相关论文: Symmetry Protected Topological Order by Folding a …

We reveal the connection between two-dimensional subsystem symmetry-protected topological (SSPT) states and two-dimensional topological orders via a self-dual frustrated toric code model. This model, an enrichment of the toric code (TC)…

Usually $Z_2$ topological insulators are protected by time reversal symmetry. Here, we present a new type of $Z_2$ topological insulators in a cubic lattice which is protected by a novel hidden symmetry, while time reversal symmetry is…

We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…

Symmetry protected topological states cannot be deformed to a trivial state so long as the symmetry is preserved, yet there is no local order parameter that can distinguish them from a trivial state. We demonstrate how to detect whether a…

Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the…

We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve…

We study $\mathbb{Z}_2$ topological ordered phases in 2+1 dimensions characterized by generalized modulated symmetries. Such phases have explicit realizations in terms of fixed-point Hamiltonians involving commuting projectors with support…

In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here 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…

We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is…

We show that whereas spin-1/2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladder-like lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry…

Topological phenomena are commonly studied in phases of matter which are separated from a trivial phase by an unavoidable quantum phase transition. This can be overly restrictive, leaving out scenarios of practical relevance -- similar to…

We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current interactions. The model is shown to have…

We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although an exact solution of a spin-orbital ring with SU(2) spin and XY orbital interactions separates spins from…

The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels.…

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any…

We study two-dimensional bosonic symmetry protected topological (SPT) phases which are protected by reflection symmetry and local symmetry [$Z_N\rtimes R$, $Z_N\times R$, U(1)$\rtimes R$, or U(1)$\times R$], in the search for…

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In…

The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the…

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological…