arXiv subjects

Zheng-Xin Liu

Publications and source records attributed to Zheng-Xin Liu.

At least 19 recordsLinked to original sources

arXiv2026

Spin-Charge Groups for Fermions in Fluids and Crystals: General Structures and Physical Consequences

Known symmetry groups are insufficient to describe the various couplings among spin, charge, and spatial degrees of freedom in fermionic systems. To address this problem, we introduce spin-charge groups (SCGs), which provide a unified framework for fermionic symmetries. SCGs incorporate spin and charge operations as `internal' symmetries, spatial and temporal operations as `external' symmetries, together with their couplings and projective twists. After deriving the general group structure of SCGs, we explore their applications in concrete physical systems, including $^3$He superfluids, charge-4e superconductors, collinear magnets with spin-fluxes, and superconductors with coexisting magnetic orders. We show that SCGs can enforce additional band degeneracies, Chern numbers and cross spin-charge responses. Hence SCGs provide a symmetry-based route toward the classification and exploration of new phases of matter even when strong interactions are included.

cond-mat.str-el↗

arXiv2026

Deconfined Gapless phases and criticalities in Shastry-Sutherland Antiferromagnet

Antiferromagnets on the Shastry-Sutherland lattice have attracted lots of research interest due to the possible existence of deconfined criticality. In the present work, we study the $J_1$-$J_2$-$J_r$ model using Variational Monte Carlo (VMC) method, where $J_1$, $J_2$, $J_r$ stand for the nearest-neighbor, next nearest neighbor and ring exchange interactions respectively. An empty plaquette (EP) phase with spontaneous mirror symmetry breaking is reproduced. However, the EP phase in the VMC approach is $Z_2$ deconfined and have Majorana-type gapless spinon excitations, which is qualitatively different from the EP phase in literature. The central observation of the present study is the gapless $Z_2$ Quantum spin liquid phase resulting from the competition between the EP phase, the full plaquette (FP) phase and the antiferromagnetic Néel phase. While the phase transition from the $Z_2$ QSL phase to the EP phase is likely of Landau-Ginzburg type, the continuous transitions to the confined FP and Néel phases are exotic and need to be further explored.

cond-mat.str-el↗

arXiv2026

Excitonic Quantum Anomalous Hall Effect in Collinear Magnets Without Spin-Orbit Coupling

Spin-orbit coupling (SOC) is thought to be necessary in realizing quantum anomalous Hall (QAH) insulators in magnetic materials. In this Letter, we propose an exciton-condensation mechanism to realize QAH effect in collinear magnets with negligible spin-orbit coupling. This mechanism is realized by two steps: first prepare a spin-splitting nodal-ring band structure, and then gap out the nodal-ring via triplet exciton condensation. A nonzero Chern number can be obtained if the in-plane spin texture resulting from the triplet exciton condensation is noncollinear in momentum space. We show that the electron-phonon coupling can switch the spin texture from a colinear pattern to a noncolinear one and plays an essential role in realizing QAH effect. The above mechanism is not only suitable for ferrogmagnets but also applicable for altermagnets. Finally, through first-principles calculations we propose the bilayer material V2SeTeO to be a promising candidate of excitonic QAH insulator.

cond-mat.mes-hall↗

arXiv2026

Spurious Strange Correlators in Symmetry-Protected Topological Phases

Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Focusing on 1D gapped bosonic/spin systems described by matrix product states (MPS), we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations (abbreviated as \emph{irrep}) in the eigenspace corresponding to the entanglment spectrum (entanglement space); (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators.

cond-mat.str-el↗

arXiv2026

Super-Solid phase in a U(2) symmetric S = 1 Magnet on the Triangular Lattice

A spin supersolid is characterized by the simultaneous breaking of lattice translation and continuous spin rotation symmetries. In this work, we study a spin-1 model with $U(2)\cong SU(2)\times U(1)/Z_2$ symmetry on the triangular lattice, and the phase diagram is figured out using a variational $\mathbb CP^2$ approach. We identify a novel $SU(2)$-supersolid phase which contains a 3-sublattice solid order and a spin-superfluid order. Unlike usual supersolid phases having noncollinear magnetic order and only one Goldstone mode, the $SU(2)$-supersolid phase has collinear Neel order and two Goldstone modes. Another important feature of this supersolid is that the magnon excitation spectrum has symmetry protected double degeneracy in the whole Brillouin zone. As by-products, several other ordered phases are obtained, including the ferromagnetic and the antiferromagnetic states breaking the $SU(2)$ symmetry, as well as genuine phases that completely break the $U(2)$ symmetry. Furthermore, the instabilities of $SU(3)$-flavor linear spin-wave theory are consistent with the phase boundaries between different ordered phases. %dispersions confirm the stability of the classically ordered phases and provides insights into their excitation spectra.

cond-mat.str-el↗

arXiv2025

Altermagnetic Weyl node-network semimetals protected by spin symmetry

Symmetry protected topology has been studied extensively in the past twenty years, but the topology protected by spin symmetry has just begun to be studied. In this work, based on spin symmetry analysis, we propose that a class of Weyl nodal line semimetals is protected by the spin symmetry. Then, by the first-principles electronic structure calculations, we predict that both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ are node-network semimetals protected by the spin symmetry. Moreover, both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ have nodal rings protected by the mirror symmetry and Dirac points protected by nonsymmorphic spin symmetry. Furthermore, both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ transform node-network semimetal phase into Weyl semimetal phase when considering spin-orbit coupling. Therefore, our work not only enriches the topological phases protected by spin symmetry, but also provides an excellent material platform to investigate the exotic physical properties of multiple altermagnetic topological semimetal phases in experiment.

cond-mat.mtrl-sci↗

arXiv2025

Universal Rule for Topological Hopf Term via Dirac-Spin Coupling

It is known that the topological Hopf term in two-dimensional (2D) spin systems can be derived by coupling to massless Dirac fermions. We establish a universal rule governing the generation of Hopf terms in 2D quantum spin systems coupled to Dirac fermions. The key insight identifies the Hopf coefficient as the oriented volume in the $\mathfrak{su}(2)$ Lie algebra space formed by Dirac cone matrix bases. This geometric interpretation allows direct determination of Hopf term without path integral computations. Applying this framework, we demonstrate nontrivial Hopf term in tailored checkerboard lattice models and recover known results in graphene-based systems.

cond-mat.str-el↗

arXiv2025

Type-II quantum spin Hall insulator

Quantum spin Hall effect is usually realized in two-dimensional materials with time-reversal symmetry, but whether it can be realized without symmetry protection remains unexplored. Here, we propose type-II quantum spin Hall insulator with quantized spin Hall conductivity, whose edge states with opposite chirality and polarization, distributed in different Brillouin zone regions, connect the conduction and valence bands at the boundary. Thus, the type-II quantum spin Hall insulator does not require any symmetry protection other than translational symmetry. Then, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that type-II quantum spin Hall insulator can be realized in both altermagnetic materials and Luttinger compensated magnetic materials. Furthermore, based on lattice model, we find that as long as $U(1)$ symmetry exists, type-II quantum spin Hall insulator phase can always exist stably. However, if $U(1)$ symmetry is broken, type-II quantum spin Hall insulator phase transforms into an obstructed atomic insulator phase as spin-orbit coupling effect is enhanced. Therefore, our work not only proposes a new mechanism for realizing the quantum spin Hall effect, but also enriches the types of unconventional magnetic topological phases.

cond-mat.mes-hall↗

arXiv2025

Crystal valley Hall effect

The time-reversal symmetry is thought to be a necessary condition for realizing valley Hall effect. If the time-reversal symmetry is broken, whether the valley Hall effect can be realized has not been explored. In this letter, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that the vally Hall effect without time-reversal symmetry can be realized in two-dimensional altermagnetic materials Fe$_2$WSe$_4$ and Fe$_2$WS$_4$. Due to crystal symmetry required, the vally Hall effect without time-reversal symmetry is called crystal vally Hall effect. In addition, under uniaxial strain, both monolayer Fe$_2$WSe$_4$ and Fe$_2$WS$_4$ can realize piezomagnetic effect. Under biaxial compressive stress, both monolayer Fe$_2$WSe$_4$ and Fe$_2$WS$_4$ will transform from altermagnetic semiconductor phase to bipolarized topological Weyl semimetal phase. Our work not only provides a new direction for exploring the novel valley Hall effect, but also provides a good platform for exploring altermagnetic semiconductors and altermagnetic topological phase transitions.

cond-mat.mtrl-sci↗

arXiv2024

Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo

We discuss the discovery by variational Monte Carlo (VMC) methods of a series of multinode quantum spin liquids (QSLs) in extended Kitaev models on the honeycomb lattice. Like the gapless Kitaev spin liquid with its two nodes at K and K$^\prime$, these multinode QSLs are characterized by an emergent Z$_2$ gauge structure and a discrete number of symmetry-protected Majorana cones in their low-energy excitation spectrum. Because the cones are gapped by weak magnetic fields, nonzero Chern numbers are obtained and the ground state becomes one of many possible Abelian or non-Abelian chiral spin liquids. Here we focus on the projective symmetry group (PSG)-guided VMC approach to the Kitaev model with various symmetry-allowed extended interactions. Based on the VMC phase diagrams of these models, we propose a framework for the classification of nodal QSLs that includes the PSG, the chiralities of the cones, and the way in which the cones are symmetry-related. At present, the known candidate Kitaev materials seem to lie outside the parameter regimes of the multinode QSL phases. However, with more than 100 Z$_2$ PSGs for spin-orbit-coupled states on the honeycomb lattice, we anticipate that more than one multinode QSL will be realized experimentally in future work.

cond-mat.str-el↗

arXiv2024

Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling

Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full rotation group $\mathrm{O(3)}$, leading to new quasiparticles restricted to lattices that do not have any counterpart in a vacuum. We focus on the fermionic quasiparticle excitations under ``spin-space group'' symmetries, applicable to materials where long-range magnetic order and itinerant electrons coexist. We provide a list of 218 classes of new quasiparticles that can only be realized in the spin-space groups. These quasiparticles have at least one of the following properties that are qualitatively distinct from those discovered in magnetic space group(MSG)s, and distinct from each other:(i) degree of degeneracy,(ii) dispersion as function of momentum, and(iii) rules of coupling to external probe fields. We rigorously prove this result as a theorem that directly relates these properties to the symmetry invariants, and then illustrate this theorem with a concrete example, by comparing three 12-fold fermions having different sets of symmetry invariants including one discovered in MSG. Our approach can be generalized to realize more quasiparticles whose little co-groups are beyond those considered in our work.

cond-mat.mes-hall↗

arXiv2024

Constructions and Applications of Irreducible Representations of Spin-Space Groups

Spin-space groups (SSGs), including the traditional space groups (SGs) and magnetic space groups (MSGs) as subsets, describe the complete symmetries of magnetic materials with weak spin-orbit coupling (SOC). In the present work, we systematically study the irreducible representations (irreps) of SSGs by focusing on the projective irreps of the little co-group $L(k)$ of any momentum point $\pmb k$. We analysis the factor systems of $L(k)$, and then reduce the projective regular representation of $L(k)$ into direct sum of irreps using the Hamiltonian approach. Especially, for collinear SSGs which contain continuous spin rotation operations, we adopt discrete subgroups to effectively capture their characteristics. Furthermore, we apply the representation theory of SSGs to study the band structure of electrons and magnons in magnetic materials. After identifying the SSG symmetry group, we extract relevant irreps and determine the $k\cdot p$ models. As an example, we illustrate how our approach works for the material \ch{Mn3Sn}. Degeneracies facilitated by SSG symmetry are observed, underscoring the effectiveness of application in material analysis. The SSG recognition and representation code is uploaded to GitHub, the information of irreps of all SSGs is also available in the online Database. Our work provides a practical toolkit for exploring the intricate symmetries of magnetic materials and paves the way for future advances in materials science.

cond-mat.mtrl-sci↗

arXiv2024

Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups (SGs). Symmetries of three-dimensional periodic (pseudo-) vector fields, however, are described by the spin-space groups (SSGs), which were initially used to describe the symmetries of magnetic orders. In SSGs, the real-space and spin degrees of freedom are unlocked in the sense that an operation could have different spacial and spin rotations. SSGs gives a complete symmetry description of magnetic structures, and have natural applications in the band theory of itinerary electrons in magnetically ordered systems with weak spin-orbit coupling. Altermagnetism, a concept raised recently that belongs to the symmetry-compensated collinear magnetic orders but has non-relativistic spin splitting, is well described by SSGs. Due to the vast number and complicated group structures, SSGs have not yet been systematically enumerated. In this work, we exhaust SSGs based on the invariant subgroups of SGs, with spin operations constructed from three-dimensional (3D) real representations of the quotient groups for the invariant subgroups. For collinear and coplanar magnetic orders, the spin operations can be reduced into lower dimensional real representations. As the number of SSGs is infinite, we only consider SSGs that describe magnetic unit cells up to 12 times crystal unit cells. We obtain 157,289 non-coplanar, 24,788 coplanar-non-collinear, and 1,421 collinear SSGs. The enumerated SSGs are stored in an online database at \url{https://cmpdc.iphy.ac.cn/ssg} with a user-friendly interface. We also develop an algorithm to identify SSG for realistic materials and find SSGs for 1,626 magnetic materials. Our results serve as a solid starting point for further studies of symmetry and topology in magnetically ordered materials.

cond-mat.mtrl-sci↗

arXiv2024

Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems

Gapless quasiparticles can exist in the Bogoliubov-de Gennes (BdG) Hamiltonians in the mean field description of superconductors (SCs), fermionic superfluids (SFs) and quantum spin liquids (QSLs). The mechanism of gapless quasiparticles in superconductors was studied in literature based on the homotopy theory or symmetry-indicators. However, important properties of the gapless quasiparticles including the degeneracy, the energy-momentum dispersion and the responses to external probe fields need to be determined. In the present work, we investigate gapless quasiparticles in general BdG systems by using projective representation theory for the full `symmetry' groups formed by combinations of lattice, spin and charge operations. We find that (I) charge conjugation (or effective charge conjugation) symmetry can yield gapless quasiparticles with linear, quadratic or higher order dispersions at high symmetry points of the Brillouin zone; (II) different quantum numbers protected level crossing can give rise to zero modes along high symmetry lines; (III) combined spatial inversion and time reversal symmetry can protect zero modes appearing at generic $k$ points. To obtain the low energy properties of gapless quasiparticles, the $k\cdot p$ theory is provided using a high efficient method--the Hamiltonian approach. Based on generalized band representation theory for BdG systems, several lattice models are constructed to illustrate the above results. Our theory provides a method to classify nodal SCs/SFs/QSLs with given symmetries, and enlightens the realization of Majorana type massless quasiparticles in condensed matter physics.

cond-mat.str-el↗

arXiv2023

Realization and detection of Kitaev quantum spin liquid with Rydberg atoms

The Kitaev chiral spin liquid has captured widespread interest in recent decades because of its intrinsic non-Abelian excitations, yet the experimental realization is challenging. Here we propose to realize and detect Kitaev chiral spin liquid in a deformed honeycomb array of Rydberg atoms. Through a novel laser-assisted dipole-dipole interaction mechanism to generate both effective hopping and pairing terms for hard-core bosons, together with van der Waals interactions, we achieve the pure Kitaev model with high precision. The gapped non-Abelian spin liquid phase is then obtained by introducing Zeeman fields. Moreover, we propose innovative strategies to probe the chiral Majorana edge modes by light Bragg scattering and by imagining their chiral motion. Our work broadens the range of exotic quantum many-body phases that can be realized and detected in atomic systems, and makes an important step toward manipulating non-Abelian anyons.

cond-mat.str-el↗

arXiv2023

Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices

Realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact interaction on optical Kagome lattices. In the strong coupling regime, the system is described by an effective spin-1 model with two- and three-body interactions between neighboring spins. By mapping out the phase diagram via variational Monte Carlo method, we find a non-Abelian chiral spin liquid phase in which the Ising-type anyons obey non-Abelian braiding statistics. The gapless chiral edge states can be detected by measuring the spin-spin correlation from atomic population. Furthermore, an interesting Z2 QSL phase is observed exhibiting both topological order and lattice symmetry breaking order. Our scheme can be implemented in cold quantum gases of bosonic atoms.

cond-mat.quant-gas↗

arXiv2023

Effect of ring-exchange interactions in the extended Kitaev honeycomb model

Motivated by the possible triple-$\bf Q$ classical order in the Kitaev candidate material Na$_2$Co$_2$TeO$_6$, we investigate microscopic models that may stabilize the triple-$\bf Q$ order by studying an extended Kitaev honeycomb model with ring-exchange interactions (namely, the $K$-$Γ$-$Γ'$-$J_{\rm R}$ model) using the variational Monte Carlo method. It turns out that with positive ring-exchange interaction ($J_{\rm R}>0$) there indeed appears an exotic non-coplanar triple-$\bf Q$ ordered state featured by three Bragg peaks at symmetry-related M points in the crystallographic Brillouin zone. A magnetic field in the honeycomb plane can suppress the triple-$\bf Q$ order and induce a gapless quantum spin liquid (QSL) with 8 cones. Furthermore, with the increase of $J_{\rm R}$ a proximate Kitaev spin liquid with eight Majorana cones labeled "PKSL8" is found which is very stable over a large range of $Γ$ interactions. The PKSL8 state shares the same projective symmetry group with the Kitaev spin liquid (KSL) which is located at small $Γ$ and $J_{\rm R}$. In a weak magnetic field applied normal to the honeycomb plane, the PKSL8 turns into an Abelian chiral spin liquid with Chern number $ν=-4$, unlike the KSL which yields a chiral spin liquid with $ν=1$. Since the triple-$\bf Q$ phase is adjacent to two QSLs in the phase diagram, our work suggests that it is more hopeful to experimentally realize the exotic QSL phases starting from the triple-$\bf Q$ order.

cond-mat.str-el↗

arXiv2023

Nematic chiral spin liquid in a Kitaev magnet under external magnetic field

The possible existence of a quantum spin liquid (QSL) phase, an exotic state of matter with long-range quantum entanglement and fractionalized excitations, in $α$-RuCl$_3$ has sparked widespread interests in exploring QSLs in various Kitaev models under magnetic fields. Recently, a $K$-$J$-$Γ$-$Γ'$ model has been proposed to accurately describe the compound by fitting the measured thermodynamic data, where $J$ is Heisenberg interaction, and $Γ$, $Γ'$ are off-diagonal exchanges on top of the dominant Kitaev coupling $K$. Based on this effective model, an intermediate QSL phase in presence of an out-of-plane fields along the $[1 1 1]$ direction, between the low-field zigzag order and high-field polarized phase, has been predicted. By combining density matrix renormalization group (DMRG), exponential tensor renormalization group (XTRG), and variational Monte Carlo (VMC) calculations, we address the nature of this QSL phase in the honeycomb $K$-$J$-$Γ$-$Γ'$ model under the $[1 1 1]$-direction field. Our DMRG calculations find the algebraic-like decay of spin correlation function, the finite spin scalar chiral order, and lattice nematic order. Together with the XTRG results of power-law specific heat at low temperature, our findings naturally suggest a gapless nematic chiral spin liquid. On the other hand, our VMC study finds a gapped nematic chiral spin liquid with the variational energy very close to that obtained in DMRG. As VMC finds a very small gap that is beyond the current resolution of both ground-state DMRG and finite-temperature XTRG calculations on finite-width cylinders, we resort the full clarification for the nature of the intermediate QSL to future studies. Lastly, we discuss the implications of our results to the recent experiment on $α$-RuCl$_3$ and the QSL-like phase in a similar $K$-$Γ$-$Γ'$ model.

cond-mat.str-el↗