Related papers: One-dimensional symmetric phases protected by frie…
Symmetry protected topological phases of one-dimensional spin systems have been classified using group cohomology. In this paper, we revisit this problem for general spin chains which are invariant under a continuous on-site symmetry group…
By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime,…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one…
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…
We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer…
We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this work we use symmetry as a guide to map…
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…
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…
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported…
We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite $A_4$, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry…
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain…
We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build…
We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the…
We propose that ultracold alkaline-earth-like atoms confined in one-dimensional optical lattice can realize a Kondo lattice model which hosts a symmetry-protected topological (SPT) phase and an associated quantum phase transition in a…
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…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
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.…