Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions

Mondal, Saikat; Bandyopadhyay, Souvik; Bhattacharjee, Sourav; Dutta, Amit

doi:10.1103/physrevb.105.085106

Cited by 11 publications

(11 citation statements)

References 43 publications

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“…Following the explicit calculation presented in Ref. [57], it can be shown that the effective maximum range r max of the couplings in the effective Hamiltonian H eff increases with the stroboscopic time t = N T . Now, if the maximum range of interaction of H eff spans the complete disconnected partition D or greater (see Fig.…”

Section: Discussionmentioning

confidence: 80%

“…1), bulk states start becoming entangled over regions exceeding the disconnected partition size. This starts introducing bulk contributions to the DEE just as in long-ranged interacting Hamiltonians [57], which in turn breaks the temporal invariance of the DEE. Hence, a finite disconnected partition size gives rise to a criti-cal time scale in a short-ranged system until which the DEE remains temporally invariant.…”

Section: Discussionmentioning

confidence: 99%

“…integer multiple of ln(2), i.e., S D = p ln(2), where p is the total number of modes at the edges of an open system (see Ref. [55][56][57]). The total number of edge modes is twice the number of modes at each edge.…”

Section: Kitaev Chainmentioning

confidence: 99%

“…) is the Floquet operator, and H F is the Floquet Hamiltonian. We define an effective Hamiltonian [56,57] [56,57]).…”

Section: Appendix A: Equivalence Of Two Different Configurations Of T...mentioning

confidence: 99%

“…Rather, it extracts the entanglement between the Majorana modes localized at the edges. Although the DEE can take any real value by its construction, it turns out to be integer-quantized for a short-ranged Kitaev chain in the topological phase, where the integer is the total number of edge modes of the system [55][56][57].…”

Section: Introductionmentioning

confidence: 99%

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Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

Mondal¹,

Sen²,

Dutta³

2022

Preprint

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We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically driven in various ways, namely, δ-pulses, square pulse and sinusoidal modulation. In all these cases, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes generated by the periodic driving. Thus, the DEE can be considered as a marker for detecting Majorana edge modes in a periodically driven Kitaev chain. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance.

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Section: Discussionmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Kitaev Chainmentioning

confidence: 99%

“…) is the Floquet operator, and H F is the Floquet Hamiltonian. We define an effective Hamiltonian [56,57] [56,57]).…”

Section: Appendix A: Equivalence Of Two Different Configurations Of T...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

Mondal¹,

Sen²,

Dutta³

2022

Preprint

Self Cite

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Resilience of quantum spin fluctuations against Dzyaloshinskii–Moriya interaction

Mahdavifar,

Salehpour,

Cheraghi

et al. 2024

Sci Rep

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In low-dimensional systems, the lack of structural inversion symmetry combined with the spin-orbit coupling gives rise to an anisotropic antisymmetric superexchange known as the Dzyaloshinskii–Moriya interaction (DMI). Various features have been reported due to the presence of DMIs in quantum systems. We here study the one-dimensional spin-1/2 transverse field XY chains with a DMI at zero temperature. Our focus is on the quantum fluctuations of the spins measured by the spin squeezing and the entanglement entropy. We find that these fluctuations are resistant to the effect of the DMI in the system. This resistance will fail as soon as the system is placed in the chiral phase where its state behaves as a squeezed state, suggesting the merit of the chiral phase to be used for quantum metrology. Remarkably, we prove that the central charge vanishes on the critical lines between gapless chiral and ferromagnetic/paramagnetic phases where there is no critical scaling versus the system size for the spin squeezing parameter. Our phenomenal results provide a further understanding of the effects of the DMIs in the many-body quantum systems which may be testable in experiments.

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Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

Mondal¹,

Sen²,

Dutta³

2022

J. Phys.: Condens. Matter

Self Cite

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We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically modulated with δ-function pulses within the framework of Floquet theory. For this driving protocol, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes localized at each edge of the chain generated by the periodic driving, thereby establishing the DEE as a marker for detecting Floquet Majorana edge modes. Analysing the DEE, we further show that these Majorana edge modes are robust against weak spatial disorder and temporal noise. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance and not robust against spatial disorder. We also probe the behaviour of the DEE for a kicked Ising chain in the presence of an integrability breaking interaction which has been experimentally realized.

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Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions

Cited by 11 publications

References 43 publications

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

Resilience of quantum spin fluctuations against Dzyaloshinskii–Moriya interaction

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

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