Related papers: Gapless Symmetry Protected Topological Order
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge…
Critical edge states appear at the bulk gap closing points of topological transitions. Their emergence signify the existence of topologically nontrivial critical points, whose descriptions fall outside the scope of gapped topological…
We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the…
The interplay of symmetry, topology, and many-body effects in the classification of possible phases of matter poses a formidable challenge that is attracting great attention in condensed-matter physics. Such many-body effects are typically…
Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it…
Symmetry-Protected Topological (SPT) phases are gapped phases of quantum matter protected by global symmetries that cannot be adiabatically deformed to a trivial phase without breaking symmetry. In this work, we show that, for several SPT…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
Symmetry-protected phases are gapped phases of matter which are distinguished only in the presence of a global symmetry G. These quantum phases lack any symmetry-breaking or topological order, and have short-range entangled ground states.…
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 have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT) phase…
The concept of gapped symmetry-protected topological (SPT) states has been generalized to gapless SPT (gSPT) states. Similar to gapped SPT states, gSPT states in one dimension exhibit universal degeneracies in their entanglement spectra.…
A large class of symmetry-protected topological phases (SPT) in boson / spin systems have been recently predicted by the group cohomology theory. In this work, we consider SPT states at least with charge symmetry (U(1) or Z$_N$) or spin…
Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing…
Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet…
Symmetry protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For non-interacting fermion systems with time…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…
This paper attempts to establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and fault-tolerantly implementable logical gates in quantum…
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state(or atomic insulator) as long as…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
Symmetry protected topological states (SPTs) have the same symmetry and the phase transition between them are beyond Landau's symmetry breaking formalism. In this paper we study (1) the critical theory of phase transition between trivial…