Abstract
We compare the capacity of entanglement with the entanglement entropy by considering various aspects of these quantities for free bosonic and fermionic models in one spatial dimension, both in the continuum and on the lattice. Substantial differences are observed in the subleading terms of these entanglement quantifiers when the subsystem is made by two disjoint intervals, in the massive scalar field and in the fermionic chain. We define c-functions based on the capacity of entanglement similar to the one based on the entanglement entropy, showing through a numerical analysis that they display a monotonic behaviour under the renormalisation group flow generated by the mass. The capacity of entanglement and its related quantities are employed to explore the symmetry resolution. The temporal evolutions of the capacity of entanglement and of the corresponding contour function after a global quench are also discussed.
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References
H. Yao and X.-L. Qi, Entanglement entropy and entanglement spectrum of the Kitaev model, Phys. Rev. Lett. 105 (2010) 080501 [arXiv:1001.1165] [INSPIRE].
J. Schliemann, Entanglement spectrum and entanglement thermodynamics of quantum Hall bilayers at ν = 1, Phys. Rev. B 83 (2011) 115322 [arXiv:1008.5289].
E. Perlmutter, A universal feature of CFT Rényi entropy, JHEP 03 (2014) 117 [arXiv:1308.1083] [INSPIRE].
J. De Boer, J. Järvelä and E. Keski-Vakkuri, Aspects of capacity of entanglement, Phys. Rev. D 99 (2019) 066012 [arXiv:1807.07357] [INSPIRE].
Y. Nakaguchi and T. Nishioka, A holographic proof of Rényi entropic inequalities, JHEP 12 (2016) 129 [arXiv:1606.08443] [INSPIRE].
D. Reeb and M.M. Wolf, An improved landauer principle with finite-size corrections, New J. Phys. 16 (2014) 103011.
P. Boes, N.H.Y. Ng and H. Wilming, Variance of Relative Surprisal as Single-Shot Quantifier, PRX Quantum 3 (2022) 010325 [INSPIRE].
C.T. Chubb, M. Tomamichel and K. Korzekwa, Beyond the thermodynamic limit: finite-size corrections to state interconversion rates, Quantum 2 (2018) 108 [arXiv:1711.01193].
E. Verlinde and K.M. Zurek, Spacetime Fluctuations in AdS/CFT, JHEP 04 (2020) 209 [arXiv:1911.02018] [INSPIRE].
R. Arias, M. Botta-Cantcheff, P.J. Martinez and J.F. Zarate, Modular Hamiltonian for holographic excited states, Phys. Rev. D 102 (2020) 026021 [arXiv:2002.04637] [INSPIRE].
J. de Boer, V. Godet, J. Kastikainen and E. Keski-Vakkuri, Quantum hypothesis testing in many-body systems, SciPost Phys. Core 4 (2021) 019 [arXiv:2007.11711] [INSPIRE].
K.M. Zurek, On vacuum fluctuations in quantum gravity and interferometer arm fluctuations, Phys. Lett. B 826 (2022) 136910 [arXiv:2012.05870] [INSPIRE].
K. Kawabata, T. Nishioka, Y. Okuyama and K. Watanabe, Probing Hawking radiation through capacity of entanglement, JHEP 05 (2021) 062 [arXiv:2102.02425] [INSPIRE].
K. Okuyama, Capacity of entanglement in random pure state, Phys. Lett. B 820 (2021) 136600 [arXiv:2103.08909] [INSPIRE].
K. Kawabata, T. Nishioka, Y. Okuyama and K. Watanabe, Replica wormholes and capacity of entanglement, JHEP 10 (2021) 227 [arXiv:2105.08396] [INSPIRE].
S. Iso, T. Mori and K. Sakai, Wilsonian Effective Action and Entanglement Entropy, Symmetry 13 (2021) 1221 [arXiv:2105.14834] [INSPIRE].
P. Nandy, Capacity of entanglement in local operators, JHEP 07 (2021) 019 [arXiv:2106.00228] [INSPIRE].
H.L. Prihadi, F.P. Zen and D. Dwiputra, Fluctuations and non-Gaussianity in de Sitter spacetime from holographic entanglement entropy, arXiv:2106.15174 [INSPIRE].
T. Banks and K.M. Zurek, Conformal description of near-horizon vacuum states, Phys. Rev. D 104 (2021) 126026 [arXiv:2108.04806] [INSPIRE].
B. Bhattacharjee, P. Nandy and T. Pathak, Eigenstate capacity and Page curve in fermionic Gaussian states, Phys. Rev. B 104 (2021) 214306 [arXiv:2109.00557] [INSPIRE].
P. Caputa, J.M. Magan and D. Patramanis, Geometry of Krylov complexity, Phys. Rev. Res. 4 (2022) 013041 [arXiv:2109.03824] [INSPIRE].
C. Boudreault, C. Berthiere and W. Witczak-Krempa, Entanglement and separability in continuum Rokhsar-Kivelson states, Phys. Rev. Res. 4 (2022) 033251 [arXiv:2110.04290] [INSPIRE].
D. Patramanis, Probing the entanglement of operator growth, PTEP 2022 (2022) 063A01 [arXiv:2111.03424] [INSPIRE].
Y. Huang and L. Wei, Second-order statistics of fermionic Gaussian states, J. Phys. A 55 (2022) 105201 [arXiv:2111.08216] [INSPIRE].
K. Allameh, A.F. Astaneh and A. Hassanzadeh, Aspects of holographic entanglement entropy for \( T\overline{T} \)-deformed CFTs, Phys. Lett. B 826 (2022) 136914 [arXiv:2111.11338] [INSPIRE].
E. Bianchi, L. Hackl, M. Kieburg, M. Rigol and L. Vidmar, Volume-Law Entanglement Entropy of Typical Pure Quantum States, PRX Quantum 3 (2022) 030201 [arXiv:2112.06959] [INSPIRE].
M. Mintchev, D. Pontello, A. Sartori and E. Tonni, Entanglement entropies of an interval in the free Schrödinger field theory at finite density, JHEP 07 (2022) 120 [arXiv:2201.04522] [INSPIRE].
D.E. Sommer and S.T. Dunham, Entangling Solid Solutions: Machine Learning of Tensor Networks for Materials Property Prediction, arXiv:2203.09613 [INSPIRE].
K.M. Zurek, Snowmass 2021 White Paper: Observational Signatures of Quantum Gravity, arXiv:2205.01799 [INSPIRE].
S. Gukov, V.S.H. Lee and K.M. Zurek, Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity, Phys. Rev. D 107 (2023) 016004 [arXiv:2205.02233] [INSPIRE].
L. Wei, Average capacity of quantum entanglement, J. Phys. A 56 (2023) 015302 [arXiv:2205.06343] [INSPIRE].
G. Chiriacò, M. Dalmonte and T. Chanda, Critical light-matter entanglement at cavity mediated phase transitions, Phys. Rev. B 106 (2022) 155113 [arXiv:2207.06444] [INSPIRE].
D. Shrimali, S. Bhowmick, V. Pandey and A.K. Pati, Capacity of entanglement for a nonlocal Hamiltonian, Phys. Rev. A 106 (2022) 042419 [arXiv:2207.11459] [INSPIRE].
E. Bianchi, L. Hackl, M. Kieburg, M. Rigol and L. Vidmar, Volume-Law Entanglement Entropy of Typical Pure Quantum States, PRX Quantum 3 (2022) 030201 [arXiv:2112.06959] [INSPIRE].
E. Verlinde and K.M. Zurek, Modular fluctuations from shockwave geometries, Phys. Rev. D 106 (2022) 106011 [arXiv:2208.01059] [INSPIRE].
D. Li, V.S.H. Lee, Y. Chen and K.M. Zurek, Interferometer response to geontropic fluctuations, Phys. Rev. D 107 (2023) 024002 [arXiv:2209.07543] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
V. Alba and P. Calabrese, Entanglement and thermodynamics after a quantum quench in integrable systems, Proc. Natl. Acad. Sci. 114 (2017) 7947.
A. Coser, E. Tonni and P. Calabrese, Entanglement negativity after a global quantum quench, J. Stat. Mech. 1412 (2014) P12017 [arXiv:1410.0900] [INSPIRE].
A. Botero and B. Reznik, Spatial structures and localization of vacuum entanglement in the linear harmonic chain, Phys. Rev. A 70 (2004) 052329 [quant-ph/0403233].
Y. Chen and G. Vidal, Entanglement contour, J. Stat. Mech. 2014 (2014) P10011.
I. Frérot and T. Roscilde, Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations, Phys. Rev. B 92 (2015) 115129 [arXiv:1506.00545].
A. Coser, C. De Nobili and E. Tonni, A contour for the entanglement entropies in harmonic lattices, J. Phys. A 50 (2017) 314001 [arXiv:1701.08427] [INSPIRE].
H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
H. Liu and M. Mezei, A Refinement of entanglement entropy and the number of degrees of freedom, JHEP 04 (2013) 162 [arXiv:1202.2070] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
T. Nishioka, Entanglement entropy: holography and renormalization group, Rev. Mod. Phys. 90 (2018) 035007 [arXiv:1801.10352] [INSPIRE].
H. Casini, C.D. Fosco and M. Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions, J. Stat. Mech. 0507 (2005) P07007 [cond-mat/0505563] [INSPIRE].
H. Casini and M. Huerta, Entanglement and alpha entropies for a massive scalar field in two dimensions, J. Stat. Mech. 0512 (2005) P12012 [cond-mat/0511014] [INSPIRE].
J.I. Latorre, E. Rico and G. Vidal, Ground state entanglement in quantum spin chains, Quant. Inf. Comput. 4 (2004) 48 [quant-ph/0304098] [INSPIRE].
R. Orus, Entanglement and majorization in (1 + 1)-dimensional quantum systems, Phys. Rev. A 71 (2005) 052327 [quant-ph/0501110] [Erratum ibid. 73 (2006) 019904] [INSPIRE].
A. Riera and J.I. Latorre, Area law and vacuum reordering in harmonic networks, Phys. Rev. A 74 (2006) 052326 [quant-ph/0605112] [INSPIRE].
R. Arias, J. de Boer, G. Di Giulio, E. Keski-Vakkuri and E. Tonni, Sequences of resource monotones from modular Hamiltonian polynomials, arXiv:2301.01053 [INSPIRE].
I. Bengtsson and K. Życzkowski, Geometry of quantum states: an introduction to quantum entanglement, Cambridge University Press (2017).
A. Lukin et al., Probing entanglement in a many-body-localized system, Science 364 (2019) 256 [arXiv:1805.09819].
V. Vitale et al., Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12 (2022) 106 [arXiv:2101.07814] [INSPIRE].
A. Neven et al., Symmetry-resolved entanglement detection using partial transpose moments, npj Quantum Inf. 7 (2021) 152 [arXiv:2103.07443] [INSPIRE].
M. Goldstein and E. Sela, Symmetry-resolved entanglement in many-body systems, Phys. Rev. Lett. 120 (2018) 200602 [arXiv:1711.09418] [INSPIRE].
J.C. Xavier, F.C. Alcaraz and G. Sierra, Equipartition of the entanglement entropy, Phys. Rev. B 98 (2018) 041106 [arXiv:1804.06357] [INSPIRE].
N. Laflorencie and S. Rachel, Spin-resolved entanglement spectroscopy of critical spin chains and luttinger liquids, J. Stat. Mech. 2014 (2014) P11013.
R. Bonsignori, P. Ruggiero and P. Calabrese, Symmetry resolved entanglement in free fermionic systems, J. Phys. A 52 (2019) 475302 [arXiv:1907.02084] [INSPIRE].
S. Fraenkel and M. Goldstein, Symmetry resolved entanglement: Exact results in 1D and beyond, J. Stat. Mech. 2003 (2020) 033106 [arXiv:1910.08459] [INSPIRE].
S. Murciano, G. Di Giulio and P. Calabrese, Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach, SciPost Phys. 8 (2020) 046 [arXiv:1911.09588] [INSPIRE].
G. Parez, R. Bonsignori and P. Calabrese, Quasiparticle dynamics of symmetry-resolved entanglement after a quench: Examples of conformal field theories and free fermions, Phys. Rev. B 103 (2021) L041104 [arXiv:2010.09794] [INSPIRE].
D. Azses, E.G. Dalla Torre and E. Sela, Observing Floquet topological order by symmetry resolution, Phys. Rev. B 104 (2021) L220301 [arXiv:2109.01151] [INSPIRE].
S. Murciano, P. Calabrese and L. Piroli, Symmetry-resolved Page curves, Phys. Rev. D 106 (2022) 046015 [arXiv:2206.05083] [INSPIRE].
L. Piroli, E. Vernier, M. Collura and P. Calabrese, Thermodynamic symmetry resolved entanglement entropies in integrable systems, arXiv:2203.09158 [INSPIRE].
S. Murciano, G. Di Giulio and P. Calabrese, Entanglement and symmetry resolution in two dimensional free quantum field theories, JHEP 08 (2020) 073 [arXiv:2006.09069] [INSPIRE].
D.X. Horváth and P. Calabrese, Symmetry resolved entanglement in integrable field theories via form factor bootstrap, JHEP 11 (2020) 131 [arXiv:2008.08553] [INSPIRE].
P. Calabrese, J. Dubail and S. Murciano, Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models, JHEP 10 (2021) 067 [arXiv:2106.15946] [INSPIRE].
S. Zhao, C. Northe and R. Meyer, Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory, JHEP 07 (2021) 030 [arXiv:2012.11274] [INSPIRE].
C.G. Callan, Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech. 1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE].
M. Caraglio and F. Gliozzi, Entanglement Entropy and Twist Fields, JHEP 11 (2008) 076 [arXiv:0808.4094] [INSPIRE].
S. Furukawa, V. Pasquier and J. Shiraishi, Mutual Information and Compactification Radius in a c = 1 Critical Phase in One Dimension, Phys. Rev. Lett. 102 (2009) 170602 [arXiv:0809.5113] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, J. Stat. Mech. 0911 (2009) P11001 [arXiv:0905.2069] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 1101 (2011) P01021 [arXiv:1011.5482] [INSPIRE].
A. Coser, L. Tagliacozzo and E. Tonni, On Rényi entropies of disjoint intervals in conformal field theory, J. Stat. Mech. 1401 (2014) P01008 [arXiv:1309.2189] [INSPIRE].
T. Grava, A.P. Kels and E. Tonni, Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice, Phys. Rev. Lett. 127 (2021) 141605 [arXiv:2104.06994] [INSPIRE].
C.A. Agon, M. Headrick, D.L. Jafferis and S. Kasko, Disk entanglement entropy for a Maxwell field, Phys. Rev. D 89 (2014) 025018 [arXiv:1310.4886] [INSPIRE].
C. De Nobili, A. Coser and E. Tonni, Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations, J. Stat. Mech. 1506 (2015) P06021 [arXiv:1501.04311] [INSPIRE].
B.-Q. Jin and V.E. Korepin, Quantum Spin Chain, Toeplitz Determinants and the Fisher-Hartwig Conjecture, J. Stat. Phys. 116 (2004) 79.
P. Calabrese, M. Campostrini, F. Essler and B. Nienhuis, Parity effects in the scaling of block entanglement in gapless spin chains, Phys. Rev. Lett. 104 (2010) 095701 [arXiv:0911.4660] [INSPIRE].
P. Calabrese and F.H.L. Essler, Universal corrections to scaling for block entanglement in spin-1/2 XX chains, J. Stat. Mech. 2010 (2010) P08029.
M. Mintchev, D. Pontello and E. Tonni, Entanglement entropies of an interval in the free Schrödinger field theory on the half line, JHEP 09 (2022) 090 [arXiv:2206.06187] [INSPIRE].
I. Peschel, M. Kaulke and Ö. Legeza, Density-matrix spectra for integrable models, Ann. Phys. 8 (1999) 153 [cond-mat/9810174].
H. Itoyama and H.B. Thacker, Lattice Virasoro Algebra and Corner Transfer Matrices in the Baxter Eight Vertex Model, Phys. Rev. Lett. 58 (1987) 1395 [INSPIRE].
T. Nishino, Density Matrix Renormalization Group Method for 2D Classical Models, J. Phys. Soc. Jpn. 64 (1995) 3598.
T. Nishino and K. Okunishi, Density matrix and renormalization for classical lattice models, Lect. Notes Phys. 478 (1997) 167.
I. Peschel and T.T. Truong, Corner transfer matrices for the gaussian model, Ann. Phys. 503 (1991) 185.
I. Peschel and M.-C. Chung, Density matrices for a chain of oscillators, J. Phys. A 32 (1999) 8419.
P. Calabrese, J. Cardy and I. Peschel, Corrections to scaling for block entanglement in massive spin-chains, J. Stat. Mech. 1009 (2010) P09003 [arXiv:1007.0881] [INSPIRE].
V. Alba, P. Calabrese and E. Tonni, Entanglement spectrum degeneracy and the Cardy formula in 1 + 1 dimensional conformal field theories, J. Phys. A 51 (2018) 024001 [arXiv:1707.07532] [INSPIRE].
I. Peschel and V. Eisler, Reduced density matrices and entanglement entropy in free lattice models, J. Phys. A 42 (2009) 504003.
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories, J. Stat. Mech. 1606 (2016) 064003 [arXiv:1603.02889] [INSPIRE].
F.H.L. Essler and M. Fagotti, Quench dynamics and relaxation in isolated integrable quantum spin chains, J. Stat. Mech. 1606 (2016) 064002 [arXiv:1603.06452] [INSPIRE].
M. Fagotti and F.H.L. Essler, Reduced density matrix after a quantum quench, Phys. Rev. B 87 (2013) 245107 [arXiv:1302.6944].
X. Wen, S. Ryu and A.W.W. Ludwig, Entanglement hamiltonian evolution during thermalization in conformal field theory, J. Stat. Mech. 1811 (2018) 113103 [arXiv:1807.04440] [INSPIRE].
G. Di Giulio, R. Arias and E. Tonni, Entanglement hamiltonians in 1D free lattice models after a global quantum quench, J. Stat. Mech. 1912 (2019) 123103 [arXiv:1905.01144] [INSPIRE].
G. Torlai, L. Tagliacozzo and G.D. Chiara, Dynamics of the entanglement spectrum in spin chains, J. Stat. Mech. 2014 (2014) P06001.
J. Surace, L. Tagliacozzo and E. Tonni, Operator content of entanglement spectra in the transverse field Ising chain after global quenches, Phys. Rev. B 101 (2020) 241107(R) [arXiv:1909.07381] [INSPIRE].
J. Kudler-Flam, I. MacCormack and S. Ryu, Holographic entanglement contour, bit threads, and the entanglement tsunami, J. Phys. A 52 (2019) 325401 [arXiv:1902.04654] [INSPIRE].
G. Di Giulio and E. Tonni, Complexity of mixed Gaussian states from Fisher information geometry, JHEP 12 (2020) 101 [arXiv:2006.00921] [INSPIRE].
G. Di Giulio and E. Tonni, Subsystem complexity after a global quantum quench, JHEP 05 (2021) 022 [arXiv:2102.02764] [INSPIRE].
V. Alba and P. Calabrese, Entanglement dynamics after quantum quenches in generic integrable systems, SciPost Phys. 4 (2018) 017 [arXiv:1712.07529] [INSPIRE].
M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, Relaxation in a Completely Integrable Many-Body Quantum System: An AbInitio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons, Phys. Rev. Lett. 98 (2007) 050405 [cond-mat/0604476].
S. Sotiriadis and P. Calabrese, Validity of the GGE for quantum quenches from interacting to noninteracting models, J. Stat. Mech. 1407 (2014) P07024 [arXiv:1403.7431] [INSPIRE].
E. Ilievski, J. De Nardis, B. Wouters, J.S. Caux, F.H.L. Essler and T. Prosen, Complete Generalized Gibbs Ensembles in an Interacting Theory, Phys. Rev. Lett. 115 (2015) 157201 [arXiv:1507.02993].
E. Ilievski, M. Medenjak, T. Prosen and L. Zadnik, Quasilocal charges in integrable lattice systems, J. Stat. Mech. 1606 (2016) 064008 [arXiv:1603.00440] [INSPIRE].
L. Vidmar and M. Rigol, Generalized gibbs ensemble in integrable lattice models, J. Stat. Mech. 2016 (2016) 064007.
P. Calabrese and J. Cardy, Quantum Quenches in Extended Systems, J. Stat. Mech. 0706 (2007) P06008 [arXiv:0704.1880] [INSPIRE].
V. Alba and P. Calabrese, Quench action and Renyi entropies in integrable systems, Phys. Rev. B 96 (2017) 115421 [arXiv:1705.10765] [INSPIRE].
I. Peschel, Calculation of reduced density matrices from correlation functions, J. Phys. A 36 (2003) L205.
V. Eisler and I. Peschel, Evolution of entanglement after a local quench, J. Stat. Mech. 2007 (2007) P06005.
A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [INSPIRE].
L. Amico, R. Fazio, A. Osterloh and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80 (2008) 517 [quant-ph/0703044] [INSPIRE].
J. Eisert, M. Cramer and M.B. Plenio, Area laws for the entanglement entropy — a review, Rev. Mod. Phys. 82 (2010) 277 [arXiv:0808.3773] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
C. Weedbrook et al., Gaussian quantum information, Rev. Mod. Phys. 84 (2012) 621 [arXiv:1110.3234].
R. Bhatia, Positive Definite Matrices, Princeton University Press (2007).
A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, Edizioni della Normale (2011).
A. Czerwinski, Quantum tomography of three-qubit generalized Werner states, Int. J. Mod. Phys. B 36 (2022) 2250108 [arXiv:2104.11258] [INSPIRE].
D. Petz and D. Virosztek, Some inequalities for quantum Tsallis entropy related to the strong subadditivity, Math. Ineq. Appl. 18 (2015) 555 [INSPIRE].
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] [INSPIRE].
E. Whittaker and G. Watson, A course of modern analysis, Cambridge University Press (1996).
S. Murciano, G. Di Giulio and P. Calabrese, Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach, SciPost Phys. 8 (2020) 046 [arXiv:1911.09588] [INSPIRE].
R.J. Baxter, Exactly solved models in statistical mechanics, Academic Pres (1982), [INSPIRE].
E.H. Fradkin, Field Theories of Condensed Matter Physics, Cambridge Universite Press (2013) [INSPIRE].
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Arias, R., Di Giulio, G., Keski-Vakkuri, E. et al. Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement. J. High Energ. Phys. 2023, 175 (2023). https://doi.org/10.1007/JHEP03(2023)175
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DOI: https://doi.org/10.1007/JHEP03(2023)175