Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with r...
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Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here 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>12. 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=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 partition size 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-law-decaying interaction with α=2. Only for small l≪L, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge c=ln(2). Furthermore, we find using ED that the conc
Background: Silicone implants are biomaterials that are frequently used in the medical industry due to their physiological inertness and low toxicity. However, capsular contracture remains a concern in long-term trans...
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Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. Ho...
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This research studied the quantity of free formaldehyde released from 2- [(hydroxymethyl)amino]ethanol (HAE) in DI water and natural rubber latex mixture using high-performance liquid chromatography (HPLC) technique. ...
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Purpose: This study aimed to assess inter- and intra-fractional motion for extremity Soft Tissue Sarcoma (STS) patients, by using in-house real-time optical image-based monitoring system (ROIMS) with infra-red (IR) ex...
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Purpose: This study aimed to assess inter- and intra-fractional motion for extremity Soft Tissue Sarcoma (STS) patients, by using in-house real-time optical image-based monitoring system (ROIMS) with infra-red (IR) external markers. Methods: Inter- and intra-fractional motions for five extremity (1 upper, 4 lower) STS patients received postoperative 3D conformal radiotherapy (3D-CRT) were measured by registering the image acquired by ROIMS with the planning CT image (REG_ROIMS). To compare with the X-ray image-based monitoring, pre- and post-treatment cone beam computed tomography (CBCT) scans were performed once per week and registered with planning CT image as well (REG_CBCT). If the CBCT scan is not feasible due to the large couch shift, AP and LR on-board imager (OBI) images were acquired. The comparison was done by calculating mutual information (MI) of those registered images. Results: The standard deviation (SD) of the inter-fractional motion was 2.6 mm LR, 2.8 mm SI, and 2.0 mm AP, and the SD of the intra-fractional motion was 1.4 mm, 2.1 mm, and 1.3 mm in each axis, respectively. The SD of rotational inter-fractional motion was 0.6° pitch, 0.9° yaw, and 0.8° roll and the SD of rotational intra-fractional motion was 0.4° pitch, 0.9° yaw, and 0.7° roll. The derived averaged MI values were 0.83, 0.92 for REG_CBCT without rotation and REG_ROIMS with rotation, respectively. Conclusion: The in-house real-time optical image-based monitoring system was implemented clinically and confirmed the feasibility to assess inter- and intra-fractional motion for extremity STS patients while the daily basis and real-time CBCT scan is not feasible in clinic.
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