arXiv subjects

Hoi Chun Po

Publications and source records attributed to Hoi Chun Po.

At least 19 recordsLinked to original sources

arXiv2026

Local spectroscopy of loop current order with individual magnetic atoms

Hidden ordered states--characterized by order parameters that elude conventional probes--pose a fundamental challenge for their identification in quantum materials. Recent experiments report evidence for time-reversal symmetry breaking orbital magnetic order and anomalous transport signatures in the $2a\times2a$ charge density wave state of the kagome metal CsV$_3$Sb$_5$ at a temperature $T<30\,$K. Theoretical analyses propose that a time-reversal symmetry breaking loop-current order could exist as the ground state of this charge density wave. However, this microscopic interpretation remains debated and experimentally unverified. In this work, we employ individual magnetic atoms as local quantum sensors to examine the quasiparticle excitations of the charge density wave in CsV$_3$Sb$_5$ with the scanning tunneling microscope. Our spectroscopic measurements show that the magnetic moment of Co induces a spatially localized $dI/dV$ peak inside the spectral gap of the charge density wave near the Fermi energy. Conducting temperature-dependent spectroscopy, we find that this spectral feature emerges at $T<30\,$K. By comparing our experimental observations with results of quantum many-body simulations and realistic tight-binding model calculations, we show that this spectroscopic signature can be naturally interpreted as a local flux defect in a loop current ordered state, arising from the Kondo coupling of the magnetic moment of Co with the loop current electrons. The excellent agreement between our experimental and theoretical results suggests the presence of loop-current order in the $2a\times2a$ charge density wave of CsV$_3$Sb$_5$ at $T<30\,$K. Our results provide a microscopic picture to the observation of time-reversal symmetry breaking orbital magnetism and anomalous transport signatures detected in measurements of the macroscopic material properties.

cond-mat.str-el↗

arXiv2026

Spectroscopic fingerprints of a ferroaxial charge density wave

Unconventional charge density waves (CDWs) with complex order parameters can host exotic collective modes and non-trivial topologies. They have emerged as a new frontier in the study of quantum matter. Recent experiments on rare-earth tritellurides have reported evidence for a ferroaxial CDW through the detection of characteristic Raman modes. This phase, often regarded as a hidden order, has been recognized to arise from the coupling between charge and orbital degrees of freedom in these materials. Yet, spectroscopic insight into its underlying electronic structure and the explicit form of its order parameter symmetry has remained elusive. Here, we present results from linearly polarized angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) measurements of the CDW phase in LaTe$_3$. Our ARPES measurements reveal a complex landscape of spectral gaps across the reconstructed Fermi surface, while our STM-based quasiparticle interference (QPI) mapping, enhanced through the selective deposition of atomic scattering centers, directly reveals an inter-orbital CDW with mixed $p_x$-$p_z$ orbital character. The detailed analysis of the QPI characteristics in terms of the order parameter symmetry within the orbital subspace of the Fermi surface suggests a mixed CDW phase with substantial ferroaxial component, which breaks all vertical mirror symmetries. More broadly, our work establishes a powerful spectroscopic pathway, based on scattering off individual atoms, for identifying and characterizing hidden, multi-component electronic orders in quantum materials using STM and ARPES measurements.

cond-mat.str-el↗

arXiv2026

Ising Dirac fermions across a topological phase transition

Dirac fermions have attracted significant interest due to their relativistic dispersions and close connections to topological physics, yet they are generally expected to be gapped in two-dimensional systems with strong Ising spin orbit coupling, making their realization in such materials an outstanding challenge. Here we report the emergence of six fold degenerate Dirac fermions in an Ising moire system across a quantum spin Hall transition in twisted WSe2. In a 3.65 degree device, we observe a quantum spin Hall phase at high electric fields with nearly quantized resistance h/(2e2), and a Dirac semimetal phase over a broad range of electric fields near zero field. Magnetotransport measurements of the Dirac phase exhibit a half-integer Landau fan sequence, characteristic of Dirac fermions, with six-fold degeneracy on the hole-doped side and two fold degeneracy on the electron-doped side. Temperature dependence shows weakly metallic behavior consistent with a semimetallic state. Our twist-angle-dependent transport measurements map out a complete phase diagram and identify a critical twist angle of 3.3 degree, establishing the phase boundary between the quantum spin Hall and Dirac semimetal regimes. Our work establishes a new route to realizing Dirac fermions in strongly spin orbit coupled moire systems through a topological phase transition, providing a promising platform for high mobility spintronics.

cond-mat.mes-hall↗

arXiv2026

Moire driven edge reconstruction in Fractional quantum anomalous Hall states

We investigate fractional edge modes in moire fractional quantum anomalous Hall states, focusing on the role of lattice momentum conservation and umklapp scattering. For the hierarchical nu=2/3 state, we show that, for a class of microscopic edge realizations, moire-enabled umklapp processes can stabilize the Kane-Fisher-Polchinski fixed point even in the absence of disorder. Our results illustrate how lattice momentum constraints can qualitatively reshape the interaction structure and low-energy behavior of fractional edge modes. The study of Umklapp processes in edge reconstruction serves as a crucial bridge to understanding thermal and electrical transport in the hierarchical fractional quantum anomalous Hall states found in lattice systems of quantum simulators.

cond-mat.mes-hall↗

arXiv2026

Peak-valley mechanism for Hilbert space fragmentation

Ergodicity breaking in isolated systems has emerged as an important frontier in the study of quantum many-body physics. While generic Hamiltonians are expected to obey the eigenstate thermalization hypothesis (ETH), recent studies on Hilbert space fragmentation (HSF) have revealed possible robust nonthermal behavior even in disorder-free systems. Although numerous models exhibiting strong HSF are already known, existing analyses are typically model dependent, and a general organizing principle remains elusive. In this work, we introduce a simple mechanism for achieving strong HSF in one-dimensional integer spin chains, which we term "peak-valley (PV) fragmentation". The key idea is to devise a simple local rule which ensures the spin states in the computational basis can be labeled by a set of emergent good quantum numbers corresponding to the heights and depths of alternating peaks and valleys in a geometrical representation. We demonstrate that some known examples of strong HSF models, as well as their variants which break the HSF property, can be understood within the framework of PV fragmentation. Our approach also enables systematic construction of new fragmented models in higher-spin systems, and allows us to identify higher-order HSF models.

quant-ph↗

arXiv2026

Interplay of ferromagnetism, nematicity and Fermi surface nesting in kagome flat band

Recent experiment on Fe-doped CoSn has uncovered a series of correlated phases upon hole doping of the kagome flat bands. Among the phases observed, a nematic phase with a six- to two-fold rotation symmetry breaking is found to prevail over a wide doping and temperature range. Motivated by these observations, we investigate the interaction-driven phases realized in a kagome model with partially filled, weakly dispersing flat bands. Density-density interactions up to second-nearest neighbors are considered. We identify a close competition between ferromagnetic and nematic phases in our self-consistent Hartree-Fock calculations: while on-site interaction favors ferromagnetism, the sizable inter-sublattice interactions stabilize nematicity over a wide doping window. Competition from translational-symmetry-breaking phases is also considered. Overall, our results show that nematicity is a generic outcome of partially filled kagome flat bands and establish a minimal framework for understanding correlated flat-band phases.

cond-mat.str-el↗

arXiv2026

Toward bootstrapping tensor-network contractions

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars. We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem, thereby yielding certified lower and upper bounds on expectation values of physical observables. As a proof-of-principle, we construct such constraints explicitly for translationally invariant matrix product states and demonstrate that, assuming a canonical form, second-order-cone relaxation can provide tight bounds on the contraction result. We further demonstrate that when the requirement on canonical form is lifted, a more general semidefinite-programming approach could yield similar tight bounds at higher but still polynomial computational cost. Our work suggests numerical bootstrap could be a possible way forward for the rigorous contractions of tensor networks.

cond-mat.str-el↗

arXiv2026

Catalog of phonon emergent particles and chiral phonons: Symmetry-based classification and materials database investigation

Chirality and topology are fundamental and ubiquitous in nature. Symmetry has proven to be a powerful tool for predicting topological phonons. However, to date, topological phonon emergent particles (EMPs) have not been systematically cataloged in material databases. Moreover, traditional symmetry methods are often inadequate for predicting chiral phonons, because realistic calculations can yield negative results even when symmetry analysis permits phonon chirality. Here, we first establish a complete symmetry-based classification: given any space group and Wyckoff positions (WYPOs) occupied by atoms, the number of occurrences of all (co-)irreducible representations ((co-)irreps) (that can host EMPs) can be unambiguously known without omission prior to expensive and parameter-dependent calculation. Moreover, whether a phonon mode (belonging to one (co-)irrep) is chiral can also be determined from the occupied WYPOs. We then perform a materials database investigation identifying over 25 million EMPs at high-symmetry points and along high-symmetry lines and computing the concrete value of phonon angular momentum for each mode. We demonstrate two main applications: identifying ideal materials with surface chirality momentum locking and identifying materials with giant phonon magnetic moment. All computational data are compiled into a website: http://phonon.nju.edu.cn, which is expected to stimulate future studies on topological and chiral phonons.

cond-mat.mtrl-sci↗

arXiv2026

Frustration-free free fermions

We develop a general theory of frustration-free free-fermion systems and derive the necessary and sufficient conditions for such Hamiltonians. Assuming locality and translation invariance, we find that any band touching between the valence and the conduction bands is always quadratic or softer, which rules out the possibility of describing Dirac and Weyl semimetals using frustration-free local Hamiltonians. We further construct a frustration-free free-fermion model on the honeycomb lattice and show that its density fluctuations acquire an anomalous gap originating from the diverging quantum metric associated with the quadratic band-touching points. Nevertheless, an $O(1/L^2)$ finite-size scaling of the charge-neutral excitation gap can be verified even in the presence of interactions, consistent with the more general results we derive in an accompanying work [arXiv:2503.12879].

cond-mat.str-el↗

arXiv2026

Frustration-free free fermions and beyond

Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems. In this paper, we establish a general framework for frustration-free fermionic systems. First, we derive a necessary and sufficient condition for a free fermion model to be frustration-free. In the case of translation-invariant, noninteracting systems, we show that any band touching between the valence and conduction bands is at least quadratic. Furthermore, by extending the Gosset-Huang inequality to fermionic systems, we demonstrate that even in interacting and non-translation-invariant cases, the finite-size gap of gapless excitations scales as $O((\log L)^2/L^2)$, provided the ground-state correlation function exhibits a power-law decay. Our results provide a foundation for studying frustration-free fermionic systems, including flat-band ferromagnetism and $η$-pairing states.

cond-mat.str-el↗

arXiv2025

Mirror-Selective Quasiparticle Interference in Bilayer Nickelate Superconductor

The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates has garnered significant attention. In this study, inspired by recent STM experiments on thin films, we investigate the quasiparticle interference (QPI) characteristics of bilayer nickelates in both normal and superconducting states to identify their Fermiology and pairing symmetry. We demonstrate that the mirror symmetry inherent in the bilayer structure induces mirror-selective quasiparticle scattering by establishing selection rules based on the mirror properties of impurities and the mirror eigenvalues of electronic wavefunctions. This mirror-selective scattering allows for the differentiation of distinct Fermiologies, as QPI patterns vary markedly between scenarios with and without the $d_{z^2}$-bonding Fermi surface (FS). Furthermore, it enables the separate detection of sign changes in superconducting gaps both within the same FS and between different FSs. Crucially, if the mirror-symmetry-enforced selection rules are ignored, the QPI response of an $s_\pm$-wave state can masquerade as that of a conventional $s$-wave state, leading to a misidentification of the pairing symmetry. When combined with field-dependent and reference QPI measurements, this approach facilitates the precise determination of pairing symmetry, even in the presence of FS-dependent gaps and gap anisotropy. Additionally, we discuss practical considerations for STM measurements to effectively identify the pairing symmetry. Our findings demonstrate that mirror-selective QPI is a powerful tool for distinguishing between different Fermiologies and pairing states, which is helpful in pinning down pairing symmetry and revealing the pairing mechanism in bilayer nickelates.

cond-mat.supr-con↗

arXiv2025

Stabilizer Perturbation Theory: A Systematic Construction via Schrieffer-Wolff Transformation

Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have gained increasing prominence as another class of models for quantum systems thanks to the recent advances in experimentally realizing mesoscopic quantum devices. Stabilizer states, innately defined on systems of qudits, have correspondingly emerged as another class of classically simulatable starting point for the study of quantum error-correcting codes and topological phases of matter in such devices. As a step towards analyzing more general quantum many-body problems on these platforms, we develop a systematic stabilizer perturbation theory in qubit systems. Our approach relies on the local Schrieffer-Wolff transformation, which we show can be efficiently performed through the binary encoding the Pauli algebra. As demonstrations, we first benchmark the stabilizer perturbation theory on the transverse field Ising chain in one dimension. The method is then further applied to $\mathbb{Z}_2$ toric code on square lattice and kagome lattice to probe the tendency toward confinement for anyonic excitations.

quant-ph↗

arXiv2025

Anomalous Landau levels and quantum oscillation in rotation-invariant insulators

Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field Fermi surface. Focusing on two-dimensional multi-band low-energy models of electrons with continuous rotation symmetry, we show that an effective-band description, akin to the semiclassical treatment of Landau level problems in metals, can be used to predict the Landau level spectrum, including possible ALLs. This description then describes ALL induced quantum oscillation for certain insulating models, which we demonstrate through numerical calculations.

cond-mat.str-el↗

arXiv2025

Unitary network: Tensor network unitaries with local unitarity

We introduce unitary network, an oriented architecture for tensor network unitaries. Compared to existing architectures, in a unitary network each local tensor is required to be a unitary matrix upon suitable reshaping. Global unitarity is ensured when the network obeys a suitable ordering property. Unitary operators represented by unitary networks need not preserve locality. In particular, we show that the class of unitary networks encompasses global unitaries which preserve locality up to exponentially suppressed tails, as in those that naturally arise from the finite-time evolution of local Hamiltonians. Non-invertible symmetries, as exemplified by the non-local Kramers-Wannier duality in one dimension, can also be represented using unitary networks. We also show that information flow in a unitary network can be characterized by a flow index, which matches the known index for quantum cellular automata as a special case.

quant-ph↗

arXiv2025

Quasi-local Frustration-Free Free Fermions

Recent studies have revealed that frustration-free models, expressed as sums of finite-range interactions or hoppings, exhibit several properties markedly different from those of frustrated models. In this work, we demonstrate that, by relaxing the finite-range condition to allow for exponentially decaying hoppings, one can build gapped frustration-free systems that realize Chern insulators as well as quasi-degenerate ground states with finite-size splittings. Moreover, by permitting power-law decaying hoppings, we also construct a gapless band metal whose finite-size gap scales inversely with the system size $L$. These findings serve as an important step toward clarifying the general properties of frustration-free systems and those represented by tensor network states.

cond-mat.str-el↗

arXiv2025

Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor

Vortex lines, known as topological defects, are cable of trapping Majorana modes in superconducting topological materials. Previous studies have primarily focused on topological bands with conventional s-wave pairing. However, topological Dirac semimetals exhibiting a unique orbital texture can favor unconventional pairing when electronic correlations are significant. The topology of vortices in these systems has yet to be explored. In this work, we investigate the vortex bound states in superconducting Dirac semimetals, with a particular focus on the orbital-singlet unconventional pairing, which generates higher-order Majorana hinge modes. Remarkably, we identify robust double Majorana vortex flat bands at zero energy. In type-I Dirac semimetals, these Majorana flat bands are located between the projections of two superconduting Dirac points. In contrast, in type-II Dirac semimetals, they extend across the entire 1D Brillouin zone. These double flat bands arise from a nontrivial $\mathbb{Z}_2$ topology defined by an effective particle-hole symmetry and are protected by the four-fold rotational symmetry. Additionally, we observe that moving the vortex line close to a hinge can trivialize the higher-order Majorana arc on the hinge, leaving a single Majorana mode at the vortex core due to the hybridization of Majorana modes. Finally, we discuss the potential experimental implications for correlated Dirac semimetals, such as electron-doped iron-based superconductors.

cond-mat.supr-con↗

arXiv2024

Catalog of phonon emergent particles

The outcome of conventional topological materials prediction scheme could sensitively depend on first-principles calculations parameters. Symmetry, as a powerful tool, has been exploited to enhance the reliability of predictions. Here, we establish the relationship between the Wyckoff positions (WYPOs) and the phonon wavefunctions at each high-symmetry point (HSP) in all 230 space groups (SGs). Based on this, on one hand, we obtain a complete mapping from WYPO to the occurrence of emergent particles (EMPs) at each HSP in 230 SGs, and establish several rules of enforcing EMPs for phonons; on the other hand, we determine the contribution of the WYPO to the phonon angular momentum. Then we unambiguously identify 20,516,167 phonon EMPs in 111,872 materials in two databases. The purely symmetry-determined wavefunctions generalize the conventional Bloch theorem, could find a wide scope of application to physical properties related with basis functions of irreducible representations.

cond-mat.mtrl-sci↗

arXiv2024

Cascade of strongly correlated quantum states in a partially filled kagome flat band

Coulomb interactions among charge carriers that occupy an electronic flat band have a profound impact on the macroscopic properties of materials. At sufficient strength, these interactions can give rise to captivating phenomena such as quantum criticality, Mott-Hubbard states, and unconventional superconductivity. The appearance of these characteristics sensitively depends on the number of electrons occupying the flat band states. In this work, we present experimental evidence obtained from scanning tunneling microscopy measurements for a cascade of strongly correlated states appearing in the partially occupied kagome flat bands of Co$_{1-x}$Fe$_x$Sn whose filling can be controlled by the Fe-doping level $x$. At elevated temperatures ($T\geq16\,K$), we detect a nematic electronic state across a broad doping range $0.05 100\,$meV) blend the states of two $3d$-orbital derived flat bands and impart a nematic order parameter. This state serves as the parent phase of a strongly correlated phase diagram: At lower temperatures $T<16\,$K, we find spectroscopic evidence for an orbital-selective Mott state enabled by the $3d$-orbital degeneracy of the Co atom. This state can only be detected in samples with ideal Fe doping ($x=0.17$) and descends into pseudogap phases upon electron and hole doping. At $T<8\,$K, the pseudogap phase evolves into another nematic low temperature state. Our observations demonstrate that the electronic ground state of a kagome flat band depends on the complex interplay between strong Coulomb repulsion, $3d$-orbital degeneracy, and flat band filling fraction at different temperatures.

cond-mat.str-el↗