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Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement…

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization…

A fundamental issue in the renormalization-group (RG) theory of critical phenomena concerns the allowed values of critical exponents that are consistent with the continuous nature of a phase transition. Here we conjecture a lower bound for…

This paper studies the properties of solutions to a class of elliptic and parabolic problems involving the fractional Laplacian. By applying the mountain pass theorem, we prove the existence of bounded classical positive solutions in the…

We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and…

For a system near a quantum critical point (QCP), above its lower critical dimension $d_L$, there is in general a critical line of second order phase transitions that separates the broken symmetry phase at finite temperatures from the…

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…

A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by…

For a functional $\E$ and a peak selection that picks up a global maximum of $\E$ on varying cones, we study the convergence up to a subsequence to a critical point of the sequence generated by a mountain pass type algorithm. Moreover, by…

Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…

In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.

Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in $2+1$-spacetime…

Let $G=(V,E)$ be a locally finite graph, whose measure $\mu(x)$ have positive lower bound, and $\Delta$ be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti-Rabinowitz, we establish existence results for some…

We study the resonant prescribed T-curvature problem on a compact 4-dimensional Riemannian manifold with boundary. We derive sharp energy and gradient estimates of the associated Euler-Lagrange functional to characterize the critical points…

We prove a technical lemma, the $C^{1+\alpha }$-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a $C^{1+\alpha }$ one-dimensional mapping $f:M\mapsto M$ with finitely many, non-recurrent, power law critical…

It has been proposed that the deconfined criticality in $(2+1)d$ -- the quantum phase transition between a Neel anti-ferromagnet and a valence-bond-solid (VBS) -- may actually be pseudo-critical, in the sense that it is a weakly first-order…

On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…

Utilizing a new variational principle that allows dealing with problems beyond the usual locally compactness structure, we study problems with a supercritical nonlinearity of the type $ -\Delta u + u= a(x) f(u)$ in $ \Omega$ with…

We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase…

We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths and…