Related papers: Resolving modular flow: a toolkit for free fermion…
As a new ingredient for analyzing the fine structure of entanglement, we study the symmetry resolution of the modular flow of $U(1)$-invariant operators in theories endowed with a global $U(1)$ symmetry. We provide a consistent definition…
Modular flows probe important aspects of the entanglement structures, especially those of QFTs, in a dynamical framework. Despite the expected non-local nature in the general cases, the majority of explicitly understood examples feature…
We study the modular Hamiltonian and the entanglement entropy of the BMS-invariant free fermion model. Starting from the modular Hamiltonian on a half-line interval, we calculate the modular Hamiltonian for a region consisting of two…
We determine explicitly the modular flow and the modular Hamiltonian for massless free fermions in diamonds on a cylinder in 1+1 dimensions. We consider both periodic and antiperiodic boundary conditions, the ground state in the…
Recent years have witnessed significant progress in the entanglement-based characterization of quantum phases of matter. The primary objects of interest are the reduced density matrix and its associated entanglement Hamiltonian. As…
The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from…
We apply modular flow -- entanglement generated dynamics -- to characterize quantum orders of ground state wavefunctions. In particular, we study the linear response of the entanglement entropy of a simply connected region with respect to…
We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing together the single interval modular flows.…
We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial…
In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both…
We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement…
In this paper we present the detailed calculation of a new modular Hamiltonian, namely that of a chiral fermion on a circle at non-zero temperature. We provide explicit results for an arbitrary collection of intervals, which we discuss at…
Separation of enantiomers by flows is a promising chiral resolution method using cost-effective microfluidics. Notwithstanding a number of experimental and numerical studies, a fundamental understanding still remains elusive, and an…
We study geometric modular flows in two-dimensional conformal field theories. We explore which states exhibit a geometric modular flow with respect to a causally complete subregion and, conversely, how to construct a state from a given…
We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of…
The two-dimensional ideal fluid and the plasma confined by a strong magnetic field exhibit an intrinsic tendency to organization due to the inverse spectral cascade. In the asymptotic states reached at relaxation the turbulence has vanished…
The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a…
We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in $1+1$ spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely…
We calculate the two-loop and one-loop/one-emission contributions required for soft gluon evolution at the next-to-leading order. The colour structures are expressed in the colour flow basis, and the kinematic dependence and loop integrals…
We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent…