相关论文: Symmetry-resolved Page curves
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the…
Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states…
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…
We study bipartite entanglement entropies in the ground and excited states of model fermion systems, where a staggered potential, $\mu_s$, induces a gap in the spectrum. Ground state entanglement entropies satisfy the `area law', and the…
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…
Symmetry protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension (1D). Here, we formulate this phenomenon in the framework of symmetry-resolved entanglement (SRE) using cohomology…
We compute various averages over bulk geometries of quantum states prepared by the Chern-Simons path integral, for any level $k$ and compact simple gauge group $G$. We do so by carefully summing over all topologically distinct bulk…
In two recent works, we studied the symmetry resolved R\'enyi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically…
The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the…
In a recent paper we studied the entanglement content of zero-density excited states in complex free quantum field theories, focusing on the symmetry resolved entanglement entropy (SREE). By zero-density states we mean states consisting of…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking…
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to…
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…
The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several…