Related papers: More on symmetry resolved operator entanglement
We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…
For a quantum system with Hilbert space ${\cal H}$ of dimension $N$ and a set $S$ of $n$ Hermitian operators ${\cal O}_i$, a basic question is to understand the set $E_S \subset \mathbb{R}^n$ of points $\vec{e}$ where $e_i = {\rm tr}(\rho…
Recent numerical and theoretical studies on the two-dimensional $J$-$Q_3$ model suggests that the deconfined quantum critical point is actually a $SO(5)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $O(4)$.…
The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…
Spin-orbital entanglement in quantum spin-orbital systems is quantified by a reduced von Neumann entropy, and is calculated for the ground state of a coupled spin-orbital chain with $SU(2)\times SU(2)$ symmetry. By analyzing the…
The relation between the quark-gluon description of QCD and the hadronic picture is studied up to order alpha_s. The analysis of the spin-1 correlators is developed within the large NC framework. Both representations are shown to be…
We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even…
The complexity of simulating the out-of-equilibrium evolution of local operators in the Heisenberg picture is governed by the operator entanglement, which grows linearly in time for generic non-integrable systems, leading to an exponential…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
We study Sinkhorn's algorithm for solving the entropically regularized optimal transport problem. Its iterate $\pi_{t}$ is shown to satisfy $H(\pi_{t}|\pi_{*})+H(\pi_{*}|\pi_{t})=O(t^{-1})$ where $H$ denotes relative entropy and $\pi_{*}$…
A spin-rotation-invariant Green's-function theory of long-range and short-range order (SRO) in the $S=1/2$ antiferromagnetic Heisenberg model with spatially anisotropic couplings on a simple cubic lattice is presented. The staggered…
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m\geq2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform…
We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over…
We develop the computational method of entanglement entropy based on the idea that $Tr\rho_{\Omega}^n$ is written as the expectation value of the local operator, where $\rho_{\Omega}$ is a density matrix of the subsystem $\Omega$. We apply…
We investigate the non-equilibrium time evolution of symmetry-resolved entanglement entropy (SREE) following an inhomogeneous quench in a critical one-dimensional free fermion system. Using conformal field theory, we derive an exact…
In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators…
Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation in interacting quantum many-body systems. It was recently argued that the expected exponential growth of…
We explain how to apply a Gaussian-preserving operator to a fermionic Gaussian state. We use this method to study the evolution of the entanglement entropy of an Ising spin chain following a Lindblad dynamics with string measurement…
Operator product expansions (OPEs) in quantum field theory (QFT) provide an asymptotic relation between products of local fields defined at points $x_1, \dots, x_n$ and local fields at point $y$ in the limit $x_1, \dots, x_n \to y$. They…
The string hypothesis of Bethe roots is a cornerstone in the thermodynamic analysis of quantum integrable systems, since it connects root configurations with physical quantities such as the ground-state energy, surface energy and excitation…