arXiv subjects

Zi Yang Meng

Publications and source records attributed to Zi Yang Meng.

At least 37 records · Page 2Linked to original sources

arXiv2026

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↗

arXiv2026

Emergent gauge flux in mixed QED$_3$ with flavor chemical potential: application to magnetized U(1) Dirac spin liquids

We design a lattice model of a "mixed" U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations, For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics (QED$_3$) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, corresponding to a Zeeman field perturbing the Dirac spin liquid, we find a "chiral flux" phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. In this state, the U(1)$_m$ magnetic symmetry is spontaneously broken, leading to a gapless free photon mode which, due to spin-flux-attachment, is observable in the longitudinal spin structure factor. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

cond-mat.str-el↗

arXiv2026

Vestigial Gapless Boson Density Wave Emerging between $ν= 1/2$ 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 $ν$ = 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↗

arXiv2026

Quantum Fisher Information as a Probe of Critical Scaling in Frustrated Magnets: Signatures from Kagome Quantum Spin Liquid

Quantum Fisher information (QFI) is a measure of multipartite quantum entanglement that can be obtained from inelastic neutron scattering data on quantum magnets. In this work, we demonstrate that the QFI can distinguish an unconventional quantum critical point (QCP) with fractionalization and emergent gauge structure from conventional ones within the Landau paradigm. We compute the QFI, via large-scale quantum Monte Carlo (QMC) simulations and exact diagonalization, in a kagome lattice quantum spin liquid (QSL) model with an XY and a cluster-Ising interactions. When the XY interaction is ferromagetic, the QFI obtained by QMC reveals a large anomalous dimension, which is a fingerprint of the (2+1)d XY$^\ast$ universality class for the transition from the ferromagnetic phase to the $\mathbb{Z}_2$ QSL. The investigation of thermal and dynamical properties of QFI is further extended to the case of antiferromagnetic XY interaction via exact diagonalization. In this regime, a transition to a possibly distinct QSL phase is suggested via both entanglement-based probes, such as QFI and genuine multipartite negativity, and analyses of the energy spectrum and structure factors. These results not only demonstrate the versatility of QFI in identifying QSL states and unconventional QCPs but also provide useful guidance for future theoretical and experimental studies of frustrated magnets.

cond-mat.str-el↗

arXiv2026

Thermodynamics of Shastry-Sutherland Model under Magnetic Field

Motivated by the recent experimental discovery of the $T$-linear specific heat in pressurized and magnetized Shastry-Sutherland Mott insulator SrCu$_2$(BO$_3$)$_2$, we perform the state-of-the-art thermal tensor-network computation on the Shastry-Sutherland model under a magnetic field. Our simulation results suggest the existence of a symmetric intermediate phase with $T$-linear specific heat at low temperature, occupying a large parameter space and between the plaquette-singlet phase and antiferromagnetic phase at low fields and other symmetry-breaking phases at high fields before the system is fully polarized. Such an unexpected novel state bears an astonishing similarity to the experimental findings in the material. It opens the door to further investigations of the possible liberation of deconfined magnetized Dirac spinons by the competing interactions in this highly frustrated quantum magnet model, and by the combined effects of magnetic field and pressure in the associated Shastry-Sutherland Mott insulator SrCu$_2$(BO$_3$)$_2$.

cond-mat.str-el↗

arXiv2026

Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU

We develop a GPU-accelerated hybrid quantum Monte Carlo (QMC) algorithm to solve the fundamental yet difficult problem of $U(1)$ gauge field coupled to fermions, which gives rise to a $U(1)$ Dirac spin liquid state under the description of (2+1)d quantum electrodynamics QED$_3$. The algorithm renders a good acceptance rate and, more importantly, nearly linear space-time volume scaling in computational complexity $O(N_τ V_s)$, where $N_τ$ is the imaginary time dimension and $V_s$ is spatial volume, which is much more efficient than determinant QMC with scaling behavior of $O(N_τV_s^3)$. Such acceleration is achieved via a collection of technical improvements, including (i) the design of the efficient problem-specific preconditioner, (ii) customized CUDA kernel for matrix-vector multiplication, and (iii) CUDA Graph implementation on the GPU. These advances allow us to simulate the $U(1)$ Dirac spin liquid state with unprecedentedly large system sizes, which is up to $N_τ\times L\times L = 660\times66\times66$, and reveal its novel properties. With these technical improvements, we see the asymptotic convergence in the scaling dimensions of various fermion bilinear operators and the conserved current operator when approaching the thermodynamic limit. The scaling dimensions find good agreement with field-theoretical expectation, which provides supporting evidence for the conformal nature of the $U(1)$ Dirac spin liquid state in the QED$_3$. Our technical advancements open an avenue to study the Dirac spin liquid state and its transition towards symmetry-breaking phases at larger system sizes and with less computational burden.

cond-mat.str-el↗

arXiv2026

T-linear specific heat in pressurized and magnetized Shastry-Sutherland Mott insulator SrCu2(BO3)2

The pressurized Shastry-Sutherland Mott insulator SrCu2(BO3)2 has been found to host a plaquette-singlet phase and an antiferromagnetic phase that break different symmetries spontaneously.The recent experiment showed that their transition is of a first order nature, which seems against the pursuit of exotic and deconfined degrees of freedom in this famous frustrated quantum magnet. We found a new direction in this study. By applying a magnetic field to the material, we discover that SrCu2(BO3)2 exhibits a universal and metallic T-linear specific heat behavior in a large magnetitic field range close to the pressure of zero-field first order transition between plaquette-singlet and antiferromagnetic phases. Such an unexpected gapless response from an electronically gapped Mott insulator could be attributed to magnetized Dirac spinons liberated by the combined effect of magnetic field and pressure, consistently seen from our quantum many-body thermal tensor network computation of the Shastry-Sutherland model under magnetic field. Such a robust and universal T-linear specific heat phase points out the richness of the phase diagram of the material expanded by the axes of pressure and magnetic field and is calling for new theoretical frameworks to its full explanation.

cond-mat.str-el↗

arXiv2026

Hybrid Monte Carlo for Fractional Quantum Hall States

We develop a hybrid Monte Carlo method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology, including global updates and double stereographic projection on spherical geometry, our hybrid Monte Carlo simulation is significantly faster than the widely used Metropolis Monte Carlo scheme. As a result, we can readily simulate systems with electron numbers $N > 1000$ on both disk and sphere geometries. We apply this method to investigating the topological shift obtained from the edge dipole moment, computed from the density of the wave function on the disk. We also numerically computed the non-Abelian braiding matrices for different braiding schemes of the Moore-Read quasiholes on the sphere. Results with much better quality compared with previous works have been achieved. With the thermodynamic limit results obtained at ease, we also discuss the future usage of our method to clarify the questions on the instability of fractional quantum Hall states in an ideal Chern band setting or under quantum decoherence.

cond-mat.str-el↗

arXiv2025

Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model

The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg arrays quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of non-bipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [1] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and $\mathbb{Z}_{2}$ quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of ``remnants of fractionalization" at finite temperature, in that, both the cubic order parameter -- the plaquette loop resonance -- and its constituent -- the vison field -- exhibit independent criticality signatures. This phase transition is connected to a 3-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.

cond-mat.str-el↗

arXiv2025

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 moiré materials and the cold-atom systems.

cond-mat.str-el↗

arXiv2025

Entanglement architecture of beyond-Landau quantum criticality

Quantum critical points beyond the Landau paradigm exhibit fractionalized excitations and emergent gauge fields. Here, we use entanglement microscopy--full tomography of the reduced density matrix of small subregions and subsequent extraction of their quantum correlations--to resolve the entanglement architecture near such exotic critical points. We focus on genuine multipartite entanglement (GME). Through unbiased quantum Monte Carlo sampling of RDMs across conventional O(2)/O(3) Wilson-Fisher transitions, and unconventional XY$^*$, and Néel-VBS transitions in (2+1)d, we discover a dichotomy: Landau criticality amplifies GME within compact subregions, while non-Landau criticality redistributes entanglement into larger, loopy configurations. Key signatures at non-Landau criticality include the absence of three-spin GME, and the loss of non-loopy entanglement in unicursal regions. Similar results in a critical resonating valence bond wavefunction confirm this multipartite entanglement structure as a common feature of emergent gauge theories. Our findings reveal a distinct entanglement architecture in beyond-Landau quantum critical theories.

cond-mat.str-el↗

arXiv2025

Scaling of Disorder Operator and Entanglement Entropy at Easy-Plane Deconfined Quantum Criticalities

We systematically investigate the scaling behaviors of the disorder operator and the entanglement entropy (EE) of the easy-plane JQ (EPJQ) model at its transitions between the antiferromagnetic XY ordered phase (AFXY) and the valence bond solid (VBS) phase. We find there exists a tiny yet finite value of the order parameters at the AFXY-VBS phase transition points of the EPJQ model, and the finite order parameter is strengthened as anisotropy $Δ$ varies from the Heisenberg limit ($Δ=1$) to the easy-plane limit ($Δ=0$). This observation provides evidence that the Néel-VBS transition in the JQ model setting evolves from weak to prominent first-order transition as the system becomes anisotropic. Furthermore, both EE and disorder operator with smooth boundary cut exhibit anomalous scaling behavior at the transition points, resembling the scaling inside the Goldstone mode (AFXY) phase, and the anomalous scaling becomes strengthened as the transition becomes more first order. In particular, for $Δ\le 0.3$, the obtained log-coefficients converge to 0.5 which is the same as the contribution from one Goldstone mode in the Néel phase. For $Δ> 0.3$, the log-coefficients are smaller and our findings might suffer from strong finite-size effects due to the fact that the remaining Néel order here is quite tiny.

cond-mat.str-el↗

arXiv2025

Self-learning Monte Carlo Method: A Review

The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of interacting many-body systems, SLMC significantly improves sampling efficiency by constructing an effective model -- via machine learning methods -- based on configurations generated by conventional Monte Carlo methods and then proposes global updates based on the effective model. This enhancement leads to a substantial reduction in autocorrelation time, especially near the critical region, where traditional methods typically suffer from critical slowing down and increased computation complexity. Moreover, SLMC maintains statistical accuracy by implementing a cumulative update scheme that rigorously satisfies the detailed balance condition. And more recent applications have extended the SLMC to convolutional neural networks with applications not only in condensed matter physics but also high-energy physics, quantum chemistry, and quantum simulations. The generic applicability and high computational efficiency make SLMC a powerful and scalable framework for quantum Monte Carlo simulations of strongly correlated electron systems, extending the reach of numerical investigations beyond the limitations of conventional techniques.

cond-mat.str-el↗

arXiv2025

Spin excitations arising from anisotropic Dirac spinons in YCu$_3$(OD)$_6$Br$_2$[Br$_{0.33}$(OD)$_{0.67}$]

A Dirac quantum spin liquid hosts Dirac spinons, which are low-energy fractionalized neutral quasiparticles with spin 1/2 that obey the Dirac equation. Recent inelastic neutron scattering studies have revealed a cone spin continuum in YCu$_3$(OD)$_6$Br$_2$[Br$_{x}$(OD)$_{1-x}$], consistent with the convolution of two Dirac spinons. In this work, we further studied spin excitations using the inelastic neutron scattering technique. The width of low-energy spin excitations shows a linear temperature dependence, which can be explained by spinon-spinon interactions with a Dirac dispersion. Polarized neutron scattering measurements reveal that in-plane magnetic fluctuations are about 1.5 times stronger than the out-of-plane ones, suggesting the presence of Dzyaloshinskii-Moriya interaction and consistent with our theoretical modeling and simulations. Moreover, the high-energy spin excitations around 14 meV agree with the one-pair spinon-antispinon excitations in Raman studies. The real part of the dynamical susceptibility derived from the Kramers-Kronig relationship also agrees with the Knight shift measured by nuclear magnetic resonance, clearly demonstrating the negligible effects of magnetic impurities on static susceptibility. These results provide a rare example in studying quantum-spin-liquid materials where different experimental techniques can be directly compared, and they give further insights for the possible Dirac quantum spin liquid in this system.

cond-mat.str-el↗

arXiv2025

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 $ν=1/2$ (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 $Γ$ 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↗

arXiv2025

Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d

Entanglement microscopy reveals the true quantum correlations among the microscopic building blocks of many-body systems [Nat. Commun. 16, 96 (2025)]. Using this approach, we study the multipartite entanglement of the quantum Ising model in 1d, 2d, and 3d. We first obtain the full reduced density matrix (tomography) of subregions that have at most 4 sites via quantum Monte Carlo, exact diagonalization, and the exact solution in 1d. We then analyze both bipartite and genuine multipartite entanglement (GME) among the sites in the subregion. To do so, we use a variety of measures including the negativity, as well as a true measure of GME: the genuinely multipartite concurrence (or GME concurrence), and its computationally cheaper lower bound, $I_2$. We provide a complete proof that $I_2$ bounds the GME concurrence, and show how the symmetries of the state simplify its evaluation. For adjacent sites, we find 3- and 4-spin GME present across large portions of the phase diagram, reaching maximum near the quantum critical point. In 1d, we identify the singular scaling of the derivative $dI_2/dh$ approaching the critical point. We observe a sharp decrease of GME with increasing dimensionality, coherent with the monogamous nature of entanglement. Furthermore, we find that GME disappears for subregions consisting of non-adjacent sites in both 2d and 3d, offering a stark illustration of the short-ranged nature of entanglement in equilibrium quantum matter arXiv:2402.06677. Finally, we analyze the most collective form of entanglement by evaluating the GME concurrence among all spins in the lattice, which can be obtained from a simple observable: the single-site transverse magnetization. This global concurrence is larger in 1d compared to 2d/3d, but it is relatively less robust against perturbations such as local measurements.

cond-mat.str-el↗

arXiv2025

Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study

The fascinating quantum many-body states in twisted bilayber graphene (TBG) at magic angle, due to the interplay of Coulomb interactions and the quantum metrics of flat bands, have been well understood both experimentally and theoretically. However, the phase diagram and excitations as functions of twist angle and permittivity are still largely unknown. Here, via a newly developed momentum-space continuous-field quantum Monte Carlo method fully taking into account long-ranged Coulomb interactions and flat bands' quantum metrics with system sizes that were not accessible before, we show that charge-neutral TBG realizes an angle-tuned quantum phase transition from a gapped Kramers intervalley coherence (KIVC) state to a Dirac semimetal with critical angles around 1.2$°$. In single-particle spectra we demonstrate the evolution of a minimum gap at $Γ$ at the magic angle and towards touching points at Brillouin zone corners as the angle increases. The free energy and KIVC order parameter show that the transition belongs to fermionic Gross-Neveu criticality, and is robust upon varying the permittivity or the interlayer hopping.

cond-mat.str-el↗

arXiv2025

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 $ν=1/2$ filling of a flat Chern band to two SF states with bosons condensed at momenta M or $Γ$, respectively. While the FCI-SF(M) transition is first-order, the FCI-SF($Γ$) 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 $β\approx$ 0.35(5) and $ν\approx$ 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↗