Thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type.

We analyze the thermodynamics and criticality properties of four families of su(m|n) supersymmetric spin chains of Haldane-Shastry (HS) type, related to both the A_{N-1} and the BC_{N} classical root systems. Using a known formula expressing the thermodynamic free energy per spin of these models in terms of the Perron (largest in modulus) eigenvalue of a suitable inhomogeneous transfer matrix, we prove a general result relating the su(kp|kq) free energy with arbitrary k=1,2,⋯, to the su(p|q) free energy. In this way we are able to evaluate the thermodynamic free energy per spin of several infinite families of supersymmetric HS-type chains, and study their thermodynamics.

Myeloid sarcoma presenting as fingertip necrosis with underlying suppurative tenosynovitis: A case report.

We report an unusual case presentation of a patient with necrotic tissue changes of the right second and third fingers, found to have myeloid sarcoma with -positive tenosynovitis and underlying acute myeloid leukemia, to highlight the importance of comprehensive evaluation in patients with atypical wounds.

Thermodynamics and criticality of su(m) spin chains of Haldane-Shastry type.

We study the thermodynamics and critical behavior of su(m) spin chains of Haldane-Shastry type at zero chemical potential, both in the A_{N-1} and BC_{N} cases. We evaluate in closed form the free energy per spin for arbitrary values of m, from which we derive explicit formulas for the energy, entropy, and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for m≲10 by the corresponding temperature for an m-level system with uniformly spaced levels.

Optimization and comparative evaluation of nonlinear deformation algorithms for atlas-based segmentation of DBS target nuclei.

Nonlinear registration of individual brain MRI scans to standard brain templates is common practice in neuroimaging and multiple registration algorithms have been developed and refined over the last 20 years. However, little has been done to quantitatively compare the available algorithms and much of that work has exclusively focused on cortical structures given their importance in the fMRI literature. In contrast, for clinical applications such as functional neurosurgery and deep brain stimulation (DBS), proper alignment of subcortical structures between template and individual space is important.

A duality principle for the multi-block entanglement entropy of free fermion systems.

The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set A of sites of the subsystem considered and the set K of excited momentum modes.

Supersymmetric spin chains with nonmonotonic dispersion relation: Criticality and entanglement entropy.

We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1+1)-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions.

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation.

Level density of spin chains of Haldane-Shastry type.

We provide a rigorous proof of the fact that the level density of all known su(m) spin chains of Haldane-Shastry type associated with the A(N-1) root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large-N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the transfer matrix.

1/falpha noise and integrable systems.

In this paper, we show that there is a family of well-known integrable systems whose spectral fluctuations decay as 1/f(4), and thus do not follow the 1/f(2) law recently conjectured for integrable systems. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.

Spin chains of Haldane-Shastry type and a generalized central limit theorem.

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.