Related papers: Determining topological order from infinite projec…
We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…
It has been proposed recently by some of the authors that the quantum phase transition of a topological insulator like the SSH model may be detected by the eigenvalues and eigenvectors of the reduced density matrix. Here we further extend…
The information theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity) and multi information are used to analyze ground-state spin configurations for disordered and frustrated model systems in 2D and…
We extend the concept of strange correlators, defined for symmetry-protected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between string-net ground states and…
An algorithm for imaginary time evolution of a fermionic projected entangled pair state (PEPS) with ancillas from infinite temperature down to a finite temperature state is presented. As a benchmark application, it is applied to spinless…
Topological phases open a door to such intriguing phenomena as unidirectional propagation and disorder-resilient localization at a stable frequency. Recently discovered higher-order topological phases further extend the concept of…
The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…
We propose the convex-roof extension of quantum conditional mutual information ("co(QCMI)") as a diagnostic of topological order in a mixed state. We focus primarily on topological states subjected to local decoherence, and employ the…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination…
We study how the color code under decoherence gives rise to an intrinsic mixed-state topological order (imTO), which has no counterpart in pure ground states of local gapped Hamiltonians. For decoherence induced by XX-type operators on red…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
An important aspect in categorizing topological phases is whether the system is spinless or spinful, given that these classes exhibit distinct symmetry algebras, leading to disparate topological classifications. By utilizing the projective…
Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by…
The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS),…
The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the…
We investigate the extension of pure-state symmetry protected topological phases to mixed-state regime with a strong U(1) and a weak $\mathbb{Z}_2$ symmetries in one-dimensional spin systems by the concept of quantum channels. We propose a…
We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to…
The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low…
Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary…