Related papers: Entanglement renormalization and topological order

A non-minimal coupling $\eta$ has been attracting growing interest particularly in the context of inflation models, though its quantum nature is not clear yet. We study the renormalization of a non-minimal coupling in the scalar quantum…

Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…

We established important relationships between entanglement measures and the order parameter (spin polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily…

We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…

We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using…

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…

We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define electromagnetic (EM) duality for all of Kitaev's quantum double models…

We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different…

We study quantum quenches in the two-dimensional Kitaev toric code model and compute exactly the time-dependent entanglement entropy of the non-equilibrium wave-function evolving from a paramagnetic initial state with the toric code…

Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively…

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…

It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, $-\gamma$, called the topological entanglement entropy. We theoretically study the…

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that…

Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined…

Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we…

A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that in a topological…

We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network…

We prove that the rank 3 analogue of the tensor model defined in [arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop $\gamma$- and $\beta$-functions of the model…