Extremal correlators and random matrix theory

A Grassi, Z Komargodski, L Tizzano - Journal of High Energy Physics, 2021 - Springer
A bstract We study the correlation functions of Coulomb branch operators of four-
dimensional\(\mathcal {N}\)= 2 Superconformal Field Theories (SCFTs). We focus on rank …

The classical β-ensembles with β proportional to 1/N: from loop equations to Dyson's disordered chain

PJ Forrester, G Mazzuca - Journal of Mathematical Physics, 2021 - pubs.aip.org
In the classical β-ensembles of random matrix theory, setting β= 2α/N and taking the N→∞
limit gives a statistical state depending on α. Using the loop equations for the classical β …

Entanglement spectrum statistics of a time reversal invariant spin chain system: insights from random matrix theory

A Sarkar, S Kumar - The European Physical Journal B, 2023 - Springer
The entanglement spectrum statistics (ESS) of a disordered and generalised time reversal
invariant XXZ model is inspected in the bipartite framework using exact finite-N results from …

Robust nonergodicity of the ground states in the ensemble

AK Das, A Ghosh, IM Khaymovich - Physical Review B, 2024 - APS
In various chaotic quantum many-body systems, the ground states show nontrivial athermal
behavior despite the bulk states exhibiting thermalization. Such athermal states play a …

Free energy expansions of a conditional GinUE and large deviations of the smallest eigenvalue of the LUE

SS Byun, SM Seo, M Yang - arXiv preprint arXiv:2402.18983, 2024 - arxiv.org
We consider a planar Coulomb gas ensemble of size $ N $ with the inverse temperature
$\beta= 2$ and external potential $ Q (z)=| z|^ 2-2c\log| za| $, where $ c> 0$ and …

Recursion scheme for the largest-Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport

PJ Forrester, S Kumar - Journal of Physics A: Mathematical and …, 2019 - iopscience.iop.org
The largest eigenvalue distribution of the Wishart–Laguerre ensemble, indexed by Dyson
parameter and Laguerre parameter a, is fundamental in multivariate statistics and finds …

Differential identities for the structure function of some random matrix ensembles

PJ Forrester - Journal of Statistical Physics, 2021 - Springer
The structure function of a random matrix ensemble can be specified in terms of the
covariance of the linear statistics∑ j= 1 N eik 1 λ j,∑ j= 1 N e-ik 2 λ j for Hermitian matrices …

Joint moments of a characteristic polynomial and its derivative for the circular β-ensemble

PJ Forrester - Probability and Mathematical Physics, 2022 - msp.org
The problem of calculating the scaled limit of the joint moments of the characteristic
polynomial, and the derivative of the characteristic polynomial, for matrices from the unitary …

Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance

A Laha, S Kumar - Physical Review E, 2023 - APS
One of the key issues in problems related to quantum information theory is concerned with
the distinguishability of quantum states. In this context, Bures distance serves as one of the …

[HTML][HTML] Random density matrices: Closed form expressions for the variance of squared Hilbert-Schmidt distance

A Laha, S Kumar - Physics Letters A, 2024 - Elsevier
One of the fundamental aspects of quantum information theory is the study of distance
measures between quantum states. Hilbert-Schmidt distance serves as a convenient choice …