Explanipedia

Ramp from replica trick Open

Xuchen Cao, Thomas Faulkner · 2025

A bstract We compute the spectral form factor of the modular Hamiltonian K = −ln ρ A associated to the reduced density matrix of a Haar random state. A ramp is demonstrated and we find an analytic expression for its slope. Our method invol…

Reflected entropy in random tensor networks. Part III. Triway cuts Open

Chris Akers, Thomas Faulkner, Simon Lin, Pratik Rath · 2024

A bstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the m…

Conformally invariant charge fluctuations in a strange metal Open

Xuefei Guo, Jin Chen, Farzaneh Hoveyda-Marashi, Simon Bettler, Dipanjan Chaudhuri , et al. · 2024

The strange metal is a peculiar phase of matter in which the electron scattering rate, $τ^{-1} \sim k_B T/\hbar$, which determines the electrical resistance, is universal across a wide family of materials and determined only by fundamental…

Ramp from Replica Trick Open

Xuchen Cao, Thomas Faulkner · 2024

We compute the spectral form factor of the modular Hamiltonian $K=-\lnρ_A$ associated to the reduced density matrix of a Haar random state. A ramp is demonstrated and we find an analytic expression for its slope. Our method involves an app…

The reflected entanglement spectrum for free fermions Open

Souvik Dutta, Thomas Faulkner, Simon Lin · 2023

A bstract We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the s…

Reflected entropy in random tensor networks. Part II. A topological index from canonical purification Open

Chris Akers, Thomas Faulkner, Simon Lin, Pratik Rath · 2023

A bstract In ref. [1], we analyzed the reflected entropy ( S R ) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section ( EW ) in holographic theories, $$ {S}_R=2\frac{EW}{4G} $$ . In…

Entropy variations and light ray operators from replica defects Open

Srivatsan Balakrishnan, Venkatesa Chandrasekaran, Thomas Faulkner, Adam C. Levine, Arvin Shahbazi-Moghaddam · 2022

Scattering strings off quantum extremal surfaces Open

Venkatesa Chandrasekaran, Thomas Faulkner, Adam Levine · 2022

A bstract We consider a Hayden & Preskill like setup for both maximally chaotic and sub-maximally chaotic quantum field theories. We act on the vacuum with an operator in a Rindler like wedge R and transfer a small subregion I of R to the …

A general proof of the quantum null energy condition Open

Srivatsan Balakrishnan, Thomas Faulkner, Zuhair U. Khandker, Huajia Wang · 2022

We prove a conjectured lower bound on ⟨T_ _(x)⟩ $ψ$ in any state $ψ$ of a CFT on Minkowski space, dubbed the Quantum Null Energy Condition (QNEC). The bound is given by the second order shape deformation, in the null direction, o…

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition Open

Thomas Faulkner, Robert G. Leigh, Onkar Parrikar, Huajia Wang · 2022

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R^1,d-1. We show that in addition to the usual boost generator, there is a contribution to the mod…

Quantum corrections to holographic mutual information Open

César A. Agón, Thomas Faulkner · 2022

We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expans…

Shape dependence of entanglement entropy in conformal field theories Open

Thomas Faulkner, Robert G. Leigh, Onkar Parrikar · 2022

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R^1,d--1. We consider the entanglement entropy across a deformed planar or spherical entan…

Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras Open

Thomas Faulkner, Stefan Hollands · 2022

Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras Open

Thomas Faulkner, Stefan Hollands, Brian Swingle, Yixu Wang · 2022

We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of…

A canonical purification for the entanglement wedge cross-section Open

Souvik Dutta, Thomas Faulkner · 2021

Approximate recoverability and relative entropy II: 2-positive channels of general v. Neumann algebras Open

Thomas Faulkner, Stefan Hollands · 2020

We generalize our results in paper I in this series to quantum channels between general v. Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end…

The holographic map as a conditional expectation Open

Thomas Faulkner · 2020

We study the holographic map in AdS/CFT, as modeled by a quantum error correcting code with exact complementary recovery. We show that the map is determined by local conditional expectations acting on the operator algebras of the boundary/…

Recovering the QNEC from the ANEC Open

Fikret Ceyhan, Thomas Faulkner · 2020

A modular toolkit for bulk reconstruction Open

Thomas Faulkner, Min Li, Huajia Wang · 2019

Gravitational dual of the Rényi displacement operator Open

Srivatsan Balakrishnan, Souvik Dutta, Thomas Faulkner · 2017

We give a recipe for computing correlation functions of the displacement\noperator localized on a spherical or planar higher dimensional twist defect\nusing AdS/CFT. Such twist operators are typically used to construct the $n$'th\nRenyi en…

Bulk locality from modular flow Open

Thomas Faulkner, Aitor Lewkowycz · 2017

We study the reconstruction of bulk operators in the entanglement wedge in\nterms of low energy operators localized in the respective boundary region. To\nleading order in $N$, the dual boundary operators are constructed from the\nmodular …

Two-cylinder entanglement entropy under a twist Open

Xiaohong Chen, William Witczak‐Krempa, Thomas Faulkner, Eduardo Fradkin · 2017

We study the von Neumann and R\'enyi entanglement entropy (EE) of scale-invariant theories defined on tori in 2+1 and 3+1 spacetime dimensions. We focus on spatial bi-partitions of the torus into two cylinders, and allow for twisted bounda…

Gravitational dual of the Rényi twist displacement operator Open

Srivatsan Balakrishnan, Souvik Dutta, Thomas Faulkner · 2016

We give a recipe for computing correlation functions of the displacement operator localized on a spherical or planar higher dimensional twist defect using AdS/CFT. Such twist operators are typically used to construct the $n$'th Renyi entro…

Bulk emergence and the RG flow of entanglement entropy Open

Thomas Faulkner · 2015

We further develop perturbative methods used to calculate entanglement entropy (EE) away from an interacting CFT fixed point. At second order we find certain universal terms in the renormalized EE which were predicted previously from holog…

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