arXiv subjects

Han-Qing Wu

Publications and source records attributed to Han-Qing Wu.

At least 19 recordsLinked to original sources

arXiv2026

Spiral and Mixed Plaquette-Dimer Phases in the $S=1$ and $3/2$ Shastry-Sutherland Heisenberg Model

We investigate the ground-state phase diagram of the $S=1$ and $S=3/2$ Heisenberg model on the two-dimensional Shastry-Sutherland lattice (SSL) using density matrix renormalization group (DMRG) and cluster mean-field theory (CMFT). Between the dimer phase and N\'{e}el antiferromagnetic phases, we identify two intermediate phases: a mixed plaquette-dimer (MPD) phase and a spiral phase. These phases are characterized via bond energies and spin-spin correlation functions; phase boundaries are located from the ground-state energy derivative and entanglement entropy. The MPD phase exhibits strong intradimer correlations and weak tetramerization on the empty plaquettes, and its transitions to the dimer and spiral phases are first order. Combining our results with the known boundaries for $S=1/2$ and the classical limit $S\to\infty$, we construct a global $S$-$g$ phase diagram. This diagram reveals the progressive suppression of quantum effects with increasing $S$ and offers a theoretical framework for larger-$S$ SSL materials.

cond-mat.str-el↗

arXiv2026

Spiral Phase and Phase Diagram of the $S$=1/2 XXZ Model on the Shastry-Sutherland Lattice

We investigate the ground-state phase diagram of the $S$=1/2 XXZ model on the two-dimensional Shastry-Sutherland lattice using exact diagonalization (ED), density-matrix renormalization group (DMRG), and cluster mean-field theory (CMFT) with DMRG as a solver. In the isotropic case ($\Delta=1$), CMFT results reveal an intermediate empty plaquette (EP) phase that has a lower energy than the full plaquette (FP) phase. However, due to mean-field artifacts, CMFT alone is not suitable for accurately determining phase boundaries. Therefore, we combined three methods to map out the reliable phase diagram. Our calculations show that the EP phase narrows as $\Delta$ deviates from unity and eventually vanishes. More importantly, we identify a spiral phase at small $\Delta$, which has not been reported in previous studies. This phase is clearly captured by DMRG simulations on long cylindrical geometries. The competition between the EP, spiral, and $xy$-AFM phases near their boundaries provides a plausible explanation for the emergent spin-liquid-like behavior in RE$_2$Be$_2$GeO$_2$, while shedding new light on the role of XXZ anisotropy in the Shastry-Sutherland XXZ model.

cond-mat.str-el↗

arXiv2025

Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice

Using stochastic series expansion quantum Monte Carlo and density matrix renormalization group methods, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg model on the two-dimensional square-hexagon-octagon (SHO) lattice. The model incorporates nearest-neighbor interactions $J_1$ (intrahexagon interaction) and $J_2$ (interhexagon), as well as a selected third-neighbor interaction $J_3$ along the $x$ direction. We identify five distinct phases in the parameter regime $0<\lambda_1=J_2/J_1<4, 0<\lambda_2=J_3/J_1<4$: a N\'eel antiferromagentic phase, two dimer phases (orthogonal and ladder staggered dimers), a hexagon singlet phase, and notably a Haldane-like symmetry-protected topological (SPT) phase. The topological nature of the Haldane-like phase is confirmed by the degeneracy of the ground-state energy under open boundary conditions and the twofold degeneracy of the entanglement spectrum. Phase boundaries are accurately determined using finite-size scaling of the spin stiffness and Binder cumulant. Data collapse analysis reveals that all transitions from nonmagnetic phases to the antiferromagnetic phase belong to the three-dimensional $O(3)$ Heisenberg universality class. In addition, we investigate the robustness of the SPT phase to other interactions, such as those that could arise in experimental materials. Our work establishes a comprehensive theoretical framework for understanding magnetic and topological phases on the SHO lattice.

cond-mat.str-el↗

arXiv2025

Mott Glass and Criticality in a S=1/2 Bilayer Heisenberg Model with Interlayer Bond Dilution

We employ the stochastic series expansion quantum Monte Carlo (SSE-QMC) method to investigate the $S = 1/2$ antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a N\'eel-ordered phase to a quantum disordered phase, consistent with the $O(3)$ universality class. In contrast, random dilution gives rise to a two-step transition: from the N\'eel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence $\chi_u \sim \exp(-b/T^\alpha)$, $0 < \alpha < 1$. At the N\'eel-to-glass transition, quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.

cond-mat.str-el↗

arXiv2025

Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding

Among the extensive studies of fractional quantum anomalous Hall (FQAH) states, there recently appears a growing interest in the topological states with coexisting charge density wave (CDW) orders. Such states are referred to as Hall crystals. However, compared to those with integer Hall conductivities, the FQAH crystal (FQAHC) is still elusive even at the level of microscopic model. In this work, we numerically study a topological flat-band model on triangular lattice with spinless fermions. At fractional filling of the Chern band, the nearest-neighbor interaction leads to a commensurate and topologically trivial CDW state. Interestingly, the folded mini-band above the CDW gap is non-trivial, and we focus on the doping of it without any projection. A series of (F)QAHC states at (fractional) integer fillings of this mini-band are discovered and some FQAHC state might even exist in less "ideal" conditions. The ground-state degeneracies of such (F)QAHC states are enlarged by the CDW degeneracy and the Hall conductivities -- determined by the fillings of the mini-band -- are different from the fillings of the original Chern band. We also study the thermodynamics of an FQAHC state and find a compressible CDW phase at intermediate temperatures, which might serve as a precursor of lower temperature FQAHC phase. Moreover, we numerically demonstrate that such a generic scheme of doping CDW-folded topological mini-band could be applied to bosonic systems, broadening the platforms of Hall-crystal physics and motivating its exploration in quantum moire and cold-atom systems.

cond-mat.str-el↗

arXiv2025

Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction

Using Lanczos exact diagonalization (ED), we study the spin-1/2 $J_1$-$J_2$ Heisenberg model with the four-spin ring-exchange interaction $J_r$ on triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer and chiral correlation functions. The ground state has rich phases including several magnetic ordered phases like zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction, and help to understand the relevant triangular materials.

cond-mat.str-el↗

arXiv2025

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↗

arXiv2024

Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator

Employing the state-of-the-art time-dependent variational principle (TDVP) algorithm, we compute the spectra of charge-neutral excitations in the $\nu=1/2$ (bosonic) \updated{ and $1/3$ (fermionic) fractional Chern insulator (FCI)} on the Haldane honeycomb lattice model. The magnetoroton visualized from the dynamic density structure factor acquires a minimum gap at finite momentum that can go soft with increasing interaction and give rise to a charge density wave (CDW) at the same wavevector. As the system approaches the FCI-to-CDW transition point, we observe a pronounced sharpening of the roton mode, suggesting that the magnetoroton behaves more like a quasiparticle as it softens. Notably, this occurs while the single-particle gap remains finite. Besides the magnetoroton at finite momentum, we also construct quadrupolar chiral operators in a discrete lattice and resolve the chiral graviton mode around the $\Gamma$ point of the Brillouin zone. Furthermore, we show the different chiralities of the gravitons of FCIs with opposite-sign Hall conductance for the first time.

cond-mat.str-el↗

arXiv2024

Correlation Effects in a Simplified Bilayer Two-Orbital Hubbard Model at Half Filling

Motivated by the discovery of high-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure, we investigate the ground-state phase diagram and correlation effects using determinant quantum Monte Carlo simulations in a simplified bilayer two-orbital Hubbard model at half filling. Our results reveal the emergence of a nonmagnetic weakly insulating phase at weak on-site Hubbard interactions, transitioning to an antiferromagnetic Mott insulating phase as the interaction strength exceeds a critical value $U/t_1^x\approx 4.15$. This phase transition is consistent with the 3D O(3) Heisenberg universality class. Additionally, we analyze dynamical properties such as the single-particle spectral function and dynamic spin structure factor. The pronounced inter-layer correlation of $d_{3z^2-r^2}$ orbitals results in a downward trend and an extended flatness in the $\gamma$ band, mirroring the angle-resolved photoemission spectroscopy findings under ambient pressure. Our numerical results provide important clues for understanding the strong correlation effects in La$_3$Ni$_2$O$_7$.

cond-mat.str-el↗

arXiv2024

Vestigial Gapless Boson Density Wave Emerging between $\nu = 1/2$ Fractional Chern Insulator and Finite-Momentum Supersolid

The roton-triggered charge-density-wave (CDW)is widely studied in fractional quantum Hall (FQH) and fractional Chern insulator (FCI) systems, and there also exist field theoretical and numerical realizations of continuous transition from FCI to superfluid (SF). However, the theory and numerical explorations of the transition between FCI and supersolid (SS) are still lacking. In this work, we study the topological flat-band lattice models with $\nu$ = 1/2 hard-core bosons, where the previous studies have discovered the existence of FCI states and possible direct FCI-SS transitions. While the FCI is robust, we find the direct FCI-SS transition is absent, and there exist more intriguing scenarios. In the case of checkerboard lattice, we find an intermediate gapless CDW state without SF, sandwiched between FCI and SS. This novel state is triggered by the roton instability in FCI and it further continuously brings about the intertwined finite-momentum SF fluctuation when the CDW order is strong enough, eventually transiting into an unconventional finite-momentum SS state. The intermediate gapless CDW state is a vestige from the SS state, since the increasing quantum fluctuation melts only the Larkin-Ovchinnikov-type SF order in SS but its (secondary) product -- the CDW order -- survives. On honeycomb lattice, we find no evidence of SS, but discover an interesting sequence of FCI-Solid I-Solid II transitions, with both solids incompressible. Moreover, in contrast to previous single-roton condensation, this sequence of FCI-Solid I-Solid II transitions is triggered by the softening of multi-roton modes in FCI. Considering the intertwined wave vectors of the CDW orders, Solid I is a vestige of Solid II. Our work provides new horizon not only for the quantum phase transitions in FCI but also for the intertwined orders and gapless states in bosonic systems, which will inspire future studies.

cond-mat.mes-hall↗

arXiv2024

Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid

The properties of fractional Chern insulator (FCI) phases and the phase transitions between FCI and Mott insulators (MI) in bosonic systems are well studied. The continuous transitions between FCI and superfluid (SF), however, despite the inspiring field theoretical predictions, have not been directly verified. The existing numerical results of the FCI-SF transition are either indirect or clearly first-order. Here, by simply tuning the bandwidth of the Haldane honeycomb lattice model, we find direct transitions from a bosonic FCI at $\nu=1/2$ filling of a flat Chern band to two SF states with bosons condensed at momenta M or $\Gamma$, respectively. While the FCI-SF(M) transition is first-order, the FCI-SF($\Gamma$) transition is found continuous, and the bipartite entanglement entropy at the critical point with the area-law scaling is consistent with the critical theories. Through finite size criticality analysis, the obtained critical exponents $\beta\approx$ 0.35(5) and $\nu\approx$ 0.62(12) are both compatible with those of the 3D XY universality class within numerical uncertainty and possibly more exotic beyond-Landau ones. This letter thence presents a direct numerical demonstration of a continuous FCI-SF transition between topologically ordered phase and spontaneous continuous symmetry-breaking phase, and further indicates the zero-field bosonic FCI might be realized from a SF state by gradually flattening the dispersion of the Chern band, through the (quasi)adiabatic preparation in ultracold atom systems.

cond-mat.str-el↗

arXiv2024

Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands

Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous time-reversal-symmetry breaking have garnered attention. While the thermodynamics of integer quantum anomalous Hall (IQAH) states have been systematically studied, our theoretical knowledge on thermodynamic properties of FQAH states has been severely limited. Here, we delve into the general thermodynamic response and collective excitations of both IQAH and FQAH states within the paradigmatic flat Chern-band model with remote band considered. Our key findings include: i) In both $ν$ = 1 IQAH and $ν$ = 1/3 FQAH states, even without spin fluctuations, the charge-neutral collective excitations would lower the onset temperature of these topological states, to a value significantly smaller than the charge gap, due to band-mixing and multi-particle scattering; ii) By employing large-scale thermodynamic simulations in FQAH states in the presence of strong inter-band mixing between C = $\pm1$ bands, we find that the lowest collective excitations manifest as the zero-momentum excitons in the IQAH state, whereas in the FQAH state, they take the form of magneto-rotons with finite momentum; iii) The unique charge oscillations in FQAH states are exhibited with distinct experimental signatures, which we propose to detect in future experiments.

cond-mat.str-el↗

arXiv2024

Continuous transition and gapless roton inside fractional quantum anomalous Hall states

Collective excitations play a vital role in understanding the exotic phases of matter and phase transitions in quantum many-body systems. For the first time, we numerically (via exact diagonalization and density matrix renormalization group) report the microscopic realization of a transition from a translationally invariant fractional quantum anomalous Hall (FQAH) state to the same FQAH state with spontaneously broken translation symmetry, by softening the magnetoroton mode (intrinsic collective excitations in such systems) through isotropic interactions in a topological flat-band model. At the critical point, the gap of collective neutral excitations closes at finite momentum, while the charge gap remains robust. This mechanism echoes with the integer quantum Hall crystals and fractional quantum Hall nematics in Landau levels, but exhibits unique features. Further through criticality analysis, we identify that this non-trivial transition is consistent with the Ising universality class. Such spontaneous translation symmetry breaking inside the topological ordered FQAH state could serve as a generic scheme in various systems, with experimental implications to the quantum moir\'e materials and the cold-atom systems.

cond-mat.str-el↗

arXiv2024

Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_χ$ model on the square lattice

We study the spin-$1/2$ Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$, as well as the three-spin scalar chiral coupling $J_χ$. Using density matrix renormalization group calculations, we obtain a quantum phase diagram of this system for $0 \leq J_2/J_1 \leq 1.0$ and $0 \leq J_χ/J_1 \leq 1.5$. We identify the Néel and stripe magnetic order phase at small $J_χ$ coupling. With growing $J_χ$, we identify the emergent chiral spin liquid (CSL) phase characterized by the quantized spin Chern number $C = 1/2$ and entanglement spectrum with the quasidegenerate group of levels agreeing with chiral SU(2)$_1$ conformal field theory, which is an analog of the $ν= 1/2$ Laughlin state in spin system. In the vicinity of the Néel and CSL phase boundary, our numerical results do not find evidence to support the phase coexistence of Néel order and topological order that was conjectured by mean-field calculations. In the larger $J_2$ and $J_χ$ coupling regime, the entanglement spectrum of the ground state also exhibits the chiral quasidegeneracy consistent with a CSL, but the adiabatic flux insertion simulations fail to obtain the quantized Chern number. By analyzing the finite-size scaling of magnetic order parameter, we find the vanished magnetic order suggesting a magnetic disorder phase, whose nature needs further studies. Different from the spin-$1$ $J_1$-$J_2$-$J_χ$ model, we do not find the coexistent stripe magnetic order and topological order. We also investigate the $J_χ$ dominant regime and find a strong tendency of the system to develop a dimer order rather than the chiral spin magnetic order observed in the spin-$1$ model.

cond-mat.str-el↗

arXiv2024

Interaction-driven Roton Condensation in C = 2/3 Fractional Quantum Anomalous Hall State

The interplay of topological order and charge order exhibits rich physics. Recent experiments that succesfully realized the frational quantum anomalous Hall (FQAH) effect in twisted MoTe$_2$ bilayers and rhombohedral multilayer graphene without external magnetic field further call for deeper understanding of the relation between topological order and charge order in quantum moiré materials. In the archetypal correlated flat-band model on checkerboard lattice, a FQAH smectic state with coexistent topological order and smectic charge order has been numerically discovered at filling $ν$ = 2/3. In this work, we explore the global ground-state phase diagram of the model with competing interactions and find a C = 2/3 FQAH phase surrounded by four different charge density wave (CDW) phases. In particular, we identify a FQAH-CDW transition triggered by roton condensation, in that, the minimal roton gap continues to decrease at the same finite momentum, along with the diverging density flucuations at the transition point, after which the system enters into a CDW metal phase with the same ordered wavevector. Our discovery points out that the charge-neutral roton modes can play a significant role in a transition from FQAH topological order to CDW symmetry-breaking order, discussed in FQH literature while severely neglected in FQAH systems.

cond-mat.str-el↗

arXiv2024

Quantum phase transitions and composite excitations of antiferromagnetic spin trimer chains in a magnetic field

Motivated by recent advancements in theoretical and experimental studies of the high-energy excitations on an antiferromagnetic trimer chain, we numerically investigate the quantum phase transition and composite dynamics in this system by applying a magnetic field. The numerical methods we used include the exact diagonalization, density matrix renormalization group, time-dependent variational principle, and cluster perturbation theory. From calculating the entanglement entropy, we have revealed the phase diagram which includes the XY-I, $1/3$ magnetization plateau, XY-II, and ferromagnetic phases. Both the critical XY-I and XY-II phases are characterized by the conformal field theory with a central charge $c \simeq 1$. By analyzing the dynamic spin structure factor, we elucidate the distinct features of spin dynamics across different phases. In the regime with weak intertrimer interaction, we identify the intermediate-energy and high-energy modes in the XY-I and $1/3$ magnetization plateau phases as internal trimer excitations, corresponding to the propagating of doublons and quartons, respectively. Notably, applying a magnetic field splits the high-energy spectrum into two branches, labeled as the upper quarton and lower quarton. Furthermore, we explore the spin dynamics of a frustrated trimerized model closely related to the quantum magnet \ce{Na_2Cu_3Ge_4O_12}. In the end, we extend our discuss on the possibility of the quarton Bose-Einstein condensation in the trimer systems. Our results are expected to be further verified through the inelastic neutron scattering and resonant inelastic X-ray scattering, and also provide valuable insights for exploring high-energy exotic excitations.

cond-mat.str-el↗

arXiv2023

Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models

We investigate the magnetic excitations of the trimerized Heisenberg models with intra-trimer interaction $J_1$ and inter-trimer interaction $J_2$ on four different two-dimensional lattices using a combination of stochastic series expansion quantum Monte Carlo (SSE QMC) and stochastic analytic continuation methods (SAC), complemented by cluster perturbation theory (CPT). These models exhibit quasi-particle-like excitations when $g=J_2/J_1$ is small, characterized by low-energy magnons, intermediate-energy doublons, and high-energy quartons. The low-energy magnons are associated with the magnetic ground states. They can be described by the linear spin wave theory (LSWT) of the effective block spin model and the original spin model. Doublons and quartons emerge from the corresponding internal excitations of the trimers with distinct energy levels, which can be effectively analyzed using perturbation theory when the ratio of exchange interactions $g$ is small. In this small $g$ regime, we observe a clear separation between the magnon and higher-energy spectra. However, as $g$ increases, these three spectra gradually merge into the magnon modes or continua. Nevertheless, the LSWT fails to provide quantitative descriptions of the higher-energy excitation bands due to significant quantum fluctuations. Notably, in the Collinear II and trimerized hexagon lattice, a broad continuum emerges above the single-magnon spectrum, originating from the quasi-1D physics due to the dilute connections between chains. Our numerical analysis of these 2D trimers yields valuable theoretical predictions and explanations for the inelastic neutron scattering (INS) spectra of 2D magnetic materials featuring trimerized lattices.

cond-mat.str-el↗

arXiv2023

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling $\nu=2/3$ and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is $\sigma_{xy}=\nu=2/3$, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

cond-mat.str-el↗