arXiv subjects

Ting-Tung Wang

Publications and source records attributed to Ting-Tung Wang.

11 recordsLinked to original sources

arXiv2026

Many-Anyon Braiding in Non-Abelian Fractional Quantum Hall Effect with Hybrid Monte Carlo Simulation

We employ the hybrid Monte Carlo method to efficiently compute the many-anyon non-Abelian braiding matrices associated with different braiding schemes of the Moore-Read quasiholes. A novel proposal in this work is that anyon braiding schemes based on a global rotation are robust against finite-size effects, as demonstrated by benchmarking their errors in the braiding matrix against those of a simple two-anyon exchange. Moreover, we investigate how electron-electron interactions and local electrostatic trapping potentials influence the energetic preference of different fusion channels. Their effect on the non-Abelian braiding matrices has been verified, a surprising phenomenon that demonstrates long-range entanglement of non-Abelian states. Our results are relevant to the experimental realization of non-Abelian physics in fractional quantum Hall and other analogous systems, including the fast-growing field of fractional quantum anomalous Hall states in moiré materials.

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

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

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

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

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↗

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

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

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↗