相关论文: A coupled wire description of surface $ADE$ topolo…

Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states with properties that could not arise in a gapped system with the same symmetry and dimensionality. igSPT states arise from gapless…

We explore the states of matter arising from the spontaneous symmetry breaking (SSB) of $\mathbb{Z}_2$ non-onsite symmetries. In one spatial dimension, we construct a frustration-free lattice model exhibiting SSB of a non-onsite symmetry,…

We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological…

The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts.…

We show that the gapless boundary signatures - namely, chiral/helical hinge modes or localized zero modes - of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry…

We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The…

Abelian Chern-Simons theory, characterized by the so-called $K$ matrix, has been quite successful in characterizing and classifying Abelian fractional quantum hall effect (FQHE) as well as symmetry protected topological (SPT) phases,…

Sub-symmetry (SubSy) protected topological states represent a concept that goes beyond the conventional framework of symmetry-protected topological (SPT) phases, demonstrating that topological boundary states can remain robust even when the…

In topological crystalline insulators the topological conducting surface states are protected by crystal symmetry, in principle making it possible to pattern nanoscale insulating and conductive motifs solely by breaking local symmetries on…

Quantum phase transitions out of a symmetry-protected topological (SPT) phase in (1+1) dimensions into an adjacent, topologically distinct SPT phase protected by the same symmetry or a trivial gapped phase, are typically described by a…

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…

We demonstrate that the non-Hermitian parity-time (PT) symmetric interfaces formed between amplifying and lossy crystals support dissipationless edge states. These PT edge states exhibit gapless spectra in the complex band structure…

We study a three-leg spin-1/2 ladder with geometrically frustrated interleg interactions. We call this model an anisotropic triangular-strip (ATS) model. We numerically and field-theoretically show that its ground state belongs to a gapless…

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…

Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless…

We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological…

SnTe materials are know to be a platform for realization of various strong and symmetry protected topological phases in one, two and three spatial dimensions. We study symmetry-protected topological states in $[110]$ SnTe nanowires in the…

In [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete spin rotation $D_2 \subset SO(3)$ and time reversal $T$ symmetries. In this paper, using…

The search for one-dimensional (1D) topologically-protected electronic states has become an important research goal for condensed matter physics owing to their potential use in spintronic devices or as a building block for topologically…