Entanglement Entropy and Scaling Laws on Non-Hermitian SSH Model with Next-next-nearest Hopping

Journal of Chuxiong Normal University ›› 2025, Vol. 40 ›› Issue (3): 35-43.

• Physics • Previous Articles Next Articles

Entanglement Entropy and Scaling Laws on Non-Hermitian SSH Model with Next-next-nearest Hopping

YANG Zhenghao, LU Chaoze, LU Xiancong^*

College of Physical Science and Technology, Xiamen University, Xiamen, Fujian Province 361005

Received:2025-01-17 Online:2025-05-20 Published:2025-07-01

Abstract

Abstract: We studied the entanglement entropy and its scaling laws on the one-dimensional non-Hermitian Su-Schrieffer-Heeger model with long-range next-next-nearest hopping. The next-next-nearest hopping leads to the appearance of the topological phase with winding number 2, and the critical points on phase boundaries are also divided into different categories. Based on this, we calculated the central charge of these critical systems using the scaling laws of entanglement entropy. The study on the generalized Brillouin zone demonstrates the self-intersection phenomenon of both energy spectra and generalized Brillouin zones induced by the next-next-nearest hopping, and the results reveal that the bulk-boundary correspondence could still be restored.

Key words: entanglement entropy, generalized Brillouin zone, non-Hermitian skin effect, quantum critical system

CLC Number:

O413.3

YANG Zhenghao, LU Chaoze, LU Xiancong. Entanglement Entropy and Scaling Laws on Non-Hermitian SSH Model with Next-next-nearest Hopping[J]. Journal of Chuxiong Normal University, 2025, 40(3): 35-43.

References

[1] Bender C M, Brody D C, Jones H F.Complex extension of quantum mechanics[J]. Physical Review Letters, 2002, 89(27): 270401.
[2] Brody D C.Biorthogonal quantum mechanics[J]. Journal of Physics A: Mathematical and Theoretical, 2014, 47(3): 035305.
[3] Lee T E.Anomalous edge state in a non-Hermitian lattice[J]. Physical Review Letters, 2016, 116(13): 133903.
[4] Lieu S.Topological phases in the non-Hermitian Su-Schrieffer-Heeger model[J]. Physical Review B, 2018, 97(4): 045106.
[5] Zhang K, Yang Z S, Fang C.Correspondence between winding numbers and skin modes in non-Hermitian systems[J]. Physical Review Letters, 2020, 125(12): 126402.
[6] Gong Z P, Ashida Y, Kawabata K, et al. Topological phases of non-Hermitian systems[J]. Physical Review X, 2018, 8(3): 031079.
[7] Kawabata K, Shiozaki K, Ryu S.Many-body topology of non-Hermitian systems[J]. Physical Review B, 2022, 105(16): 165137.
[8] Okuma N, Kawabata K, Shiozaki K, Sato M.Topological origin of non-Hermitian skin effects[J]. Physical Review Letters, 2020, 124(8): 086801.
[9] Kawabata K, Shiozaki K, Ueda M, Sato M.Symmetry and topology in non-Hermitian physics[J]. Physical Review X, 2019, 9(4): 041015.
[10] Okuma N, Sato M.Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems[J]. Physical Review B, 2021, 103(8): 085428.
[11] Yao S Y, Wang Z.Edge states and topological invariants of non-Hermitian systems[J]. Physical Review Letters, 2018, 121(8): 086803.
[12] Yokomizo K, Murakami S.Non-Bloch band theory of non-Hermitian systems[J]. Physical Review Letters, 2019, 123(6): 066404.
[13] Li H, Haldane F D M. Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states[J]. Physical Review Letters, 2008, 101(1): 010504.
[14] Horodecki R, Horodecki P, Horodecki M, Horodecki K.Quantum entanglement[J]. Reviews of Modern Physics, 2009, 81(2): 865.
[15] Peschel I.Calculation of reduced density matrices from correlation functions[J]. Journal of Physics A: Mathematical and General, 2003, 36(14): L205.
[16] Calabrese P, Cardy J.Entanglement entropy and conformal field theory[J]. Journal of Physics A: Mathematical and Theoretical, 2009, 42(50): 504005.
[17] Calabrese P, Cardy J.Entanglement entropy and quantum field theory[J]. Journal of Statistical Mechanics: Theory and Experiment, 2004, 2004(06): P06002.
[18] Lin Z K, Zhou Y, Jiang B, et al. Measuring entanglement entropy and its topological signature for phononic systems[J]. Nature Communications, 2024, 15(1): 1601.
[19] Ryu S, Hatsugai Y.Entanglement entropy and the Berry phase in the solid state[J]. Physical Review B, 2006, 73(24): 245115.
[20] Su W P, Schrieffer J R, Heeger A J.Solitons in polyacetylene[J]. Physical Review Letters, 1979, 42(25): 1698.
[21] Chen W T, Peng L T, Lu H T, Lu X C.Characterizing bulk-boundary correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy[J]. Physical Review B, 2022, 105(7): 075126.
[22] Rufo S, Lopes N, Continentino M A, Griffith M.Multicritical behavior in topological phase transitions[J]. Physical Review B, 2019, 100(19): 195432.
[23] Malakar R K, Ghosh A K.Engineering topological phases of any winding and Chern numbers in extended Su-Schrieffer-Heeger models[J]. Journal of Physics: Condensed Matter, 2023, 35(33): 335401.
[24] Yang Z S, Zhang K, Fang C, Hu J P.Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory[J]. Physical Review Letters, 2020, 125(22): 226402.
[25] Chiu C K, Teo J C Y, Schnyder A P, Ryu S. Classification of topological quantum matter with symmetries[J]. Reviews of Modern Physics, 2016, 88(3): 035005.
[26] Yokomizo K, Murakami S.Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems[J]. Physical Review Research, 2020, 2(4): 043045.
[27] Peschel I, Eisler V.Reduced density matrices and entanglement entropy in free lattice models[J]. Journal of Physics A: Mathematical and Theoretical, 2009, 42(50): 504003.
[28] Wang D, Xu S L, Wang Y, Wu C J.Detecting edge degeneracy in interacting topological insulators through entanglement entropy[J]. Physical Review B, 2015, 91(11): 115118.
[29] Herviou L, Regnault N, Bardarson J H.Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models[J]. SciPost Physics, 2019, 7(5): 069.
[30] Chang P Y, You J S, Wen X D, Ryu S.Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory[J]. Physical Review Research, 2020, 2(3): 033069.
[31] Guo Y B, Yu Y C, Huang R Z, et al. Entanglement entropy of non-hermitian free fermions[J]. Journal of Physics: Condensed Matter, 2021, 33(47): 475502.
[32] Xiong Y C, Hu H P.Graph Morphology of Non-Hermitian Bands[J]. arXiv:2311.14921.

Entanglement Entropy and Scaling Laws on Non-Hermitian SSH Model with Next-next-nearest Hopping

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 0

Recommended Articles

Metrics

Comments