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Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension (2310.20566v2)

Published 31 Oct 2023 in cond-mat.str-el

Abstract: We study the logarithmic entanglement negativity of symmetry-protected topological (SPT) phases and quantum critical points (QCPs) of one-dimensional noninteracting fermions at finite temperatures. In particular, we consider a free fermion model that realizes not only quantum phase transitions between gapped phases but also an exotic topological phase transition between quantum critical states in the form of the fermionic Lifshitz transition. The bipartite entanglement negativity between adjacent fermion blocks reveals the crossover boundary of the quantum critical fan near the QCP between two gapped phases. Along the critical phase boundary between the gapped phases, the sudden decrease in the entanglement negativity signals the fermionic Lifshitz transition responsible for the change in the topological nature of the QCPs. In addition, the tripartite entanglement negativity between spatially separated fermion blocks counts the number of topologically protected boundary modes for both SPT phases and topologically nontrivial QCPs at zero temperature. However, the long-distance entanglement between the boundary modes vanishes at finite temperatures due to the instability of SPTs, the phases themselves.

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References (44)
  1. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  2. C. L. Kane and E. J. Mele, Z2subscript𝑍2{Z}_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  3. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  4. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  5. T. D. Schultz, D. C. Mattis, and E. H. Lieb, Two-dimensional Ising model as a soluble problem of many fermions, Rev. Mod. Phys. 36, 856 (1964).
  6. J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area laws for the entanglement entropy, Rev. Mod. Phys. 82, 277 (2010).
  7. A. M. Turner, F. Pollmann, and E. Berg, Topological phases of one-dimensional fermions: An entanglement point of view, Phys. Rev. B 83, 075102 (2011).
  8. B. Zeng and D. L. Zhou, Topological and error-correcting properties for symmetry-protected topological order, EPL 113, 56001 (2016).
  9. B. Zeng and X.-G. Wen, Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity, Phys. Rev. B 91, 125121 (2015).
  10. T.-C. Lu and T. Grover, Singularity in entanglement negativity across finite-temperature phase transitions, Phys. Rev. B 99, 075157 (2019).
  11. T.-C. Lu and T. Grover, Structure of quantum entanglement at a finite temperature critical point, Phys. Rev. Research 2, 043345 (2020).
  12. T.-C. Lu, T. H. Hsieh, and T. Grover, Detecting topological order at finite temperature using entanglement negativity, Phys. Rev. Lett. 125, 116801 (2020).
  13. R. Verresen, N. G. Jones, and F. Pollmann, Topology and edge modes in quantum critical chains, Phys. Rev. Lett. 120, 057001 (2018).
  14. R. Verresen, R. Moessner, and F. Pollmann, One-dimensional symmetry protected topological phases and their transitions, Phys. Rev. B 96, 165124 (2017).
  15. R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
  16. P. Jordan and E. P. Wigner, About the Pauli exclusion principle, Z. Phys. 47, 631 (1928).
  17. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi 44, 131 (2001).
  18. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  19. G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
  20. M. B. Plenio, Logarithmic negativity: A full entanglement monotone that is not convex, Phys. Rev. Lett. 95, 090503 (2005).
  21. H. Shapourian, K. Shiozaki, and S. Ryu, Partial time-reversal transformation and entanglement negativity in fermionic systems, Phys. Rev. B 95, 165101 (2017a).
  22. A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
  23. M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223, 1 (1996).
  24. H. Shapourian, K. Shiozaki, and S. Ryu, Many-body topological invariants for fermionic symmetry-protected topological phases, Phys. Rev. Lett. 118, 216402 (2017b).
  25. V. Eisler and Z. Zimboras, On the partial transpose of fermionic Gaussian states, New J. Phys. 17, 053048 (2015).
  26. O. Hart and C. Castelnovo, Entanglement negativity and sudden death in the toric code at finite temperature, Phys. Rev. B 97, 144410 (2018).
  27. P. Calabrese, J. Cardy, and E. Tonni, Finite temperature entanglement negativity in conformal field theory, J. Phys. A: Math. Theor. 48, 015006 (2014).
  28. H. Shapourian and S. Ryu, Finite-temperature entanglement negativity of free fermions, J. Stat. Mech.: Theory Exp. 2019 (4), 043106.
  29. A. Kitaev, Periodic table for topological insulators and superconductors, AIP Conference Proceedings 1134, 22 (2009).
  30. I. Peschel, Calculation of reduced density matrices from correlation functions, J. Phys. A: Math. Gen. 36, L205 (2003).
  31. J. Eisert, V. Eisler, and Z. Zimborás, Entanglement negativity bounds for fermionic Gaussian states, Phys. Rev. B 97, 165123 (2018).
  32. M. Fagotti and P. Calabrese, Entanglement entropy of two disjoint blocks in XY chains, J. Stat. Mech.: Theory Exp. 2010 (04), P04016.
  33. L. Gurvits, Classical deterministic complexity of Edmonds’ problem and quantum entanglement (2003), arXiv:quant-ph/0303055 [quant-ph] .
  34. S. Gharibian, Strong NP-hardness of the quantum separability problem, Quantum Inf. Comput. 10, 343 (2010).
  35. P. Calabrese, J. Cardy, and E. Tonni, Entanglement negativity in quantum field theory, Phys. Rev. Lett. 109, 130502 (2012).
  36. P. Calabrese, J. Cardy, and E. Tonni, Entanglement negativity in extended systems: a field theoretical approach, J. Stat. Mech.: Theory Exp. 2013 (02), P02008.
  37. C. Boudreault, C. Berthiere, and W. Witczak-Krempa, Entanglement and separability in continuum Rokhsar-Kivelson states (2022), arXiv:2110.04290 [cond-mat.str-el] .
  38. D. Hartmann, K. Kavanagh, and S. Vandoren, Entanglement entropy with Lifshitz fermions, SciPost Phys. 11, 031 (2021).
  39. K. Wang and T. A. Sedrakyan, Universal finite-size amplitude and anomalous entanglement entropy of z=2𝑧2z=2italic_z = 2 quantum Lifshitz criticalities in topological chains, SciPost Phys. 12, 134 (2022).
  40. A. Maiellaro, A. Marino, and F. Illuminati, Topological squashed entanglement: Nonlocal order parameter for one-dimensional topological superconductors, Phys. Rev. Research 4, 033088 (2022).
  41. O. Blondeau-Fournier, O. A. Castro-Alvaredo, and B. Doyon, Universal scaling of the logarithmic negativity in massive quantum field theory, J. Phys. A Math. Theor. 49, 125401 (2016).
  42. G. Parez and W. Witczak-Krempa, Are fermionic conformal field theories more entangled? (2023), arXiv:2310.15273 [cond-mat.str-el] .
  43. M. Christandl and A. Winter, “squashed entanglement”: An additive entanglement measure, J. Math. Phys. 45, 829 (2004).
  44. W. Choi, M. Knap, and F. Pollmann, Finite temperature entanglement negativity of fermionic symmetry protected topological phases and quantum critical points in one dimension (2023).
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