A
bstract
We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, ...we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.
A
bstract
We study the temporal evolution of the circuit complexity for a subsystem in harmonic lattices after a global quantum quench of the mass parameter, choosing the initial reduced density ...matrix as the reference state. Upper and lower bounds are derived for the temporal evolution of the complexity for the entire system. The subsystem complexity is evaluated by employing the Fisher information geometry for the covariance matrices. We discuss numerical results for the temporal evolutions of the subsystem complexity for a block of consecutive sites in harmonic chains with either periodic or Dirichlet boundary conditions, comparing them with the temporal evolutions of the entanglement entropy. For infinite harmonic chains, the asymptotic value of the subsystem complexity is studied through the generalised Gibbs ensemble.
A
bstract
We study the temporal evolution of the circuit complexity after the local quench where two harmonic chains are suddenly joined, choosing the initial state as the reference state. We discuss ...numerical results for the complexity for the entire chain and the subsystem complexity for a block of consecutive sites, obtained by exploiting the Fisher information geometry of the covariance matrices. The qualitative behaviour of the temporal evolutions of the subsystem complexity depends on whether the joining point is inside the subsystem. The revivals and a logarithmic growth observed during these temporal evolutions are discussed. When the joining point is outside the subsystem, the temporal evolutions of the subsystem complexity and of the corresponding entanglement entropy are qualitatively similar.
A
bstract
We present a thorough analysis of the entanglement entropies related to different symmetry sectors of free quantum field theories (QFT) with an internal U(1) symmetry. We provide explicit ...analytic computations for the charged moments of Dirac and complex scalar fields in two spacetime dimensions, both in the massive and massless cases, using two different approaches. The first one is based on the replica trick, the computation of the partition function on Riemann surfaces with the insertion of a flux
α
, and the introduction of properly modified twist fields, whose two-point function directly gives the scaling limit of the charged moments. With the second method, the diagonalisation in replica space maps the problem to the computation of a partition function on a cut plane, that can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Within this approach, we also derive an asymptotic expansion for the short and long distance behaviour of the charged moments. Finally, the Fourier transform provides the desired symmetry resolved entropies: at the leading order, they satisfy entanglement equipartition and we identify the subleading terms that break it. Our analytical findings are tested against exact numerical calculations in lattice models.
A
bstract
As a new ingredient for analyzing the fine structure of entanglement, we study the symmetry resolution of the modular flow of U(1)-invariant operators in theories endowed with a global U(1) ...symmetry. We provide a consistent definition of symmetry-resolved modular flow that is defined for a local algebra of operators associated to a sector with fixed charge. We also discuss the symmetry-resolved modular correlation functions and show that they satisfy the KMS condition in each symmetry sector. Our analysis relies on the factorization of the Hilbert space associated to spatial subsystems. We provide a toolkit for computing the symmetry-resolved modular correlation function of the charge density operator in free fermionic theories. As an application, we compute this correlation function for a 1 + 1-dimensional free massless Dirac field theory and find that it is independent of the charge sector at leading order in the ultraviolet cutoff expansion. This feature can be regarded as a charge equipartition of the modular correlation function. Although obtained for free fermions, these results may be of potential interest for bulk reconstruction in AdS/CFT.
We study the symmetry resolved entanglement entropies in gapped integrable lattice models.
We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the ...complex
harmonic chain and the XXZ spin-chain.
While the former is a free bosonic system, the latter is genuinely interacting.
We focus on a subsystem being half of an infinitely long chain.
In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies.
While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same),
this is not the case for the harmonic system where equipartition is effectively recovered only in some limits.
Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to
test numerically our analytic results.
In recent years, the permanent seismic networks worldwide have largely increased, raising the amount of earthquake signals and the applications using seismic records. Although characterization of the ...soil properties at recording stations has a large impact on hazard estimates, it has not been implemented so far in a standardized way for reaching high-level metadata. To address this issue, we built an online questionnaire for the identification of the indicators useful for a reliable site characterization at a seismic station. We analysed the answers of a large number of experts in different fields, which allowed us to rank 24 different indicators and to identify the most relevant ones: fundamental frequency (
f
0
), shear-wave velocity profile (
V
S
), time-averaged
Vs
over 30 m (
V
S
30
), depth of seismological and engineering bedrock (
H
seis_bed
and
H
eng_bed
), surface geology and soil class. Moreover, the questionnaire proposed two additional indices in terms of cost and difficulty to obtain a reliable value of each indicator, showing that the selection of the most relevant indicators results from a complex balance between physical relevancy, average cost and reliability. For each indicator we propose a summary report, provided as editable pdf, containing the background information of data acquisition and processing details, with the aim to homogenize site metadata information at European level and to define the quality of the site characterization (see companion paper Di Giulio et al.
2021
). The selected indicators and the summary reports have been shared within European and worldwide scientific community and discussed in a dedicated international workshop. They represent a first attempt to reach a homogeneous set of high-level metadata for site characterization.
A
bstract
We study the multi-charged moments for two disjoint intervals in the ground state of two 1 + 1 dimensional CFTs with central charge
c
= 1 and global U(1) symmetry: the massless Dirac field ...theory and the compact boson (Luttinger liquid). For this purpose, we compute the partition function on the higher genus Riemann surface arising from the replica method in the presence of background magnetic fluxes between the sheets of the surface. We consider the general situation in which the fluxes generate different twisted boundary conditions at each branch point. The obtained multi-charged moments allow us to derive the symmetry resolution of the Rényi entanglement entropies and the mutual information for non complementary bipartitions. We check our findings against exact numerical results for the tight-binding model, which is a lattice realisation of the massless Dirac theory.
Purpose
Breast lesions classified as of “uncertain malignant potential” represent a heterogeneous group of abnormalities with an increased risk of associated malignancy. Clinical management of B3 ...lesions diagnosed on vacuum-assisted breast biopsy (VABB) is still challenging: surgical excision is no longer the only available treatment and VABB may be sufficient for therapeutic excision. The aim of the present study is to evaluate the positive predictive value (PPV) for malignancy in B3 lesions that underwent surgical excision, identifying possible upgrading predictive factors and characterizing the malignant lesions eventually diagnosed. These results are compared with a subset of patients with B3 lesions who underwent follow-up.
Methods
A total of 1250 VABBs were performed between January 2006 and December 2017 at our center. In total, 150 B3 cases were diagnosed and 68 of them underwent surgical excision. VABB findings were correlated with excision histology. A PPV for malignancy for each B3 subtype was derived.
Results
The overall PPV rate was 28%, with the highest upgrade rate for atypical ductal hyperplasia (41%), followed by classical lobular neoplasia (29%) and flat epithelial atypia (11%). Only two cases of carcinoma were detected in the follow-up cohort, both associated with atypical ductal hyperplasia at VABB.
Conclusion
Open surgery is recommended in case of atypical ductal hyperplasia while, for other B3 lesions, excision with VABB only may be an acceptable alternative if radio-pathological correlation is assessed, if all microcalcifications have been removed by VABB, and if the lesion lacks high-risk cytological features.
Key Points
•
Surgical treatment is strongly recommended in case of ADH, while the upgrade rate in case of pure FEA, especially following complete microcalcification removal by VABB, may be sufficiently low to advice surveillance as a management strategy.
•
The use of 11-G- or 8-G-needle VABB, resulting in possible complete diagnostic excision of the lesion, can be an acceptable alternative in case of RS, considering open surgery only for selected high-risk patients.
•
LN management is more controversial: surgical excision may be recommended following classical LN diagnosis on breast biopsy if an additional B3 lesion is concurrently detected while in the presence of isolated LN with adequate radiological-pathological correlation follow-up alone could be an acceptable option.
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