Dimension of non-trivial online forms

Non-trivial on-line forms (N-TOFs) are a type of form that we believe is becoming widely prevalent with the preference for on-line services in many areas of everyday life. We define N-TOFs as forms that are critical to the life and wellbeing of the form filler (aka user). By virtue of this, they are frequently complex in terms of structure, mechanics and content required. Forms providing access to government, financial, employment and educational services are commonly N-TOFs, depending upon the specifics of the service to which they relate. Other examples of N-TOFs include: tax forms, benefits forms, immigration forms, social housing applications, etc. The non-trivial nature of such forms principally arises from their close relationship to the quality of life of their users. A pernicious feature of service provision through NTOFs is that form design could in fact reflect a design bias that limits access to a service. Put simply, an N-TOF could by its character impair legitimate access to a service. For example there are forms that could be judged as unnecessarily complex for the user. Hence the interest in N-TOFs relates closely to the agendas of: design for all; and professional ethics. On a related matter it is evident that in N-TOFs some of their onerous elements serve as a means of user authentication. For example, having to enter comprehensive personal details is used to help confirm a user's identity. Hence an onerous or repetitive aspect of a form can be accounted for as a legitimate design choic

Strange correlations in spin-1 Heisenberg antiferromagnets

We study the behavior of the recently proposed "strange correlator" [Phys. Rev. Lett. {\bf 112}, 247202 (2014)] in spin-1 Heisenberg antiferromagnetic chains with uniaxial single-ion anisotropy. Using projective quantum Monte Carlo, we are able to directly access the strange correlator in a variety of phases, as well as to examine its critical behavior at the quantum phase transition between trivial and non-trivial symmetry protected topological phases. After finding the expected long-range behavior in these two symmetry conserving phases, we go on to verify the topological nature of two-leg and three-leg spin-1 Heisenberg antiferromagnetic ladders. This demonstrates the power of the strange correlator in distinguishing between trivial and non-trivial symmetry protected topological phases.Comment: 7 pages, 6 figure

A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States

In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension $d$, the critical states of fermionic SPT phase transitions has an emergent $Z_2^T$ symmetry and can be realized on the boundary of a $d+1$-dimensional bulk SPT with an extra $Z_2^T$ symmetry.Comment: 35 pages, 10 figure

Quantum phase transition as an interplay of Kitaev and Ising interactions

We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. In the absence of frustration, the 2D lattice shows a topological phase transition from the $\mathbb{Z}_2$ spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the $\mathbb{Z}_2$ spin-liquid state.Comment: 16 pages, 18 figure

Quantum Multicriticality in Disordered Weyl Semimetal

In electronic band structure of solid state material, two band touching points with linear dispersion appear in pair in the momentum space. When they annihilate with each other, the system undergoes a quantum phase transition from three-dimensional Weyl semimetal (WSM) phase to a band insulator phase such as Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a `magnetic dipole' like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases, renormalized WSM phase, CI phase, and diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized Weyl semimetal (WSM) phase turns out to be a direct phase transition whose critical exponent $\nu=0.80\pm 0.01$. We interpret these numerical results by a renormalization group analysis on the critical theory.Comment: 23 pages with 14 figures and 4 table