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Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
Published 7 Jul 2023 in cond-mat.stat-mech, math-ph, and math.MP | (2307.03345v2)
Abstract: This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-diameter limit, revealing a strict adherence to the area law. The absence of the logarithmic enhancement expected for free fermions is explained using a decomposition of folded cubes in chains based on its Terwilliger algebra and $\mathfrak{so}(3)_{-1}$. The entanglement Hamiltonian and its relation to Heun operators are also investigated.
- L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517 (2008).
- N. Laflorencie, “Quantum entanglement in condensed matter systems,” Phys. Rep. 646, 1 (2016).
- A. Osterloh, L. Amico, G. Falci, and R. Fazio, “Scaling of entanglement close to a quantum phase transitions,” Nature 416, 608 (2002).
- T. J. Osborne and M. A. Nielsen, “Entanglement in a simple quantum phase transition,” Phys. Rev. A 66, 032110 (2002).
- G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, “Entanglement in quantum critical phenomena,” Phys. Rev. Lett. 90, 227902 (2003).
- P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. P06002 (2004).
- P. Calabrese and J. L. Cardy, “Entanglement entropy and conformal field theory,” J. Phys. A: Math. Theor. 42, 504005 (2009).
- A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96, 110404 (2006).
- M. Levin and X.-G. Wen, “Detecting topological order in a ground state wave function,” Phys. Rev. Lett. 96, 110405 (2006).
- P. Calabrese and J. L. Cardy, “Evolution of entanglement entropy in one-dimensional systems,” J. Stat. Mech. P04010 (2005).
- M. Fagotti and P. Calabrese, “Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field,” Phys. Rev. A 78, 010306 (2008).
- C. Gogolin and J. Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Rep. Prog. Phys. 79, 056001 (2016).
- V. Alba and P. Calabrese, “Entanglement and thermodynamics after a quantum quench in integrable systems,” Proceedings of the National Academy of Sciences 114, 7947 (2017).
- D. Gioev and I. Klich, “Entanglement entropy of fermions in any dimension and the Widom conjecture,” Phys. Rev. Lett. 96, 100503 (2006).
- W. Li, L. Ding, R. Yu, T. Roscilde, and S. Haas, “Scaling behavior of entanglement in two- and three-dimensional free-fermion systems,” Phys. Rev. B 74, 073103 (2006).
- P.-A. Bernard, N. Crampé, and L. Vinet, “Entanglement of free fermions on Hamming graphs,” Nucl. Phys. B 986, 116061 (2023).
- G. Parez, P.-A. Bernard, N. Crampé, and L. Vinet, “Multipartite information of free fermions on Hamming graphs,” Nucl. Phys. B 990, 116157 (2023).
- P.-A. Bernard, N. Crampé, and L. Vinet, “Entanglement of free fermions on Johnson graphs,” J. Math. Phys. 64, 061903 (2023).
- G. M. Brown, “Hypercubes, Leonard triples and the anticommutator spin algebra,” arXiv:1301.0652 [math.CO].
- P. Terwilliger, “The subconstituent algebra of an association scheme (Part I),” J. Algebr. Comb. 1, 363 (1992).
- P. Terwilliger, “The subconstituent algebra of an association scheme (Part II),” J. Algebr. Comb. 2, 73 (1993).
- P. Terwilliger, “The subconstituent algebra of an association scheme (Part III),” J. Algebr. Comb. 2, 177 (1993).
- V. Eisler and I. Peschel, “Free-fermion entanglement and spheroidal functions,” J. Stat. Mech P04028 (2013).
- V. Eisler and I. Peschel, “Analytical results for the entanglement Hamiltonian of a free-fermion chain,” J. Phys. A: Math. Theor. 50, 284003 (2017).
- V. Eisler and I. Peschel, “Properties of the entanglement Hamiltonian for finite free-fermion chains,” J. Stat. Mech. 104001 (2018).
- G. Parez, “Symmetry-resolved Rényi fidelities and quantum phase transitions,” Phys. Rev. B 106, 235101 (2022).
- Springer, 2012.
- I. Peschel, “Calculation of reduced density matrices from correlation functions,” J. Phys. A: Math. Gen. 36, L205 (2003).
- World Scientific, (2018).
- N. Crampé, R. I. Nepomechie, and L. Vinet, “Free-Fermion entanglement and orthogonal polynomials,” J. Stat. Mech. 093101 (2019).
- F. Finkel and A. González-López, “Inhomogeneous XX spin chains and quasi-exactly solvable models,” J. Stat. Mech. 093105 (2020).
- F. Finkel and A. González-López, “Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions,” JHEP 1 (2021).
- N. Crampé, R. I. Nepomechie, and L. Vinet, “Entanglement in fermionic chains and bispectrality,” Rev. Math. Phys. 33, 2140001 (2021).
- P.-A. Bernard, N. Crampé, R. I. Nepomechie, G. Parez, L. P. d’Andecy, and L. Vinet, “Entanglement of inhomogeneous free fermions on hyperplane lattices,” Nucl. Phys. B 984, 115975 (2022).
- P.-A. Bernard, G. Carcone, N. Crampe, and L. Vinet, “Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz,” arXiv:2212.09805 [math-ph].
- J. Dubail, J.-M. Stéphan, J. Viti, and P. Calabrese, “Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases,” SciPost Phys. 2, 002 (2017).
- F. A. Grünbaum, L. Vinet, and A. Zhedanov, “Algebraic Heun operator and band-time limiting,” Commun. Math. Phys. 364, 1041 (2018).
- V. Eisler, E. Tonni, and I. Peschel, “On the continuum limit of the entanglement Hamiltonian,” J. Stat. Mech 073101 (2019).
- P.-A. Bernard, N. Crampé, D. Shaaban Kabakibo, and L. Vinet, “Heun operator of lie type and the modified algebraic Bethe ansatz,” J. Math. Phys. 62, 083501 (2021).
- R. Bonsignori and V. Eisler, “Private communication,” (2023).
- A. Uhlmann, “The ‘transition probability’ in the state space of a ∗∗\ast∗-algebra,” Rep. Math. Phys. 9, 273 (1976).
- R. Jozsa, “Fidelity for Mixed Quantum States,” J. Mod. Opt. 41, 2315 (1994).
- H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of Loschmidt Echo Enhanced by Quantum Criticality,” Phys. Rev. Lett. 96, 140604 (2006).
- H.-Q. Zhou and J. P. Barjaktarevič, “Fidelity and quantum phase transitions,” J. Phys. A: Math. Theor. 41, 412001 (2008).
- S.-J. Gu, “Fidelity approach to quantum phase transitions,” Int. J. Mod. Phys. B 24, 4371 (2010).
- J. Dubail and J.-M. Stéphan, “Universal behavior of a bipartite fidelity at quantum criticality,” J. Stat. Mech. L03002 (2011).
- J.-M. Stéphan and J. Dubail, “Logarithmic corrections to the free energy from sharp corners with angle 2π2𝜋2\pi2 italic_π,” J. Stat. Mech. P09002 (2013).
- C. Hagendorf and J. Liénardy, “Open spin chains with dynamic lattice supersymmetry,” J. Phys. A: Math. Theor. 50, 185202 (2017).
- G. Parez, A. Morin-Duchesne, and P. Ruelle, “Bipartite fidelity of critical dense polymers,” J. Stat. Mech. 103101 (2019).
- A. Morin-Duchesne, G. Parez, and J. Liénardy, “Bipartite fidelity for models with periodic boundary conditions,” J. Stat. Mech. 023101 (2021).
- C. Hagendorf and G. Parez, “On the logarithmic bipartite fidelity of the open XXZ spin chain at Δ=−1/2Δ12\Delta=-1/2roman_Δ = - 1 / 2,” SciPost Phys. 12, 199 (2022).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.
- J. A. Carrasco, F. Finkel, A. Gonzalez-Lopez, and P. Tempesta, “A duality principle for the multi-block entanglement entropy of free fermion systems,” Sci. Rep. 7, 11206 (2017).
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