Related papers: Boundary and Symmetry Breaking in a Deformed Toric…
In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…
We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped phases stabilized by these symmetries,…
We investigate the interplay between self-duality and spatially modulated symmetry of generalized $N$-state clock models, which include the transverse-field Ising model and ordinary $N$-state clock models as special cases. The spatially…
A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the…
Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to…
Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form…
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving…
Symmetry breaking has been a central theme in classifying quantum phases and phase transitions. Recently, this concept has been extended to the mixed states of open systems, attracting considerable attention due to the emergence of novel…
We investigate symmetry-preserving gapped boundary of (2+1)D topological phases with global symmetry, which can be either bosonic or fermionic. We develop a general algebraic description for gapped boundary condition for symmetry-enriched…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
Motivated by the growing interest in spin liquids and topological phases, as well as the rise of deformation engineering, we study the combined effects of deformation and magnetic fields on the honeycomb Kitaev model. The Kitaev model, as…
The algebraic tools used to study topological phases of matter are not clearly suited to studying processes in which the bulk energy gap closes, such as phase transitions. We describe an elementary two edge thought experiment which reveals…
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group…
The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition…
Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimension lower than the bulk have significantly opened a new perspective for understanding of…
We explore the decoherence of the gapless/critical boundary of a topological order, through interactions with the bulk reservoir of "ancilla anyons." We take the critical boundary of the $2d$ toric code as an example. The intrinsic nonlocal…
We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two…
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…