D. Renormalization-group approach to strongcoupled superconductors. Physical Review B, 72 (5), 054531, 2005. 13 [40] Wang, H., Raghu, S., Torroba, G. Non-fermi-liquid superconductivity: Eliashberg approach versus the renormalization group. Physical Review B, 95 (16), 165137, 2017. 16, 18, 19 [41] Abrikosov, A., Gorkov, L., Dzyaloshinski, I. Methods of quantum field theory in statistical physics. Courier Corporation, 2012. 18, 22, 77 [42] Aguilera Damia, J., Kachru, S., Raghu, S., Torroba, G. Two dimensional non-Fermi liquid metals: a solvable large N limit. Phys. Rev. Lett., 123 (9), 096402, 2019. 21, 25, 26, 34 [43] Fitzpatrick, A., Kachru, S., Kaplan, J., Raghu, S. Non-fermi-liquid fixed point in a wilsonian theory of quantum critical metals. Phys. Rev. B, 88, 125116, Sep 2013. URL http://link.aps.org/doi/10.1103/PhysRevB.88.125116. 21, 26 [44] Mahajan, R., Ramirez, D. M., Kachru, S., Raghu, S. Quantum critical metals in d = 3 + 1 dimensions. Phys. Rev. B, 88, 115116, Sep 2013. URL http://link.aps.org/doi/10.1103/PhysRevB.88.115116. 21, 26 [45] Senthil, T., Shankar, R. Fermi surfaces in general codimension and a new controlled nontrivial fixed point. Phys. Rev. Lett., 102, 046406, Jan 2009. URL http://link.aps.org/doi/10.1103/PhysRevLett.102.046406. [46] Fitzpatrick, A., Torroba, G., Wang, H. Aspects of Renormalization in Finite Density Field Theory. Phys.Rev., B91, 195135, 2015. 21 [47] Torroba, G., Wang, H. Quantum critical metals in 4 − ϵ dimensions. Phys.Rev., B90 (16), 165144, 2014. 21, 26 [48] Raghu, S., Torroba, G., Wang, H. Metallic quantum critical points with finite BCS couplings. Phys. Rev., B92 (20), 205104, 2015. 21, 26, 28, 31, 61, 113 [49] Fitzpatrick, A. L., Kachru, S., Kaplan, J., Raghu, S. Non-Fermi-liquid behavior of large-NB quantum critical metals. Physical Review B, 89 (16), 165114, abr. 2014. 21, 26 [50] Nagaosa, N. Quantum field theory in condensed matter physics. Springer Science & Business Media, 2013. 23 [51] Lee, S.-S. Low-energy effective theory of fermi surface coupled with u(1) gauge field in 2 + 1 dimensions. Phys. Rev. B, 80, 165102, Oct 2009. URL http://link.aps.org/doi/10.1103/PhysRevB.80.165102. 26 [52] Son, D. T. Superconductivity by long-range color magnetic interaction in high-density quark matter. Phys. Rev. D, 59, 094019, Apr 1999. URL http://link.aps.org/doi/10.1103/PhysRevD.59.094019. 26 [53] Kaplan, D., Lee, J., Son, D., Stephanov, M. Conformality Lost. Phys. Rev., D80, 125005, 2009.28 [54] Witten, E. Baryons in the 1/n Expansion. Nucl. Phys. B, 160, 57–115, 1979. 28 [55] Wang, H., Raghu, S., Torroba, G. Non-Fermi liquid Superconductivity: Eliashberg versus the Renormalization Group. Phys. Rev., B95 (16), 165137, 2017. 30, 31, 61 [56] Chubukov, A. V., Abanov, A., Wang, Y., Wu, Y.-M. The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. arXiv e-prints, arXiv:1912.01797,dic. 2019. 30, 37, 55, 62 [57] Wang, H., Wang, Y., Torroba, G. Superconductivity vs quantum criticality: effects of thermal fluctuations, 2017. 31, 55, 57, 58, 60, 61, 113 [58] Le Bellac, M. Thermal field theory. Cambridge University Press, 2000. 33 [59] Kapusta, J. I., Gale, C. Finite-Temperature Field Theory: Principles and Applications. Cambridge Monographs on Mathematical Physics, 2a ed´on. Cambridge University Press, 2006. 33 [60] Klein, A., Schattner, Y., Berg, E., Chubukov, A. Normal state properties of quantum-critical metals at finite temperatures. Bulletin of the American Physical Society, 2020. 36, 47 [61] Dell’Anna, L., Metzner, W. Fermi surface fluctuations and single electron excitations near pomeranchuk instability in two dimensions. Phys. Rev. B, 73, 045127, Jan 2006. URL https://link.aps.org/doi/10.1103/PhysRevB.73.045127. 37 [62] Moon, E.-G., Chubukov, A. Quantum-critical pairing with varying exponents. Journal of Low Temperature Physics, 161 (1-2), 263–281, 2010. 37 [63] Wu, Y.-M., Abanov, A.,Wang, Y., Chubukov, A. V. Special role of the first Matsubara frequency for superconductivity near a quantum critical point: Nonlinear gap equation below Tc and spectral properties in real frequencies. Physical Review B, 99 (14), 144512, abr. 2019. 37, 55, 62 [64] Wang, H., Torroba, G. Non-Fermi liquids at finite temperature: normal state and infrared singularities. Phys. Rev., B96 (14), 144508, 2017. 38, 39, 43 [65] Xu, X. Y., Klein, A., Sun, K., Chubukov, A. V., Meng, Z. Y. Extracting non-Fermi liquid fermionic self-energy at T = 0 from quantum Monte Carlo data, 3 2020. 45 [66] Xu, X. Y., Sun, K., Schattner, Y., Berg, E., Meng, Z. Y. Non-Fermi Liquid at ( 2+1 ) D Ferromagnetic Quantum Critical Point. Phys. Rev. X, 7 (3), 031058, 2017. 45, 47 [67] Punk, M. Finite-temperature scaling close to ising-nematic quantum critical points in twodimensional metals. Phys. Rev. B, 94, 195113, Nov 2016. URL https://link.aps.org/doi/10.1103/PhysRevB.94.195113. 47 [68] Schattner, Y., Lederer, S., Kivelson, S., Berg, E. Ising nematic quantum critical point in a metal: A monte carlo study. Phys. Rev. X, 6, 031028, Aug 2016. URL http://link.aps.org/doi/10.1103/PhysRevX.6.031028. 47 [69] Lederer, S., Schattner, Y., Berg, E., Kivelson, S. A. Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point. Proceedings of the National Academy of Science,114 (19), 4905–4910, mayo 2017. [70] Berg, E., Lederer, S., Schattner, Y., Trebst, S. Monte carlo studies of quantum critical metals. Annual Review of Condensed Matter Physics, 10 (1), 63–84, 2019. URL https://doi.org/10.1146/annurev-conmatphys-031218-013339. [71] Liu, Z. H., Pan, G., Xu, X. Y., Sun, K., Meng, Z. Y. Itinerant quantum critical point with fermion pockets and hotspots. Proceedings of the National Academy of Sciences, 116 (34),16760–16767, 2019. 47 [72] Sachdev, S. Quantum Phase Transitions. Cambridge: Cambridge University Press, 2011. 48,114 [73] Wang, Y., Abanov, A., Altshuler, B. L., Yuzbashyan, E. A., Chubukov, A. V. Superconductivity near a Quantum-Critical Point: The Special Role of the First Matsubara Frequency. Physical Review Letters, 117 (15), 157001, oct. 2016. 55, 58, 62 [74] Abanov, A., Chubukov, A. V. Interplay between superconductivity and non-fermi liquid at a quantum critical point in a metal. i. the gamma model and its phase diagram at t=0: The case 0 < γ < 1. Physical Review B, 102 (2), Jul 2020. URL http://dx.doi.org/10.1103/PhysRevB.102.024524. 60, 67 [75] Wu, Y.-M., Abanov, A., Wang, Y., Chubukov, A. V. Interplay between superconductivity and non-fermi liquid at a quantum critical point in a metal. ii. the gamma model at a finite t for 0 < γ < 1. Physical Review B, 102 (2), Jul 2020. URL http://dx.doi.org/10.1103/PhysRevB.102.024525. 55, 58, 62 [76] Luttinger, J. M.,Ward, J. C. Ground-state energy of a many-fermion system. ii. Phys. Rev., 118, 1417–1427, Jun 1960. URL https://link.aps.org/doi/10.1103/PhysRev.118.1417. 55, 67 [77] Benlagra, A., Kim, K., P´epin, C. The luttinger–ward functional approach in the eliashberg framework: a systematic derivation of scaling for thermodynamics near the quantum critical point. Journal of Physics: Condensed Matter, 23 (14), 145601, 2011. [78] Haslinger, R., Chubukov, A. V. Condensation energy in strongly coupled superconductors. Phys. Rev. B, 67, 140504, Apr 2003. URL https://link.aps.org/doi/10.1103/PhysRevB.67.140504. 55, 67 [79] Zamolodchikov, A. B. Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory. JETP Lett., 43, 730–732, 1986. [Pisma Zh. Eksp. Teor. Fiz.43,565(1986)]. 71, 97, 114 [80] Komargodski, Z., Schwimmer, A. On Renormalization Group Flows in Four Dimensions. JHEP, 12, 099, 2011. 71 [81] Swingle, B. Entanglement does not generally decrease under renormalization. J. Stat. Mech., 1410 (10), P10041, 2014. 71, 83, 87 [82] Casini, H., Huerta, M. Entanglement entropy in free quantum field theory. J. Phys., A42, 504007, 2009. 71, 83, 84, 88 [83] Cardy, J. L. Operator Content of Two-Dimensional Conformally Invariant Theories. Nucl. Phys. B, 270, 186–204, 1986. 72, 106 [84] Hellerman, S. A Universal Inequality for CFT and Quantum Gravity. JHEP, 08, 130, 2011. 72 [85] Strominger, A. Black hole entropy from near horizon microstates. JHEP, 02, 009, 1998. 72 [86] Maloney, A., Witten, E. Quantum Gravity Partition Functions in Three Dimensions. JHEP, 02, 029, 2010. 72 [87] Berg, M., Bringmann, K., Gannon, T. Massive deformations of Maass forms and Jacobi forms. Commun. Num. Theor. Phys., 15 (3), 575–603, 2021. 72, 99, 104, 107 [88] Downing, M., Murthy, S., Watts, G. M. T. Modular symmetry of massive free fermions, 2 2023. 104 [89] Berg, M. Manifest Modular Invariance in the Near-Critical Ising Model, 2 2023. 72, 99, 104, 107, 108 [90] Gonzalez, H. A., Tempo, D., Troncoso, R. Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes. JHEP, 11, 066, 2011. 72, 112 [91] Castro, A., Hofman, D. M., Sarosi, G. Warped Weyl fermion partition functions. JHEP, 11, 129, 2015. [92] Melnikov, D., Novaes, F., Pérez, A., Troncoso, R. Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy. JHEP, 06, 054, 2019. [93] Chen, B., Hao, P.-X., Yu, Z.-F. 2d Galilean Field Theories with Anisotropic Scaling. Phys. Rev. D, 101 (6), 066029, 2020. 72 [94] Fradkin, E. H. Field Theories of Condensed Matter Physics, tomo 82. Cambridge, UK: Cambridge Univ. Press, 2013. 72 [95] Polchinski, J. String theory. Vol. 2: Superstring theory and beyond. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2007. 74 [96] Peskin, M. E., Schroeder, D. V. An Introduction to quantum field theory. Reading, USA: Addison-Wesley, 1995. 77 [97] Daguerre, L., Medina, R., Solís, M., Torroba, G. Aspects of quantum information in finite density field theory. JHEP, 03, 079, 2021. 83, 97, 109, 114, 115 [98] Daguerre, L., Torroba, G., Medina, R., Solís, M. Teoría de campos no relativistas: dinámica e irreversibilidad. En: Anales (Asociación Física Argentina), tomo 32, págs. 93–98. SciELO Argentina, 2021. URL http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S1850-11682021000400093. 83 [99] Casini, H., Huerta, M. On the RG running of the entanglement entropy of a circle. Phys. Rev., D85, 125016, 2012. 83, 84 [100] Casini, H., Teste, E., Torroba, G. Markov Property of the Conformal Field Theory Vacuum and the a Theorem. Phys. Rev. Lett., 118 (26), 261602, 2017. 83 [101] Calabrese, P., Cardy, J. Entanglement entropy and conformal field theory. J. Phys., A42, 504005, 2009. 84, 88, 90, 91 [102] Casini, H., Huerta, M. A Finite entanglement entropy and the c-theorem. Phys. Lett., B600, 142–150, 2004. 84, 97, 114 [103] Peschel, I. Calculation of reduced density matrices from correlation functions. Journal of Physics A Mathematical General, 36, L205–L208, abr. 2003. 84 [104] Peschel, I. LETTER TO THE EDITOR: Calculation of reduced density matrices from correlation functions. Journal of Physics A Mathematical General, 36, L205–L208, abr. 2003. 84 [105] Casini, H., Fosco, C., Huerta, M. Entanglement and alpha entropies for a massive Dirac field in two dimensions. J. Stat. Mech., 0507, P07007, 2005. 85, 88, 92 [106] Cardy, J. 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”. 85 [107] Ogawa, N., Takayanagi, T., Ugajin, T. Holographic Fermi Surfaces and Entanglement Entropy. JHEP, 01, 125, 2012. [108] Kim, B. S. Entanglement Entropy, Chemical Potential, Current Source, and Wilson Loop, 5 2017. 85, 103, 105 [109] Hason, I. Triviality of Entanglement Entropy in the Galilean Vacuum. Phys. Lett. B, 780, 149–151, 2018. 86 [110] Cappelli, A., Friedan, D., Latorre, J. I. C theorem and spectral representation. Nucl. Phys., B352, 616–670, 1991. 87, 97, 114 [111] Calabrese, P., Campostrini, M., Essler, F., Nienhuis, B. Parity effects in the scaling of block entanglement in gapless spin chains. Physical review letters, 104 9, 095701, 2010. 87, 90, 97, 115 [112] Swingle, B., McMinis, J., Tubman, N. M. Oscillating terms in the renyi entropy of fermi gases and liquids. Physical Review B, 87 (23), Jun 2013. URL http://dx.doi.org/10.1103/PhysRevB.87.235112. 90, 92, 97, 115 [113] Cardy, J., Calabrese, P. Unusual corrections to scaling in entanglement entropy. Journal of Statistical Mechanics: Theory and Experiment, 2010, 04023, 2010. 90, 91, 92, 97, 115 [114] Cardy, J., Castro-Alvaredo, O., Doyon, B. Form factors of branch-point twist fields in quantum integrable models and entanglement entropy. J. Statist. Phys., 130, 129–168, 2008. 90 [115] Castro-Alvaredo, O. A., Doyon, B., Levi, E. Arguments towards a c-theorem from branch-point twist fields. J. Phys. A, 44, 492003, 2011. 90 [116] Levi, E. Composite branch-point twist fields in the Ising model and their expectation values. J. Phys. A, 45, 275401, 2012. [117] Bianchi, L., Meineri, M., Myers, R. C., Smolkin, M. Renyi entropy and conformal defects. JHEP, 07, 076, 2016. [118] Billo, M., Goncalves, V., Lauria, E., Meineri, M. Defects in conformal field theory. JHEP, 04, 091, 2016. [119] Gadde, A. Conformal constraints on defects. JHEP, 01, 038, 2020. 90 [120] Bousso, R., Casini, H., Fisher, Z., Maldacena, J. Entropy on a null surface for interacting quantum field theories and the Bousso bound. Phys. Rev., D91 (8), 084030, 2015. 90 [121] Guimaraes, M., Linet, B. Scalar Green’s functions in an Euclidean space with a conical-type line singularity. Commun. Math. Phys., 165, 297–310, 1994. 91 [122] Casini, H. Entropy inequalities from reflection positivity. J. Stat. Mech., 1008, P08019, 2010. 92 [123] Aristov, D. N., Luther, A. Correlations in the sine-gordon model with finite soliton density. Physical Review B, 65 (16), Apr 2002. URL http://dx.doi.org/10.1103/PhysRevB.65.165412. 92 [124] Wolf, M. M., Verstraete, F., Hastings, M. B., Cirac, J. I. Area Laws in Quantum Systems: Mutual Information and Correlations. Phys. Rev. Lett., 100 (7), 070502, 2008. 93 [125] Cardy, J. Some results on the mutual information of disjoint regions in higher dimensions. Journal of Physics A: Mathematical and Theoretical, 46 (28), 285402, 2013. URL http://stacks.iop.org/1751-8121/46/i=28/a=285402. 93, 94 [126] Agón, C., Faulkner, T. Quantum Corrections to Holographic Mutual Information. JHEP, 08, 118, 2016. 94 [127] Agon, C. A., Cohen-Abbo, I., Schnitzer, H. J. Large distance expansion of Mutual Information for disjoint disks in a free scalar theory. JHEP, 11, 073, 2016. [128] Chen, B., Chen, L., Hao, P.-x., Long, J. On the Mutual Information in Conformal Field Theory. JHEP, 06, 096, 2017. 94 [129] Fisher, D. S. Scaling and critical slowing down in random-field Ising systems. Phys. Rev. Lett., 56, 416–419, 1986. 95, 98 [130] Huijse, L., Sachdev, S., Swingle, B. Hidden Fermi surfaces in compressible states of gauge-gravity duality. Phys. Rev. B, 85, 035121, 2012. [131] Dong, X., Harrison, S., Kachru, S., Torroba, G., Wang, H. Aspects of holography for theories with hyperscaling violation. JHEP, 06, 041, 2012. 95, 98, 112, 115 [132] Swingle, B. R´enyi entropy, mutual information, and fluctuation properties of fermi liquids. Physical Review B, 86 (4), 045109, 2012. 95 [133] Islam, R., Ma, R., Preiss, P. M., Tai, M. E., Lukin, A., Rispoli, M., et al. Measuring entanglement entropy through the interference of quantum many-body twins. arXiv e-prints, arXiv:1509.01160, sep. 2015. 98 [134] Li, J., Fan, R., Wang, H., Ye, B., Zeng, B., Zhai, H., et al. Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator. Physical Review X, 7 (3), 031011, jul. 2017. 98 [135] Wolf, M. M. Violation of the entropic area law for fermions. Phys. Rev. Lett., 96, 010404, Jan 2006. URL https://link.aps.org/doi/10.1103/PhysRevLett.96.010404. 98 [136] Aguilera-Damia, J., Solís, M., Torroba, G. Nonrelativistic Dirac fermions on the torus. JHEP, 12, 060, 2023. 99, 107, 115 [137] Di Francesco, P., Mathieu, P., Senechal, D. Conformal Field Theory. Graduate Texts in Contemporary Physics. New York: Springer-Verlag, 1997. 99, 102 [138] Benjamin, N., Dyer, E., Fitzpatrick, A. L., Kachru, S. Universal Bounds on Charged States in 2d CFT and 3d Gravity. JHEP, 08, 041, 2016. 104 [139] Dyer, E., Fitzpatrick, A. L., Xin, Y. Constraints on Flavored 2d CFT Partition Functions. JHEP, 02, 148, 2018. 104 [140] D’Hoker, E., Kaidi, J. Lectures on modular forms and strings, 8 2022. 104 [141] Carlip, S. Logarithmic corrections to black hole entropy from the Cardy formula. Class. Quant. Grav., 17, 4175–4186, 2000. 106 [142] Shankar, R. Renormalization group approach to interacting fermions. Rev. Mod. Phys., 66, 129–192, 1994. 109 [143] Benjamin, N., Lee, J., Ooguri, H., Simmons-Duffin, D. Universal Asymptotics for High Energy CFT Data, 6 2023. 112 [144] Chodos, A., Healy, J. Spectral degeneracy of the lattice dirac equation as a function of lattice shape. Nuclear Physics B, 127 (3), 426 – 446, 1977. URL http://www.sciencedirect.com/science/article/pii/0550321377904497. 119 [145] Chodos, A., Healy, J. B. Continuous space-time symmetries of the lattice dirac equation. Phys. Rev. D, 16, 387–396, Jul 1977. URL https://link.aps.org/doi/10.1103/PhysRevD.16.387. [146] Susskind, L. Lattice fermions. Phys. Rev. D, 16, 3031–3039, Nov 1977. URL https://link.aps.org/doi/10.1103/PhysRevD.16.3031. 119 |
| Materias: | Física > Teoría de campos |
| Divisiones: | Investigación y aplicaciones no nucleares > Física > Partículas y campos |
| Código ID: | 1286 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 16 Sep 2024 10:44 |
| Última Modificación: | 16 Sep 2024 11:01 |
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