arXiv subjects

Zi Yang Meng

Publications and source records attributed to Zi Yang Meng.

At least 55 records · Page 3Linked to original sources

arXiv2025

Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models

We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix product operators}}. Such an implementation allows us to investigate a quantum dimer model in DMRG for any lattice geometry wrapped around a cylinder with substantial circumference. We have thence computed the ground state phase diagram of the quantum dimer model on triangular lattice, with the symmetry-breaking characteristics of the columnar solid phase and $\sqrt{12}\times\sqrt{12}$ valence bond solid phase fully captured, as well as the topological entanglement entropy of the $\mathbb{Z}_2$ quantum spin liquid phase that extends to the RK point on non-bipartite lattice accurately revealed. Our DMRG algorithm on constrained quantum lattice models opens new opportunities for matrix and tensor-based algorithms for these systems that have immediate relevance towards the frustrated quantum magnets and synthetic quantum simulators.

cond-mat.str-el↗

arXiv2025

Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation

The subleading corner logarithmic corrections in entanglement entropy (EE) are crucial for revealing universal characteristics of the quantum critical points (QCPs), but they are challenging to detect. Motivated by recent developments in the stable computation of EE in (2+1)D quantum many-body systems, we have developed a new method for directly measuring the corner contribution in EE with less computational cost. The cornerstone of our approach is to measure the subtracted corner entanglement entropy (SCEE) defined as the difference between the EEs of subregions with the same boundary length for smooth and cornered boundaries during the sign-problem free quantum Monte Carlo simulation. Our improved method inherently eliminates not only the area law term of EE but also the subleading log-corrections arising from Goldstone modes, leaving the universal corner contribution as the leading term of SCEE with greatly improved data quality. Utilizing this advanced approach, we calculate the SCEE of the bilayer Heisenberg model on both square and honeycomb lattices across their (2+1)D O(3) QCPs with different opening angles on entanglement boundary, and obtain the accurate values of the corresponding universal corner log-coefficients. These findings will encourage further theoretical investigations to access controlled universal information for interacting CFTs at (2+1)D.

cond-mat.str-el↗

arXiv2025

Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits

We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.

quant-ph↗

arXiv2025

An analog of topological entanglement entropy for mixed states

We propose the convex-roof extension of quantum conditional mutual information ("co(QCMI)") as a diagnostic of topological order in a mixed state. We focus primarily on topological states subjected to local decoherence, and employ the Levin-Wen scheme to define co(QCMI), so that for a pure state, co(QCMI) equals topological entanglement entropy (TEE). By construction, co(QCMI) is zero if and only if a mixed state can be decomposed as a convex sum of pure states with zero TEE. We show that co(QCMI) is non-increasing with increasing decoherence when Kraus operators are proportional to the product of onsite unitaries. This implies that unlike a pure state transition between a topologically trivial and a non-trivial phase, the long-range entanglement at a decoherence-induced topological phase transition as quantified by co(QCMI) is less than or equal to that in the proximate topological phase. For the 2d toric code decohered by onsite bit/phase-flip noise, we show that co(QCMI) is non-zero below the error-recovery threshold and zero above it. Relatedly, the decohered state cannot be written as a convex sum of short-range entangled pure states below the threshold. We conjecture and provide evidence that in this example, co(QCMI) equals TEE of a recently introduced pure state. In particular, we develop a tensor-assisted Monte Carlo (TMC) computation method to efficiently evaluate the Rényi TEE for the aforementioned pure state and provide non-trivial consistency checks for our conjecture. We use TMC to also calculate the universal scaling dimension of the anyon-condensation order parameter at this transition.

quant-ph↗

arXiv2025

Magnetic Bloch States at Integer Flux Quanta Induced by Super-moiré Potential in Graphene Aligned with Twisted Boron Nitride

Two-dimensional electron systems in both magnetic fields and periodic potentials are described by Hofstadter butterfly, a fundamental problem of solid-state physics. While moiré systems provide a powerful method to realize this spectrum, previous experiments, however, have been limited to fractional flux quanta regime due to the difficulty of building ~ 50 nm periodic modulations. Here, we demonstrate a super-moiré strategy to overcome this challenge. By aligning monolayer graphene (G) with 1.0° twisted hexagonal boron nitride (t-hBN), a 63.2 nm bichromatic G/t-hBN super-moiré is constructed, made possible by exploiting the electrostatic nature of t-hBN potential. Under magnetic field B, magnetic Bloch states at integer flux quanta (1-9) are achieved and observed as integer Brown-Zak oscillations, expanding the flux quanta from factions to integers. Theoretical analysis reproduces these experimental findings. This work opens new avenues to study unexplored Hofstadter butterfly, explore emergent topological order at integer flux quanta and engineer long-wavelength periodic modulations.

cond-mat.mes-hall↗

arXiv2025

Evolution of entanglement entropy at SU($N$) deconfined quantum critical points

Over the past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across the condensed matter, quantum field theory, and high-energy physics communities, as it is expected to offer a new paradigm in theory, experiment, and numerical simulations that goes beyond the Landau-Ginzburg-Wilson framework of symmetry breaking and phase transitions. However, the nature of DQCP has been controversial. For instance, in the square-lattice spin-1/2 $J$-$Q$ model, believed to realize the DQCP between Néel and valence bond solid states, conflicting results, such as first-order versus continuous transition, and critical exponents incompatible with conformal bootstrap bounds, have been reported. The enigma of DQCP is exemplified in its anomalous logarithmic subleading contribution in its entanglement entropy (EE), which was discussed in recent studies. In the current work, we demonstrate that similar anomalous logarithmic behavior persists in a class of models analogous to the DQCP. We systematically study the quantum EE of square-lattice SU($N$) DQCP spin models. Based on large-scale quantum Monte Carlo computation of the EE, we show that for a series of $N$ smaller than a critical value, the anomalous logarithmic behavior always exists in the EE, which implies that the previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when $N\ge N_c$ with a finite $N_c$ that we evaluate to lie between $7$ and $8$, the DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory with $N$ complex components.

cond-mat.str-el↗

arXiv2024

Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains

In this work, building on state-of-the-art quantum Monte Carlo simulations, we perform systematic finite-size scaling of both entanglement and participation entropies for long-range Heisenberg chain with unfrustrated power-law decaying interactions. We find distinctive scaling behaviors for both quantum entropies in the various regimes explored by tuning the decay exponent $α$, thus capturing non-trivial features through logarithmic terms, beyond the case of linear Nambu-Goldstone modes. Our systematic analysis reveals that the quantum entanglement information, hidden in the scaling of the two studied entropies, can be obtained to the same level of order parameters and other usual finite-size observables of quantum many-body lattice models. The analysis and results obtained here can readily apply to more quantum criticalities in 1D and 2D systems.

cond-mat.str-el↗

arXiv2024

Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo

We employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of microscopic subregion both in spin and fermionic many-body systems. We exemplify our method by studying the phase diagram near quantum critical points (QCP) in 2 spatial dimensions: the transverse field Ising model and a Gross-Neveu-Yukawa transition of Dirac fermions. Our main results are: i) the Ising QCP exhibits short-range entanglement with a finite sudden death of the LN both in space and temperature; ii) the Gross-Neveu QCP has a power-law decaying fermionic LN consistent with conformal field theory (CFT) exponents; iii) going beyond bipartite entanglement, we find no detectable 3-party entanglement with our two witnesses in a large parameter window near the Ising QCP in 2d, in contrast to 1d. We further establish the singular scaling of general multipartite entanglement measures at criticality, and present an explicit analysis in the tripartite case. We also analytically obtain the large-temperature power-law scaling of the fermionic LN for general interacting systems. Entanglement microscopy opens a rich window into quantum matter, with countless systems waiting to be explored.

cond-mat.str-el↗

arXiv2024

Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions

Employing large-scale quantum Monte Carlo simulations, we find that in the magnetized interacting Dirac fermion model there emerges a universal collective Larmor-Silin spin wave mode in the transverse dynamical spin susceptibility. Such mode purely originates from the interaction among Dirac fermions and distinguishes itself from the usual particle-hole continuum with finite lifetime and clear dispersion, both at small and large momenta in a large portion of the Brillouin zone. Our unbiased numerical results offer the dynamic signature of this collective excitation in interacting Dirac fermion systems, and provide experimental guidance for inelastic neutron scattering, electron spin resonance, and other spectroscopic approaches in the investigation of such universal collective modes in quantum Moire materials, topological insulators, and quantum spin liquid materials under magnetic field, with quintessential interaction nature beyond the commonly assumed noninteracting Dirac fermion or spinon approximations.

cond-mat.str-el↗

arXiv2024

Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation

Based on the recently developed resummation-based quantum Monte Carlo method for the SU($N$) spin and loop-gas models, we develop a new algorithm, dubbed ResumEE, to compute the entanglement entropy (EE) with greatly enhanced efficiency. Our ResumEE exponentially speeds up the computation of the exponentially small value of the $\langle e^{-S^{(2)}}\rangle$, where $S^{(2)}$ is the 2nd order Rényi EE, such that the $S^{(2)}$ for a generic 2D quantum SU($N$) spin models can be readily computed with high accuracy. We benchmark our algorithm with the previously proposed estimators of $S^{(2)}$ on 1D and 2D SU($2$) Heisenberg spin systems to reveal its superior performance and then use it to detect the entanglement scaling data of the Néel-to-VBS transition on 2D SU($N$) Heisenberg model with continuously varying $N$. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of SU($N$) spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.

cond-mat.str-el↗

arXiv2024

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 $ν=2/3$ 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 $σ_{xy}=ν=2/3$, 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↗

arXiv2024

Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase

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. Here we apply the spherical Landau level regularization upon the exact (2+1)D SO(5) non-linear sigma model with a topological term to study the potential DQCP therein. We perform density matrix renormalization group (DMRG) simulation with SU(2)$_\mathrm{spin}\times$U(1)$_\mathrm{charge}\times$U(1)$_\mathrm{angular-momentum}$ symmetries explicitly implemented. Using crossing point analysis for the critical properties of the DMRG data, accompanied by quantum Monte Carlo simulations, we accurately obtain the comprehensive phase diagram of the model and find various novel quantum phases, including Néel, ferromagnet (FM), valence bond solid (VBS), valley polarized (VP) states and a gapless quantum disordered phase occupying extended area of the phase diagram. The VBS-Disorder and Néel-Disorder transitions are continuous with non-Wilson-Fisher exponents. Our results show the VBS and Néel states are separated by either a weakly first-order transition or the disordered region with a multicritical point in between, thus opening up more interesting questions on the two-decade long debate on the nature of DQCP.

cond-mat.str-el↗

arXiv2024

Extracting subleading corrections in entanglement entropy at quantum phase transitions

We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity ``subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that $\mathbf{(1)}$ for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; $\mathbf{(2)}$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; $\mathbf{(3)}$ for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.

cond-mat.str-el↗

arXiv2024

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even $\mathbb{Z}_2$ quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the $(2+1)$D cubic* universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O($3$) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

cond-mat.str-el↗

arXiv2024

Cubic* criticality emerging from a quantum loop model on triangular lattice

Quantum loop and dimer models are archetypal examples of correlated systems with local constraints. Obtaining generic solutions for these models is difficult due to the lack of controlled methods to solve them in the thermodynamic limit. Nevertheless, these solutions are of immediate relevance to both statistical and quantum field theories, as well as the rapidly growing experiments in Rydberg atom arrays and quantum moiré materials, where the interplay between correlation and local constraints gives rise to a plethora of novel phenomena. In a recent work [X. Ran, Z. Yan, Y.-C. Wang, et al, arXiv:2205.04472 (2022)], it was found through sweeping cluster quantum Monte Carlo (QMC) simulations and field theory analysis that the triangular lattice quantum loop model (QLM) hosts a rich ground state phase diagram with lattice nematic, vison plaquette (VP) crystals, and the $\mathbb{Z}_2$ quantum spin liquid (QSL) close to the Rokhsar-Kivelson point. Here, we focus on the continuous quantum critical point separating the VP and QSL phases and demonstrate via both static and dynamic probes in QMC simulations that this transition is of the (2+1)D cubic* universality. In this transition, the fractionalized visons in QSL condense to give rise to the crystalline VP phase, while leaving their trace in the anomalously large anomalous dimension exponent and pronounced continua in the dimer and vison spectra compared with those at the conventional cubic or O(3) quantum critical points.

cond-mat.str-el↗

arXiv2024

Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system

Beyond the Li-Haldane-Poilblanc conjecture, we find the entanglement Hamiltonian (EH) is actually not closely similar to the original Hamiltonian on the virtual edge. Unexpectedly, the EH has some relevant long-range interacting terms which hugely affect the physics. Without loss of generality, we study a spin-1/2 Heisenberg bilayer to obtain the entanglement information between the two layers through our newly developed quantum Monte Carlo scheme, which can simulate large-scale EH. Although the entanglement spectrum carrying the Goldstone mode seems like a Heisenberg model on a single layer, which is consistent with Li-Haldane-Poilblanc conjecture, we demonstrate that there actually exists a finite-temperature phase transition of the EH. The results violate the Mermin-Wagner theorem, which means there should be relevant long-range terms in the EH. It reveals that the Li-Haldane-Poilblanc conjecture ignores necessary corrections for the EH which may lead totally different physics.

cond-mat.str-el↗

arXiv2024

An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation

Exponential observables, formulated as $\log \langle e^{\hat{X}}\rangle$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement entropy. Given that $e^{X}$ becomes exponentially large (or small) in the thermodynamic limit, accurately computing the expectation value of this exponential quantity presents a significant challenge. In this Letter, we propose a comprehensive algorithm for quantifying these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo (DQMC) method. We have applied this novel algorithm to the 2D half-filled Hubbard model. At the strong coupling limit, our method showcases a significant accuracy improvement compared to conventional methods that are derived from the internal energy. We also illustrate that this novel approach delivers highly efficient and precise measurements of the nth Rényi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be easily generalized to other models.

cond-mat.str-el↗

arXiv2024

Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet

Emergent quasiparticles with a Dirac dispersion in condensed matter systems can be described by the Dirac equation for relativistic electrons, in analogy with Dirac particles in high-energy physics. For example, electrons with a Dirac dispersion have been intensively studied in electronic systems such as graphene and topological insulators. However, charge is not a prerequisite for Dirac fermions, and the emergence of Dirac fermions without charge degree of freedom has been theoretically predicted to be realized in Dirac quantum spin liquids. These quasiparticles carry a spin of 1/2 but are charge-neutral, and so are called spinons. Here we show that the spin excitations of a kagome antiferromagnet, YCu$_3$(OD)$_6$Br$_2$[Br$_{0.33}$(OD)$_{0.67}$], are conical with a spin continuum inside, which is consistent with the convolution of two Dirac spinons. The predictions of a Dirac spin liquid model with a spinon velocity obtained from the spectral measurements are in agreement with the low-temperature specific heat of the sample. Our results thus provide spectral evidence for the Dirac quantum spin liquid state emerging in this kagome lattice antiferromagnet. However, the locations of the conical spin excitations differ from those calculated by the nearest neighbor Heisenberg model, suggesting the Dirac spinons have an unexpected origin.

cond-mat.str-el↗