arXiv subjects

Zi Yang Meng

Publications and source records attributed to Zi Yang Meng.

At least 73 records · Page 4Linked to original sources

arXiv2024

Emergent Conformal Symmetry at the Multicritical Point of (2+1)D SO(5) Model with Wess-Zumino-Witten Term on Sphere

Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Following the pioneering works with the fuzzy sphere methods [W. Zhu, et al, Phys. Rev. X 13, 021009], we apply the spherical Landau level regularization to study the effective (2+1)D SO(5) non-linear sigma model with a topological term and the potential DQCP therein. Utilizing the state-of-the-art density matrix renormalization group method with explicit $\text{SU(2)}_\text{spin}\times\text{U(1)}_\text{charge}\times\text{U(1)}_\text{angular-momentum}$ symmetry as well as exact diagonalization simulations, we provide a comprehensive phase diagram for the model with a SO(5) continuous transition line -- extension of the previous identified SO(5) multicritical point [arXiv:2307.05307] -- while tuning interaction length. The state-operator correspondence with the conformal tower structure is used to identify the emergent conformal symmetry with the best scaling dimension of relevant primary fields and they match well with the critical exponents obtained from the crossing point analysis of the correlation ratio. Our results thus further support the rich structure of the phase diagram of the SO(5) model.

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

Emus live on the Gross-Neveu-Yukawa archipelago

It is expected that the Gross-Neveu-Yukawa (GNY) chiral Ising transition of $N$ Majorana (or $N_f=N/4$ four-component Dirac) fermions coupled with scalar field in (2+1)D will be the first fermionic quantum critical point that various methods such as conformal bootstrap [1], perturbative renormalization group [2] and quantum Monte Carlo (QMC) simulations [3], would yield the converged critical exponents -- serving the same textbook role as the Ising and $O(N)$ models in the statistical and quantum phase transition. However, such expectation has not been fully realized from the lattice QMC simulations due to the obstacles introduced by the UV finite size effect. In this work, by means of the elective-momentum ultra-size (EMUS) QMC method [4], we compute the critical exponents of the GNY $N=8$ chiral Ising transition on a 2D $π$-flux fermion lattice model between Dirac semimetal and quantum spin Hall insulator phases [3, 5]. With the matching of fermionic and bosonic momentum transfer and collective update in momentum space, our QMC results provide the fully consistent exponents with those obtained from the bootstrap and perturbative approaches. In this way, the Emus now live happily on the $N=8$ island and could explore the Gross-Neveu-Yukawa archipelago [1] with ease.

cond-mat.str-el↗

arXiv2024

Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation

We propose a new method to efficiently compute the entanglement entropy (EE) of quantum many-body systems. Our approach, called the incremental SWAP operator method , combines the simplicity of the SWAP operator used in projector quantum Monte Carlo simulations with recent advances in precisely computing exponential observables using incremental algorithms. We apply this technique to obtain accurate EE data at reduced computational cost for 1d and 2d antiferromagnetic Heisenberg models with different bipartition schemes. Using the computed EE data, we extract the area law coefficient, universal logarithmic corrections from Goldstone modes, and the geometric constant, finding quantitative agreement with analytical predictions. Moreover, for the first time in an unbiased numerical simulation of 2d antiferromagnetic Heisenberg model, we successfully obtain reliable universal logarithmic corrections from sharp corners that match expected theoretical values. The consistency between our numerical results and theoretical calculations demonstrates the power of our approach for accessing challenging universal entanglement properties. The extensions of our method to other quantum spin/boson models and the interacting fermion models, are outlined.

cond-mat.str-el↗

arXiv2024

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT.

cond-mat.str-el↗

arXiv2024

Quantum criticality and entanglement for two dimensional long-range Heisenberg bilayer

The study of quantum criticality and entanglement in systems with long-range (LR) interactions is still in its early stages, with many open questions remaining. In this work, we investigate critical exponents and scaling of entanglement entropies (EE) in the LR bilayer Heisenberg model using large-scale quantum Monte Carlo (QMC) simulations and the recently developed nonequilibrium increment algorithm for measuring EE. By applying modified (standard) finite-size scaling (FSS) above (below) the upper critical dimension and field theory analysis, we obtain precise critical exponents in three regimes: the LR Gaussian regime with a Gaussian fixed point, the short-range (SR) regime with Wilson-Fisher (WF) exponents, and a LR non-Gaussian regime where the critical exponents vary continuously from LR Gaussian to SR values. We compute the Rényi EE both along the critical line and in the Néel phase and observe that as the LR interaction is enhanced, the area-law contribution in EE gradually vanishes both at quantum critical points (QCPs) and in the Néel phase. The log-correction in EE arising from sharp corners at the QCPs also decays to zero as LR interaction grows, whereas the log-correction for Néel states, caused by the interplay of Goldstone modes and restoration of the symmetry in a finite system, is enhanced as LR interaction becomes stronger. We also discuss relevant experimental settings to detect these nontrivial properties in critical behavior and entanglement information for quantum many-body systems with LR interactions.

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↗

arXiv2023

Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition

Lately there are many SLAC fermion investigations on the (2+1)D Gross-Neveu criticality of a single Dirac cone [1,2]. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the non-interacting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP) -- which a priori requires short-range interaction -- has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local $π$-flux Hubbard model on the square lattice. In particular, we find the antiferromagnetic long-range order in the SLAC fermion model has a finite temperature continuous phase transition, which violates the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous $SU(2)$ symmetry. These unusual results proclaim caution on the interpretation of the quantum phase transition in SLAC fermion model as that of GN-QCP with short-range interaction.

cond-mat.str-el↗

arXiv2023

Dimensionality crossover to 2D vestigial nematicity from 3D zigzag antiferromagnetism in an XY-type honeycomb van der Waals magnet

Fluctuations and disorder effects are substantially enhanced in reduced dimensionalities. While they are mostly considered as the foe for long-range orders, fluctuations and disorders can also stimulate the emergence of novel phases of matter, for example, vestigial orders. Taking 2D magnetism as a platform, existing efforts have been focused on maintaining 2D long-range magnetic orders by suppressing fluctuations, whereas the other side, exploiting fluctuations for realizing new 2D magnetic phases, remains as an uncharted territory. Here, using a combination of NV spin relaxometry, optical spectroscopy, and Monte Carlo simulations, we report, in an XY-type honeycomb magnet NiPS3, the phase transition from the zigzag AFM order in 3D bulk to a new Z3 vestigial Potts-nematicity in 2D few layers. Spin fluctuations are shown to significantly enhance over the GHz-THz range as the layer number of NiPS3 reduces, using the NV spin relaxometry and the optical Raman quasi-elastic scattering. As a result, the Raman signatures of the zigzag AFM for bulk NiPS3, a zone-folded phonon at ~30cm-1 from the broken translational symmetry (PBTS) and a degeneracy lift of two phonons at ~180cm-1 for the broken 3-fold rotational symmetry (PBRS), evolve into the disappearance of PBTS and the survival of PBRS in few-layer NiPS3, with a critical thickness of ~10nm. The optical linear dichroism microscopy images all three nematic domain states in a single few-layer NiPS3 flake. The large-scale Monte Carlo simulations for bilayer NiPS3 model confirms the absence of long-range zigzag AFM order but the formation of the Z3 vestigial Potts-nematic phase, corroborating with the experimental finding. Our results demonstrate the positivity of strong fluctuations in creating new phases of matter after destroying more conventional ones, and offer an unprecedented pathway for developing novel 2D phases.

cond-mat.mtrl-sci↗

arXiv2023

Deconfined quantum critical point lost in pressurized SrCu2(BO3)2

In the field of correlated electron materials, the relation between the resonating spin singlet and antiferromagnetic states has long been an attractive topic for understanding of the interesting macroscopic quantum phenomena, such as the ones emerging from magnetic frustrated materials, antiferromagnets and high-temperature superconductors. SrCu2(BO3)2 is a well-known quantum magnet, and it is theoretically expected to be the candidate of correlated electron material for clarifying the existence of a pressure-induced deconfined quantum critical point (DQCP), featured by a continuous quantum phase transition, between the plaquette-singlet (PS) valence bond solid phase and the antiferromagnetic (AF) phase. However, the real nature of the transition is yet to be identified experimentally due to the technical challenge. Here we show the experimental results for the first time, through the state-of-the-art high-pressure heat capacity measurement, that the PS-AF phase transition of the pressurized SrCu2(BO3)2 at zero field is clearly a first-order one. Our result clarifies the more than two-decade long debates about this key issue, and resonates nicely with the recent quantum entanglement understanding that the theoretically predicted DQCPs in representative lattice models are actually a first-order transition. Intriguingly, we also find that the transition temperatures of the PS and AF phase meet at the same pressure-temperature point, which signifies a bi-critical point as those observed in Fe-based superconductor and heavy-fermion compound, and constitutes the first experimental discovery of the pressure-induced bi-critical point in frustrated magnets. Our results provide fresh information for understanding the evolution among different spin states of correlated electron materials under pressure.

cond-mat.str-el↗

arXiv2023

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^α$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $α\ge 2D$. However, the situation for $α\in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of $SU(2)$ symmetry in the ferromagnetic Heisenberg model with $1/r^α$-form long-range interactions at $D=2$. We determine critical exponents through finite-size analysis for $α<3$ (above the upper critical dimension with Gaussian fixed point) and $3\leα<4$ (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope.

cond-mat.str-el↗

arXiv2023

Experimental evidence for Berry curvature multipoles in antiferromagnets

Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a 2nd order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a 3rd order NLAHE, which appears as a transverse voltage response at the 3rd harmonic frequency when a longitudinal a.c. current drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte-Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials, such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, that remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.

cond-mat.mes-hall↗

arXiv2023

Quantum optimization within lattice gauge theory model on a quantum simulator

Simulating lattice gauge theory (LGT) Hamiltonian and its nontrivial states by programmable quantum devices has attracted numerous attention in recent years. Rydberg atom arrays constitute one of the most rapidly developing arenas for quantum simulation and quantum computing. The $\mathbb{Z}_2$ LGT and topological order has been realized in experiments while the $U(1)$ LGT is being worked hard on the way. States of LGT have local constraint and are fragmented into several winding sectors with topological protection. It is therefore difficult to reach the ground state in target sector for experiments, and it is also an important task for quantum topological memory. Here, we propose a protocol of sweeping quantum annealing (SQA) for searching the ground state among topological sectors. With the quantum Monte Carlo method, we show that this SQA has linear time complexity of size with applications to the antiferromagnetic transverse field Ising model, which has emergent $U(1)$ gauge fields. This SQA protocol can be realized easily on quantum simulation platforms such as Rydberg array and D-wave annealer. We expect this approach would provide an efficient recipe for resolving the topological hindrances in quantum optimization and the preparation of quantum topological state.

quant-ph↗

arXiv2023

Classical fully-packed loop model with attractive interactions on the square lattice

We study a classical model of fully-packed loops on the square lattice, which interact through attractive loop segment interactions between opposite sides of plaquettes. This study is motivated by effective models of interacting quantum matter arising in frustrated magnets or Rydberg atom arrays, for which loop degrees of freedom appear at low energy. Through a combination of Monte Carlo simulations and an effective height field theory, we find that the critical point known to occur at infinite temperature gives rise to a high-temperature critical phase with floating exponents. At lower temperature, the system transitions via a Kosterlitz-Thouless phase transition to a nematic phase where lattice rotation symmetry is broken. We discuss consequences for the phase diagram of the quantum loop model on the same lattice.

cond-mat.str-el↗

arXiv2023

Stable computation of entanglement entropy for 2D interacting fermion systems

There is no doubt that the information hidden in entanglement entropy (EE), for example, the $n$-th order Rényi EE, i.e., $S^{A}_n=\frac{1}{1-n}\ln \Tr (ρ_A^n)$ where $ρ_A=\mathrm{Tr}_{\overline{A}}ρ$ is the reduced density matrix, can be used to infer the organizing principle of 2D interacting fermion systems, ranging from spontaneous symmetry breaking phases, quantum critical points to topologically ordered states. It is far from clear, however, whether the EE can actually be obtained with the precision required to observe these fundamental features -- usually in the form of universal finite size scaling behavior. Even for the prototypical 2D interacting fermion model -- the Hubbard model, to all existing numerical algorithms, the computation of the EE has not been succeeded with reliable data that the universal scaling regime can be accessed. Here we explain the reason for these unsuccessful attempts in EE computations in quantum Monte Carlo simulations in the past decades and more importantly, show how to overcome the conceptual and computational barrier with the incremental algorithm, such that the stable computation of the EE in 2D interacting fermion systems can be achieved and universal scaling information can be extracted. Relevance towards the experimental 2D interacting fermion systems is discussed.

cond-mat.str-el↗

arXiv2023

Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system

Quadratic band touching (QBT) points are widely observed in 2D and 3D materials, including bilayer graphene and Luttinger semimetals, and attract significant attention from theory to experiment. However, even in its simplest form, the 2D checkerboard lattice QBT model, the phase diagram characterized by temperature and interaction strength still remains unknown beyond the weak-coupling regime. Intense debates persist regarding the existence of various interaction-driven insulating states in this system. To address these uncertainties, we employ thermal tensor network simulations, specifically exponential tensor renormalization group and tangent space tensor renormalization group, along with density matrix renormalization group calculations to provide a comprehensive finite-temperature phase diagram for this model and shed light on previous ambiguities. Notably, our findings reveal the emergence of a robust bond-nematic Dirac semimetal phase with distinct thermodynamic properties that set it part from the nematic insulating state and other symmetry broken states. This previously overlooked feature is found to be ubiquitous in interacting QBT systems. We also discuss the implications of these results for experimental systems such as bilayer graphene and iridate compounds.

cond-mat.str-el↗

arXiv2023

Intrinsic nonlinear Hall effect and gate-switchable Berry curvature sliding in twisted bilayer graphene

Though the observation of the quantum anomalous Hall effect and nonlocal transport response reveals nontrivial band topology governed by the Berry curvature in twisted bilayer graphene, some recent works reported nonlinear Hall signals in graphene superlattices that are caused by the extrinsic disorder scattering rather than the intrinsic Berry curvature dipole moment. In this work, we report a Berry curvature dipole induced intrinsic nonlinear Hall effect in high-quality twisted bilayer graphene devices. We also find that the application of the displacement field substantially changes the direction and amplitude of the nonlinear Hall voltages, as a result of a field-induced sliding of the Berry curvature hotspots. Our work not only proves that the Berry curvature dipole could play a dominant role in generating the intrinsic nonlinear Hall signal in graphene superlattices with low disorder densities, but also demonstrates twisted bilayer graphene to be a sensitive and fine-tunable platform for second harmonic generation and rectification.

cond-mat.mes-hall↗

arXiv2023

Different temperature-dependence for the edge and bulk of entanglement Hamiltonian

We propose a physical picture based on the wormhole effect of the path-integral formulation to explain the mechanism of entanglement spectrum (ES), such that, our picture not only explains the topological state with bulk-edge correspondence of the energy spectrum and ES (the Li and Haldane conjecture), but is generically applicable to other systems independent of their topological properties. We point out it is ultimately the relative strength of bulk energy gap (multiplied with inverse temperature $β=1/T$) with respect to the edge energy gap that determines the behavior of the low-lying ES of the system. Depending on the circumstances, the ES can resemble the energy spectrum of the virtual edge, but can also represent that of the virtual bulk. We design models both in 1D and 2D to successfully demonstrate the bulk-like low-lying ES at finite temperatures, in addition to the edge-like case conjectured by Li and Haldane at zero temperature. Our results support the generality of viewing the ES as the wormhole effect in the path integral and the different temperature-dependence for the edge and bulk of ES.

quant-ph↗