相关论文: Universal lower bound on topological entanglement …
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
We calculate exactly the von Neumann and topological entropies of the toric code as a function of system size and temperature. We do so for systems with infinite energy scale separation between magnetic and electric excitations, so that the…
In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix…
Anyonic system not only has potential applications in the construction of topological quantum computer, but also presents a unique property known as topological entanglement entropy in quantum many-body systems. How to understand…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows…
A remarkable feature of typical ground states of strongly-correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant…
The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $\chi$. Focusing on scale…
On top of a $D$-dimensional gapped bulk state, Low Entanglement Excitations (LEE) on $d$($<D$)-dimensional sub-manifolds can have extensive energy but preserves the entanglement area law of the ground state. Due to their multi-dimensional…
In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\tr\rho_A^n$. We study the…
The ground states of topological orders condense extended objects and support topological excitations. This nontrivial property leads to nonzero topological entanglement entropy $S_{topo}$ for conventional topological orders. Fracton…
Topological feedback entropy (TFE) was introduced in 2004 to measure the intrinsic rate at which a continuous, fully observed, deterministic control system generates information for controlled set-invariance. In this paper, we generalise…
We study entanglement entropy of unusual $\mathbb{Z}_N$ topological stabilizer codes which admit fractional excitations with restricted mobility constraint in a manner akin to fracton topological phases. It is widely known that the…
Transfer entropy (TE) is an attractive model-free method to detect causality and infer structural connectivity of general digital systems. However it relies on high dimensions used in its definition to clearly remove the memory effect and…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…