arXiv subjects

Wen-Tao Xu

Publications and source records attributed to Wen-Tao Xu.

22 records · Page 2Linked to original sources

arXiv2018

Tensor network state approach to quantum topological phase transitions and their criticalities of $\mathbb{Z}_2$ topologically ordered states

We construct a general wave function with the topological order by introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both the toric code state and double semion state. Via calculating the correlation length defined from the one-dimensional quantum transfer operator of the wave function norm, we can map out the complete phase diagram in terms of the parameter $λ$ and identify three different quantum critical points (QCPs) at $λ=0$, $\pm 1.73$. The first one separates the toric code phase and double semion phase, while later two describe the topological phase transitions from the toric code phase or double semion phase to the symmetry breaking phase, respectively. When mapping to the exactly solved statistical models, the norm of the tensor network wave function is transformed into the partition function of the eight-vertex model. Actually such a quantum-classical mapping can not reveal the rich structures of low-energy excitations at these three QCPs. So we further demonstrate that the full eigenvalue spectra of the transfer operators with/without the flux insertions can describe the complete quantum criticalities, which are characterized by the two-dimensional compactified free boson conformal field theories (CFTs) with the compactified radii $R=\sqrt{6}$ for the QCPs at $λ=\pm\sqrt{3}$ and $R=\sqrt{8/3}$ for the QCP at $λ=0$. For the QCP at $λ=0$, there are no anyon condensation, and the emerged matrix product operator symmetries result in a rich structure of the low-energy excitations, distinct from those of both toric code and double semion phases. Finally, we discuss the possible relation between our conformal quantum criticalities and the general (2+1) spatial-time dimensional CFTs for quantum topological phase transitions.

cond-mat.str-el↗

arXiv2018

Classifying parafermionic gapped phases using matrix product states

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 $\mathbb{Z}_{p}$ parafermions without extra symmetry other than $\mathbb{Z}%_{p}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the non-trivial simple $\mathbb{Z}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. But the spontaneous symmetry breaking phases correspond to the trivial semisimple $\mathbb{Z}_{p/n}$ graded algebras, which can be further reduced to the trivial simple $\mathbb{Z}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results deepen our understanding of topological phases in one dimension from the viewpoints of MPS.

cond-mat.str-el↗

arXiv2018

Enriched classification of parafermionic gapped phases with time reversal symmetry

Based on the recently established parafermionic matrix product states, we study the classification of one-dimensional gapped phases of parafermions with the time reversal (TR) symmetry satisfying $T^{2}=1$. Without extra symmetry, it has been found that $\mathbb{Z}_{p}$ parafermionic gapped phases can be classified as topological phases, spontaneous symmetry breaking (SSB) phases, and a trivial phase, which are uniquely labelled by the divisors $n$ of $p$. In the presence of TR symmetry, however, the enriched classification is characterized by three indices $n$, $κ$ and $μ$, where $κ\in \mathbb{Z}_{2}$ denotes the linear or projective TR actions on the edges, and $μ\in \mathbb{Z}_{2}$ indicates the commutation relations between the TR and (fractionalized) charge operator. For the $\mathbb{Z}_{r}$ symmetric parafermionic ground states, where $r=p$ for trivial or topological phases, and $r=p/n$ for SSB phases, the original gapped phases with odd $r$ are divided into two phases, while those phases with even $r$ are further separated into four phases. The gapped parafermionic phases with the TR symmetry include the symmetry protected topological phases, symmetry enriched topological phases, and the SSB coexisting symmetry protected topological phases. From analyzing the structures and symmetries of their reduced density matrices of those resulting topological phases, we can obtain the topological protected degeneracies of their entanglement spectra.

cond-mat.str-el↗

arXiv2017

Matrix product states for topological phases with parafermions

In the Fock representation, we propose a framework to construct the generalized matrix product states (MPS) for topological phases with $\mathbb{ Z}_{p}$ parafermions. Unlike the $\mathbb{Z}_{2}$ Majorana fermions, the $% \mathbb{Z}_{p}$ parafermions form intrinsically interacting systems. Here we explicitly construct two topologically distinct classes of irreducible $% \mathbb{Z}_{3}$ parafermionic MPS wave functions, characterized by one or two parafermionic zero modes at each end of an open chain. Their corresponding parent Hamiltonians are found as the fixed point models of the single $\mathbb{Z}_{3}$ parafermion chain and two-coupled parafermion chains with $\mathbb{Z}_{3}\times \mathbb{Z}_{3}$ symmetry. Our results thus pave the road to investigate all possible topological phases with $\mathbb{Z}_{p}$ parafermions within the matrix product representation in one dimension.

cond-mat.str-el↗