Numerical Evidence for a Haagerup Conformal Field Theory.

We numerically study an anyon chain based on the Haagerup fusion category and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is ∼2. Fusion categories generalize the concept of finite group symmetries to noninvertible symmetry operations, and the Haagerup fusion category is the simplest one which comes from neither finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries. Basically the same result was independently obtained in the preceding Letter [Phys. Rev. Lett. 128, 231602 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.231602].

Quantum Ergodicity in the Many-Body Localization Problem.

We generalize Page's result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long-range interactions. This extension leads to two principal conclusions: first, for increasing disorder the "shells" of constant energy supporting a system's eigenstates fill only a fraction of its full Fock space and are subject to intrinsic correlations absent in synthetic high-dimensional random lattice systems. Second, in all regimes preceding the many-body localization transition individual eigenstates are thermally distributed over these shells. These results, corroborated by comparison to exact diagonalization for an SYK model, are at variance with the concept of "nonergodic extended states" in many-body systems discussed in the recent literature.

Characterization of quantum chaos by two-point correlation functions.

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

Migration of a Kirschner wire into the spinal cord: A case report and literature review.

CONTEXT: A Kirschner wire (K-wire) is a stainless steel pin with at least one sharpened tip that is mainly used for the internal fixation of bone fractures. While some cases of K-wire dislocation and migration have been reported as complications after fracture surgery, the intraspinal migration of a K-wire is rare. Herein, we report a case in which a K-wire used for sternal fixation 7 years earlier migrated into the spinal canal. FINDINGS: A 68-year-old male suddenly sustained severe radiating pain and numbness in his left upper extremity, and walked to our hospital. He had mild weakness in the left wrist extensor muscles and the left extensor digitorum. CT-myelography revealed a K-wire penetrating into the spinal cord at C5-6. There was no injury of the trachea, esophagus, or blood vessels. The patient had a history of surgical infection after cardiovascular surgery seven years before, and had undergone surgical debridement and sternum fixation with two K-wires. One K-wire had broken, and part of it migrated upward. Using an anterior approach, we detected the tip of K-wire below the left sternocleidomastoid muscle. We cut the K-wire into 1 to 2-cm pieces and removed it piece by piece. His postoperative course was uneventful and the symptoms improved markedly after the surgery. CONCLUSION: This is the first report of a K-wire that had been used for sternal fixation migrating into the spinal cord. This case illustrates that although rare, it is possible for a K-wire to migrate upward after sternal fixation.

Epithelioid Hemangioma of the Thoracic Spine: A Case Report and Review of the Literature.

Context: Osseous epithelioid hemangioma is uncommon, and reports of epithelioid hemangiomas of the spine are especially rare.Study Design: Case report.Findings: A 43-year-old male was referred to our department with progressive gait disturbance. CT scans showed a lucent mass in the vertebral body at the T3 level. MRI of the thoracic spine showed a strongly enhanced mass compressing the spinal cord. The patient underwent laminectomy from T2 to T4, debulking of the tumor, and posterior fusion from T1 to T5. After the operation, the patient's neurological status improved significantly, and he was able walk without assistance. Histological examination determined that the tumor was an epithelioid hemangioma. The patient was treated with 40 Gy radiation for local control of the tumor. The patient could walk without difficulty 12 months after the surgery.Conclusion: This is a rare example of an epithelioid hemangioma that developed in the thoracic spine and compressed the spinal cord, and was treated successfully.

Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.

Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.

Universality in chaos: Lyapunov spectrum and random matrix theory.

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Factors affecting the postoperative progression of thoracic kyphosis in surgically treated adult patients with lumbar degenerative scoliosis.

STUDY DESIGN: A retrospective case series of patients treated surgically for degenerative lumbar scoliosis (DLS). OBJECTIVE: To determine incidence and risk factors of progressive global thoracic kyphosis (pGTK) after surgery for DLS. SUMMARY OF BACKGROUND DATA: Sagittal balance affects the surgical treatment of spinal deformity in adults. Little is known about the loss of sagittal balance due to pGTK, or about the risk factors for pGTK, after surgery for DLS. METHODS: We reviewed records from a multicenter database of adults with DLS, treated with posterior spinal fusion. Inclusion required an age of 50 years or more at the time of surgery, an upper instrumented vertebra at T9 and below, more than 5 fused segments, and at least 2 years of follow-up. We included 73 patients with a mean age of 68.3 years (range, 51-77 yr) and a mean follow-up period of 3.6 years (range, 2-11 yr). Independent risk factors for pGTK were identified by logistic regression analysis. RESULTS: Significant pGTK, defined as an increase in thoracic kyphosis of more than 10° from before surgery to the time of final follow-up, was observed in 41% of the patients. Loss of the sagittal vertical axis was larger in patients with pGTK than without (4.7 vs. 1.5 cm; P = 0.02). Risk analysis showed larger lumbar lordosis correction in patients with pGTK. Multivariate logistic regression analysis identified an age greater than 75 (odds ratio, 5.53; P = 0.02, 95% confidence interval [1.4-22.4]) and sacropelvic fusion (odds ratio = 2.66, P = 0.02, 95% confidence interval [1.5-11.1]) as independent risk factors for pGTK. CONCLUSION: The pGTK incidence after surgery for DLS was 41%. Age, sacropelvic fusion, and a larger sagittal correction were identified as pGTK risk factors. Long-term follow-up will provide more data on the clinical impact of pGTK in elderly patients. LEVEL OF EVIDENCE: 3.

Density-matrix renormalization group study of trapped imbalanced Fermi condensates.

The density-matrix renormalization group is employed to investigate a harmonically trapped imbalanced Fermi condensate based on a one-dimensional attractive Hubbard model. The obtained density profile shows a flattened population difference of spin-up and spin-down components at the center of the trap, and exhibits phase separation between the condensate and unpaired majority atoms for a certain range of the interaction and population imbalance P. The two-particle density matrix reveals that the sign of the order parameter changes periodically, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to the quasicondensate up to at least P approximately 0.8. Possible experimental situations to test our predictions are discussed.

Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure.

The density-matrix renormalization group is used to study the pairing when both electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the charge density-wave correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.