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arXiv · 2009.11286

Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

Youcef Mohdeb·Javad Vahedi·N. Moure·A. Roshani·Hyun-Yong Lee·Ravindra N. Bhatt·Stefan Kettemann·Stephan Haas
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Abstract

We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $α$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α> 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $α$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $α$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $α$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $α=2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.

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Youcef Mohdeb, Javad Vahedi, N. Moure, A. Roshani, Hyun-Yong Lee, Ravindra N. Bhatt, Stefan Kettemann, Stephan Haas. 2020-09-23. Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions. https://doi.org/10.1103/physrevb.102.214201

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