Publications and Preprints

Here is a list of my papers with brief explanations. You can also find my publications and preprints at google scholar, research gate, or arXiv.

1. Topological order and quantum information

Figure 1: matrix-product-state quantum transistor

[26b] Towards transistor-based quantum computing

Yuan-Dong Liu, Xiang Xu, Qing-Rui Wang, and Dong-Sheng Wang

arXiv: 2605.21045 (2026)

We propose a modular quantum computing architecture based on quantum transistors, called “telesistors.” Quantum gates are stored in symmetry-protected topological ground states and executed through measurement-induced gate teleportation, with edge modes serving as input and output ports. These transistors can be interconnected to build programmable quantum circuits. We show how symmetry protection of Clifford gates, together with magic-state injection for non-Clifford gates, supports universal quantum computation, and discuss additional coding schemes to enhance fault tolerance.

Figure 14: lattice fusion of loop excitations

[25a] Bridging Microscopic Constructions and Continuum Topological Field Theory of Three-Dimensional Non-Abelian Topological Order

Yizhou Huang, Zhi-Feng Zhang, Qing-Rui Wang, and Peng Ye

arXiv: 2512.21148 (2025)

We construct microscopic lattice operators for creating, fusing, shrinking, and braiding particle and loop excitations in three-dimensional quantum double models. By matching the excitation spectrum, fusion, shrinking, and braiding data, we establish a correspondence between the \mathbb{D}_4 quantum double model and the BF field theory with an AAB twist and gauge group (\mathbb{Z}_2)^3. We also demonstrate how to control individual non-Abelian shrinking channels and verify fusion–shrinking consistency directly on the lattice, providing a microscopic foundation for the continuum description.

Figure 2(b): worldlines for particle exchange and a full spin rotation

[23b] Continuum field theory of three-dimensional topological orders with emergent fermions and braiding statistics

Zhi-Feng Zhang, Qing-Rui Wang, and Peng Ye

Phys. Rev. Research 5, 043111 (2023), arXiv: 2307.09983 (2023)

We develop a continuum field-theoretical framework for three-dimensional topological orders with emergent fermions, combining twisted BF theories with a K-matrix BB term. We derive general formulas for excitation confinement and boson–fermion statistical transmutation, using framed Wilson loops to determine particle self-statistics. Within this framework, gauge invariance constrains how emergent fermions can coexist with particle–loop, multiloop, and Borromean-rings braiding. We calculate the associated topological data, including fusion and shrinking rules, and examine how emergent fermions modify fusion processes.

Loop shrinking into vacuum, particle, and loop excitation channels

[22a] Non-Abelian fusion, shrinking, and quantum dimensions of Abelian gauge fluxes

Zhi-Feng Zhang, Qing-Rui Wang, and Peng Ye

Phys. Rev. B 107, 165117 (2023), arXiv: 2208.09228 (2022)

We calculate the fusion rules and loop-shrinking rules of the excitations in a (3+1)\mathrm{D} topological order with Borromean rings braiding statistics. The fusion rule is non-Abelian even though the gauge group is Abelian.

Associativity transformation of fermionic fusion diagrams

[21c] Towards a complete classification of nonchiral topological phases in two-dimensional fermion systems

Jing-Ren Zhou, Qing-Rui Wang, and Zheng-Cheng Gu

Phys. Rev. B 106, 245120 (2022), arXiv: 2112.06124 (2021)

A large class of 2\mathrm{D} non-chiral bosonic topological orders are described by Turaev-Viro-Levin-Wen string-net models. In this paper, we generalize the Gu-Wang-Wen construction of fermionic string-net models to include those fermionic topological phases with q-type anyon excitations. Several examples with q-type anyon excitations are discussed, including the Fermionic topological phase from Tambara-Yamagami category, which can be regarded as the parafermion generalization of Ising fermionic topological phase.

Domain-wall decoration diagrams for a spectral-sequence differential

[21b] Domain wall decorations, anomalies and spectral sequences in bosonic topological phases

Qing-Rui Wang, Shang-Qiang Ning, and Meng Cheng

arXiv: 2104.13233 (2021)

In this work, we showed basically ''domain wall decorations (in physics) = Atiyah-Hirzebruch spectral sequence (in math)''. For the bosonic topological phases classified by group cohomology theory, we derived all the differentials (anomalies in physics) at the cochain level in the Lyndon-Hochschild-Serre spectral sequence. It can be used to unify the anomaly or obstruction formulas for bosonic topological phases (such as SPT-LSM theorems, anomalous SPT phases, and symmetry-enriched gauge theories). Using the Lyndon's algorithm (implemented by this Mathematica code), we listed explicit expressions to extract different domain-wall-decoration data for a given cocycle.

A local string-net configuration carrying fractional U(1) charge

[21a] Exactly solvable models for \mathrm{U}(1) symmetry-enriched topological phases

Qing-Rui Wang and Meng Cheng

Phys. Rev. B 106, 115104 (2022), arXiv: 2103.13399 (2021)

We proposed general constructions of commuting-projector lattice models for 2\mathrm{D} Levin-Wen, 3\mathrm{D} Walker-Wang, and 3\mathrm{D} Dijkgraaf-Witten topological orders enriched by \mathrm{U}(1) symmetry, with finite-dimensional Hilbert space per site. The point-like or loop-like excitations are shown to carry fractional \mathrm{U}(1) charges.

Geometric cycles and triangulations used to evaluate topological invariants

[20a] Computing classification of interacting fermionic symmetry-protected topological phases using topological invariants

Yunqing Ouyang, Qing-Rui Wang, Zheng-Cheng Gu, and Yang Qi

Chinese Phys. Lett. 38 127101 (2021), arXiv: 2005.06572 (2020)

Using techniques from homological algebra, we developed an algorithm to calculate the topological invariants for a given cocycle of a group. It can be used to accelerate the computation of obstructions (anomalies) for SPT or SET phases. For instance, the classifications of 2\mathrm{D} fermion SPT protected by 17 2\mathrm{D} wallpaper groups are calculated using this algorithm.

Non-Abelian braiding of two loops linked to a base loop

[19c] Non-Abelian three-loop braiding statistics for 3\mathrm{D} fermionic topological phase

Jing-Ren Zhou, Qing-Rui Wang, Chenjie Wang, and Zheng-Cheng Gu

Nat. Commun. 12, 3191 (2021), arXiv: 1912.13505 (2019)

We proposed and solved the physical constraints for loop braiding statistics in (3+1)\mathrm{D} fermionic topological phases. Even for Abelian gauge symmetries, the loop braidings could be non-Abelian. The classification of fermionic Abelian SPT phases from the braiding statistics approach is consistent with that of the general group supercohomology theory (see [17a] and [18c] below).

Three-loop braiding of loops alpha and beta linked to loop gamma

[18b] Topological quantum field theory for Abelian topological phases and loop braiding statistics in (3+1)-dimensions

Qing-Rui Wang, Meng Cheng, Chenjie Wang, and Zheng-Cheng Gu

Phys. Rev. B 99, 235137 (2019), arXiv: 1810.13428 (2018)

The loop-like excitation in (3+1)\mathrm{D} may obey the so-called three-loop-braiding statistics. In this paper, we established a TQFT framework to understand the quantum statistics of point-like particles and loop-like excitations in (3+1)\mathrm{D} for Abelian topological phases.

2. Generalized symmetries and quantum criticality

Figure 2(b): SPT-decorated domain walls and boundary projective representations

[26c] E_\infty^{1,2}-type Lieb-Schultz-Mattis anomalies, deconfined quantum critical points, and non-invertible symmetry breaking

Hao-Ran Zhang, Hanlin Lin, Shuo Yang, and Qing-Rui Wang

arXiv: 2606.06343 (2026)

We show that E_\infty^{1,2}-type Lieb-Schultz-Mattis anomalies force non-invertible dual symmetries when a gaugeable Abelian normal internal symmetry is gauged. This provides a general mechanism for type-II deconfined quantum critical points, which are dual to spontaneous breaking of non-invertible symmetries. We illustrate this mechanism in a spin-1/2 chain with anomalous D_8 symmetry: a dimer-to-ferromagnet transition has numerical evidence for a critical theory with c\approx1, while gauging the internal symmetry produces the non-invertible \mathrm{Rep}(H_8) dual symmetry.

Table III: mixed anomalies between generalized symmetry background couplings

[26a] Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)\mathrm{D} twisted BF topological quantum field theories

Zhi-Feng Zhang, Yizhou Huang, Qing-Rui Wang, and Peng Ye

arXiv: 2601.01523 (2026)

We develop a conserved-current construction of generalized symmetries in (3+1)\mathrm{D} twisted BF theories describing non-Abelian topological orders with Borromean-rings braiding. Starting from the equations of motion, we obtain both invertible and intrinsically non-invertible higher-form symmetry operators. The latter require projector constraints, which lead to multi-channel fusion. We derive their fusion rules and diagnose mixed anomalies by coupling the conserved currents to background gauge fields, providing a systematic route from continuum actions to symmetry operators and gauging obstructions.

Equation (2.45): exchange of parafermionic operators

[23c] Para-fusion Category and Topological Defect Lines in \mathbb{Z}_N-parafermionic CFTs

Jin Chen, Babak Haghighat, and Qing-Rui Wang

arXiv: 2309.01914 (2023)

We introduce para-fusion categories to describe topological defect lines in two-dimensional \mathbb{Z}_N-parafermionic CFTs, generalizing super-fusion categories in fermionic theories. Parafermionic operators living on defect lines obey fractional statistics, leading to generalized q-type objects and para-pentagon consistency equations. We construct these structures through parafermionic anyon condensation, relating their fusion data to those of parent bosonic theories. We illustrate the framework with explicit CFT examples and fully classify the family of para-fusion categories obtained by condensing the \mathbb{Z}_N Tambara–Yamagami categories.

Equation (2.54): fusion of symmetry defects Ug and Uh into Ugh

[23a] Lecture Notes on Generalized Symmetries and Applications

Ran Luo, Qing-Rui Wang, and Yi-Nan Wang

Physics Reports 1065, 1–43 (2024), arXiv: 2307.09215 (2023)

We provide a pedagogical introduction to generalized symmetries, connecting perspectives from high-energy and condensed-matter physics. We emphasize higher-form and higher-group symmetries, explaining their descriptions through topological defects, background gauge fields, and classifying spaces. We discuss gauging, ’t Hooft anomalies and their relation to SPT phases, including group-cohomology and cobordism classifications. Examples range from Maxwell and Chern–Simons theories to the Haldane chain, toric code, and higher-form SPT phases. We also introduce applications to the geometric engineering of quantum field theories in string/M-theory, and briefly discuss non-invertible symmetries.

3. Fermionic symmetry-protected topological phases

Figure 11: crystalline decorations for space group No. 1

[25b] Classification of Interacting Topological Crystalline Superconductors in Three Dimensions and Beyond

Shang-Qiang Ning, Xing-Yu Ren, Qing-Rui Wang, Yang Qi, and Zheng-Cheng Gu

arXiv: 2512.25069 (2025)

We develop a domain-wall-decoration framework for classifying three-dimensional interacting topological superconductors, incorporating four layers: p+ip superconductors, Kitaev chains, complex fermions, and bosonic SPT states. We determine the allowed p+ip decorations and derive a computable O_5 obstruction formula incorporating antiunitary symmetries, completing the consistency conditions for the remaining decoration layers. Combining this framework with the fermionic crystalline equivalence principle, we obtain interacting topological crystalline superconductor classifications for all 230 space groups in electronic systems.

Figure 2: triangulated regions and interfaces

[24a] Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases

Kevin Loo and Qing-Rui Wang

Phys. Rev. B 111, 205102 (2025), arXiv: 2412.18528 (2024)

We develop a symmetry-extension approach to constructing gapped interfaces and anomalous boundaries for interacting fermionic SPT phases. Using pullback trivialization, we remove Majorana-chain and complex-fermion decorations layer by layer, tracking the nontrivial corrections induced in the remaining decoration data. We derive explicit cochain-level consistency formulas in (2+1)\mathrm{D} and (3+1)\mathrm{D} and illustrate the construction with a (3+1)\mathrm{D} phase protected by \mathbb{Z}_2^f\times\mathbb{Z}_4\times\mathbb{Z}_4, including Majorana-chain decorations. Collapsing the intermediate layers yields a gapped boundary with extended symmetry.

Figure 11: closed procedure for the pure Majorana phase

[23d] Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases

Xing-Yu Ren, Shang-Qiang Ning, Yang Qi, Qing-Rui Wang, and Zheng-Cheng Gu

Phys. Rev. B 110, 235117 (2024), arXiv: 2310.19058 (2023)

We derive explicit stacking rules for interacting fermionic SPT phases up to (2+1)\mathrm{D}, including both unitary and antiunitary symmetries. Using fermionic symmetric local unitary transformations, we combine two layers into a single effective layer and determine the resulting decoration data, including fermion-parity and Majorana-phase corrections. These rules resolve the stacking group extensions between different decoration layers. Applying the fermionic crystalline equivalence principle, we compute the stacking groups for all 17 wallpaper groups, as well as wallpaper symmetries combined with onsite time-reversal symmetry.

Charge decorations on a triangular lattice

[21d] Exactly solvable lattice models for interacting electronic insulators in two dimensions

Qing-Rui Wang, Yang Qi, Chen Fang, Meng Cheng, and Zheng-Cheng Gu

Phys. Rev. B 108, L121104 (2023), arXiv: 2112.15533 (2021)

Based on the physical picture of \mathrm{U}(1)_f-charge decorations, we illustrate the key idea by considering the well known 2\mathrm{D} interacting topological insulator. Then we generalize our construction to an arbitrary 2\mathrm{D} interacting electronic insulator with symmetry G_f=\mathrm{U}(1)_f\rtimes_{\rho_1,\omega_2}G. Finally we study more examples, including the full interacting classification of 2\mathrm{D} crystalline topological insulators.

Bulk and edge excitations in an Abelian Chern-Simons description

[19b] Edge theories of 2\mathrm{D} fermionic symmetry protected topological phases protected by unitary Abelian symmetries

Shang-Qiang Ning, Chenjie Wang, Qing-Rui Wang, and Zheng-Cheng Gu

Phys. Rev. B 104, 075151 (2021), arXiv: 1910.02925 (2019)

We utilize the Abelian Chern-Simons theory to study the fermionic SPT phases protected by Abelian symmetry. In particular, we discover the construction of Luttinger liquid edge theories with central charge n-1 for Type-III bosonic SPT phases protected by (\mathbb{Z}_n)^3 symmetry.

Fermionic block-state decorations around a rotation center

[19a] Construction and classification of point-group symmetry-protected topological phases in two-dimensional interacting fermionic systems

Jian-Hao Zhang, Qing-Rui Wang, Shuo Yang, Yang Qi, and Zheng-Cheng Gu

Phys. Rev. B 101, 100501(R) (2020), arXiv: 1909.05519 (2019)

We constructed and classified point-group SPT phases for 2\mathrm{D} interacting fermion systems via lower-dimensional block-state decorations. The crystalline equivalence principle was verified in 2\mathrm{D} interacting fermion systems, with spinless and spin-1/2 group extensions switched.

Majorana-chain and fermion decorations on a tetrahedron

[18c] Construction and classification of symmetry-protected topological phases in interacting fermion systems

Qing-Rui Wang and Zheng-Cheng Gu

Phys. Rev. X 10, 031055 (2020), arXiv: 1811.00536 (2018)

We gave a systematic fixed-point wave function construction and classification of fermionic SPT states for generic fermionic symmetry group G_f=\mathbb{Z}_2^f\times_{\omega_2}G_b, which is a central extension of bosonic symmetry group G_b (may contain time reversal symmetry) by the fermion parity symmetry group \mathbb{Z}_2^f=\{1,P_f\}. There are in total 4 layers of decoration data: (2+1)\mathrm{D} p+ip chiral superconductors, (1+1)\mathrm{D} Majorana chain, (0+1)\mathrm{D} complex fermion, and bosonic SPT. This is an all-inclusive classification work on fermionic SPT with finite onsite symmetry in physical dimensions.

Local transformation of Majorana decorations in an anomalous SPT state

[18a] Anomalous symmetry protected topological states in interacting fermion systems

Qing-Rui Wang, Yang Qi, and Zheng-Cheng Gu

Phys. Rev. Lett. 123, 207003 (2019), arXiv: 1810.12899 (2018)

To our surprise, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We demonstrated the essential idea by considering an anomalous topological superconductor with time-reversal symmetry T^2=1 in 2\mathrm{D}. The ASPT states are also crucial in the classification of fermionic SPT phases in one dimension higher, known as trivialization.

Three-dimensional local transformation of decorated Majorana chains

[17a] Towards a complete classification of symmetry-protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

Qing-Rui Wang and Zheng-Cheng Gu

Phys. Rev. X 8, 011055 (2018), arXiv: 1703.10937 (2017)

We established a relation between discrete spin structure (the Poincaré dual of the trivialization of the 2nd Stiefel-Whitney class w_2 ) and local Kasteleyn orientations on the dual lattice for arbitrary triangulations in arbitrary dimensions. The Majorana chains are then decorated to the intersection lines of domain walls to give rise to a new class of fermionic SPT phases.

4. Sign structures in doped Mott insulators

Spin currents around a doped hole on a square lattice

[18d] Single-hole wave function in two dimensions: A case study of the doped Mott insulator

Shuai Chen, Qing-Rui Wang, Yang Qi, D. N. Sheng, and Zheng-Yu Weng

Phys. Rev. B 99, 205128 (2019), arXiv: 1812.05627 (2018)

Using the variational Monte Carlo method, we studied a ground-state ansatz for the single-hole doped t\text{-}J model in two dimensions. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMGR) results.

Ground-state spin as a function of the modified hopping parameter

[15b] Exact sign structure of the t\text{-}J chain and the single hole ground state

Zheng Zhu, Qing-Rui Wang, D. N. Sheng, and Zheng-Yu Weng

Nucl. Phys. B 903, 51 (2016), arXiv: 1510.07634 (2015)

We proposed a single-hole-doped ground state ansatz with the correct sign structure of the 1\mathrm{D} t\text{-}J model (see [13a] below). The Monte Carlo simulations of this variational wave function reproduced the key DMRG results of the model (such as the characteristic momentum structure, the Luttinger liquid behavior, and the quantum phase interference of the hole under a periodic boundary condition).

Spin and hole worldlines on a two-leg ladder

[15a] Variational wave function for an anisotropic single-hole-doped t\text{-}J ladder

Qing-Rui Wang, Zheng Zhu, Yang Qi, and Zheng-Yu Weng

arXiv: 1509.01260 (2015)

Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the t\text{-}J model, a new ground state wave function has been constructed in [Weng, New J. Phys. 13, 103039 (2011)]. This paper specifically studied such kind of variational ground state ansatz for the one-hole-doped anisotropic two-leg t\text{-}J ladder using the variational Monte Carlo (VMC) method. An excellent agreement is found between the VMC and DMRG results.

Singlet and triplet energies as a function of chain length

[13a] Sign structure and ground-state properties for a spin−S t\text{-}J chain

Qing-Rui Wang and Peng Ye

Phys. Rev. B 90, 045106 (2014), arXiv: 1310.6496 (2013)

We showed that the 1\mathrm{D} t\text{-}J chain has an exact sign structure captured by the Marshall sign and the phase string sign. Using this sign structure, we proved a generalized Marshall theorem and a generalized Lieb-Mattis theorem for the t\text{-}J chain with arbitrary spin and doping. The large t/J phase supports a gapped spin sector with similar properties (ground-state degeneracy, edge state, and string order parameter) of the Haldane chain (a 1\mathrm{D} \mathrm{SO}(3) SPT), although the charge sector is gapless. This may be the first example of SPT in gapless systems.

Temperature-doping phase diagram with metallic and confined insulating regimes

[12a] Monopoles, confinement and charge localization in the t\text{-}J model with dilute holes

Peng Ye and Qing-Rui Wang

Nucl. Phys. B 874, 386 (2013), arXiv: 1206.0258 (2012)

We present a quantum field theoretic description on the t\text{-}J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. Due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account.