arXiv subjects

Leandro Martinek

Publications and source records attributed to Leandro Martinek.

5 recordsLinked to original sources

arXiv2026

Exact mutual information for free massless fermions in any dimension

We obtain an exact expression for the Rényi mutual information (RMI) between two spherical regions for a free, massless Dirac field in $d$ spacetime dimensions and for a massless Rarita-Schwinger field in $d=4$. We identify each angular momentum mode in the spherical dimensional reduction of the parent theory with a massive Dirac fermion in two dimensional anti-de Sitter space (AdS). The RMI for each mode can be computed analytically for any Rényi index $n$ in terms of solutions of a Painlevé differential equation. We explore the long and short distance asymptotics of the result, where the sum over modes can be computed explicitly. As a result we are able to find subleading contributions to the long distance expansion in $d$ dimensions for arbitrary $n$, as well as to extract the area and logarithmic coefficients for the case $n=1$ in the short distance regime.

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arXiv2026

Exact Mutual Information Difference: Scalar vs. Maxwell Fields

We compute, for any Rényi index $n$, the exact difference between the mutual Rényi informations of a pair of free massless scalars and that of a Maxwell field in $d=4$ dimensions. Using the standard dimensional reduction method in polar coordinates, the problem is mapped to that of a single scalar field in $d=2$ with Dirichlet boundary conditions, which in turn can be conveniently related to the algebra of a chiral current on the full line. This latter identification, which maps algebras on an interval to two-interval algebras, yields exact results that clarify the structure of the long-distance OPE perturbative expansion of the mutual information. We find that this series has a finite radius of convergence only for integer $n>1$, while it becomes only asymptotical for $n=1$ and general non-integer values of $n$.

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arXiv2025

Quantum microstate counting from Brownian motion: from many-body systems to black holes

We introduce a new way to produce infinite families of bases of a quantum system's Hilbert space, as well as methods to find its dimension. These families are constructed via Brownian motions in the Hilbert space, defined using disordered, time-dependent couplings. The dimension spanned by them has zero variance over the ensemble of disordered couplings, and it is determined by certain replica partition functions. We apply these methods to finite dimensional $q$-local systems (spin clusters and SYK) and black holes. For $q$-local systems we find exact expressions at finite $q$, $N$, and $t$, for replica partition functions, together with universal behavior at large times and a semiclassical analysis at large-$N$ in appropriate master field variables. The right Hilbert space dimension is obtained for any time $t>0$, $q>1$ and $N>0$. For black holes, the Brownian motions prepare quantitatively generic ensembles of black hole microstates, and the Bekenstein-Hawking entropy is universally reproduced by counting those. There the $n$-replica partition functions are constructed by gluing $n$-traversable womrholes at their future and past. This method demonstrates the robustness of black hole microstate counting methods, avoiding several limitations of previous constructions, including the non-genericity of the microstates and associated interiors, implicit statistics of heavy operators, limited microscopic control over overlaps, and the need for specific limits in the calculation.

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arXiv2025

Optimal symmetry operators

We present a constructive method to maximize the expectation value of operators that implement a symmetry on a subsystem, making use of modular tools. More generally, we study the positive cones associated with a von Neumann algebra, as defined by Araki. Given a reference vector, an algebra, and a state on the algebra, the purification of the state in the cone $α= 0$, associated with the reference vector and the algebra, yields the unique vector whose overlap with the reference vector is maximal among all possible purifications. This establishes that the supremum in Uhlmann's theorem is uniquely attained by this vector, thereby providing the fidelity between the given state and the state obtained by restricting the reference vector to the algebra. Moreover, this purification can be explicitly constructed using modular tools. In addition, given an automorphism of the algebra, we show how to construct isometries implementing the automorphism using the positive cones. We prove that the isometry constructed from the cone $α= 0$ is the one with maximal expectation value among all possible isometries implementing the automorphism. We illustrate these ideas with two simple examples: one involving a system of two spins, and the other in the theory of the massless scalar field in 3+1 dimensions.

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arXiv2023

Standard translation twists and an operator-bounded energy inequality

Twist operators implement symmetries in bounder regions of the space. Standard twists are a special class of twists constructed using modular tools. The twists corresponding to translations have interesting special properties. They can move continuously an operator from a region to a disjoint one without ever passing through the gap separating the two. In addition, they have generators satisfying the spectrum condition. We compute explicitly these twists for the two dimensional chiral fermion field. The twist generator gives place to a new type of energy inequality where the smeared energy density is bounded below by an operator.

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