Related papers: Parametrized topological phases in 1d and T-dualit…
We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the…
Duality between the E_8 x E_8 heterotic string and Type I' theory predicts a tower of D(irichlet)-particle bound states corresponding to perturbative heterotic string states. In the limit of infinite Type I' coupling, some of these bound…
We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is…
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a…
Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg…
Recently there is trend to study topological properties in one-dimensional(1D) periodic systems. Concepts such as Zak phase are considered as topological invariants that characterize the bulk bands. The bulk 1D systems are classified to…
We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
We solve the one dimensional massive Thirring model or equivalently the sine-Gordon model in the repulsive regime with general Dirichlet boundary conditions, which are characterized by two boundary fields $\phi_{L,R}$ associated with the…
We introduce the notion of higher Berry connection and curvature in the space of conformal boundary conditions in (1+1)d conformal field theories (CFT), related to each other by exactly marginal boundary deformations, forming a "boundary…
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to…
Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D…
Real topological phases protected by the spacetime inversion (P T) symmetry are a current research focus. The basis is that the P T symmetry endows a real structure in momentum space, which leads to Z2 topological classifications in 1D and…
One-dimensional gapped spin chains with symmetry PSU(N) = SU(N)/Z_N are known to possess N different topological phases. In this paper, we introduce a non-local string order parameter which characterizes each of these N phases…
Topological phases realized in time-reversal invariant (TRI) systems are foundational to experimental study of the broader canon of topological condensed matter as they do not require exotic magnetic orders for realization. We therefore…
We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A dipole symmetry comprises two sets of symmetry generators: charge and dipole operators, which together form a non-trivial algebra with…
In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for $\mathbb{Z}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of $\mathbb{Z}_{p}$…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
We classify global bifurcations in generic one-parameter local families of \vfs on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in monographs on the bifurcation theory. As a by…