Related papers: A hierarchy of topological tensor network states
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the…
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…
We study a one-dimensional topological superconductor, the Kitaev chain, under the influence of a non-Hermitian but $\mathcal{PT}$-symmetric potential. This potential introduces gain and loss in the system in equal parts. We show that the…
In the topos approach to quantum theory, the spectral presheaf plays the role of the state space of a quantum system. We show how a notion of entropy can be defined within the topos formalism using the equivalence between states and…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…
We develop a new theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of non-equilibrium statistical mechanics. The general form of the many-body density matrix is…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction of the discrete gauge symmetry with…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…
This work investigates the topological structure of multipartite entanglement in symmetric Dicke states $|D_n^{(k)}\rangle$. By viewing qubits as topological loops, we establish a direct correspondence between the recursive measurement…
Although the homotopy-knot theory has been utilized to implement effective topological classification for non-Hermitian systems, the physical implications underlying distinct knot topologies remain ambiguous and are rarely addressed. In…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
We introduce the use of entanglement entropy as a tool for studying the amount of information shared between the nodes of quantum complex networks. By considering the ground state of a network of coupled quantum harmonic oscillators, we…
In the tensor network representation, a deformed $Z_{2}$ topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase…
Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum…