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We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…

We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}+\epsilon$ and below the twist $\frac{c}{12}$ is…

We define the disentangling power of a unitary operator in a similar way as the entangling power defined by Zanardi, Zalka and Faoro [PRA, 62, 030301]. A general formula is derived and it is shown that both quantities are directly…

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…

We derive the distribution of eigenvalues of the reduced density matrix of a block of length l in a one-dimensional system in the scaling regime. The resulting "entanglement spectrum" is described by a universal scaling function depending…

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when…

In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur…

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of <phi…

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…

In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the non-equilibrium zero temperature Random Field Ising Model (RFIM), we perform a quantitative study of the…

Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:\mathbb{R}\to M_{n\times n}$ and lower $\ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for…

The argument of Rudolph and Sanders, while technically correct, raises conceptual problems. In particular, if carried to its logical conclusion, it would disallow the use in our theories of any time $t$ with implied resolution beyond that…

The survival probability of a quantum system with a finite ground energy is known to decay subexponentially at large times. Here we show that, under the same assumption, the average value of any quantum observable, whenever well-defined,…

Scale factor matrices relating mesonic fields in chiral Lagrangians and quark-level operators of QCD sum-rules are shown to be constrained by chiral symmetry, resulting in universal scale factors for each chiral nonet. Built upon this…

In this note, we use the VC dimension technique to prove the first lower bound against one-layer softmax transformers with infinite precision. We do so for two tasks: function composition, considered by Peng, Narayanan, and Papadimitriou,…

To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its…

In the 1977 paper \cite{MTW} of B. McCoy, C. Tracy and T. Wu it was shown that the limiting two-point correlation function in the two-dimensional Ising model is related to a second order nonlinear Painlev\'e function. This result identified…

The spectral form factor (SFF) can probe the eigenvalue statistic at different energy scales as its time variable varies. In closed quantum chaotic systems, the SFF exhibits a universal dip-ramp-plateau behavior, which reflects the spectrum…

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited with a left-moving superconformal primary. Despite being BPS at the orbifold point, such states can `lift' as the…

Universal theories are a broad class of well-motivated microscopic dynamics of the electroweak sector that go beyond the Standard Model description. The long distance physics is described by electroweak parameters which correspond to local…