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Yi-Ming Ding

Publications and source records attributed to Yi-Ming Ding.

18 recordsLinked to original sources
arXiv2026

Quantum Monte Carlo in the Age of Many-Body Quantum Information

Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, R\'enyi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.

quant-ph↗
arXiv2026

Strong-to-Weak Spontaneous Symmetry Breaking in a $(2+1)$D Transverse-Field Ising Model under Decoherence

Decoherence in many-body quantum systems can give rise to intrinsically mixed-state phases and phase transitions beyond the pure-state paradigm. Here we study the $(2+1)$D transverse-field Ising model subject to a strongly $\mathbb{Z}_2$-symmetric decoherence channel, with a focus on strong-to-weak spontaneous symmetry breaking (SWSSB). This problem is challenging because the relevant transitions occur in the strong-decoherence regime, beyond the reach of perturbative expansions around the pure-state limit, while conventional quantum Monte Carlo (QMC) methods are hampered by the need to access nonlinear observables and by the sign problem. We overcome these difficulties by developing a QMC algorithm that efficiently evaluates nonlinear R\'enyi-2 correlators in higher dimensions, complemented by an effective field-theoretic approach. We show that the decohered state realizes a rich mixed-state phase diagram governed by an effective 2D Ashkin-Teller theory. This theory enables analytical predictions for the mixed-state phases and the universality classes of the phase boundaries, all of which are confirmed by large-scale QMC simulations.

quant-ph↗
arXiv2026

Complete finite-size scaling theory of Renyi thermal entropy for second, first and weak first order quantum phase transitions

Establishing the nature of a quantum phase transition in finite-size simulations -- whether continuous, first-order, or weak first-order -- is a fundamental challenge in quantum many-body computation. Especially, the weak first-order phase transition is affected by a super large correlation length and always displays as a continuous critical point in simulated finite-sizes. The core difficulty lies in the fact that there is no effective finite-size theory to distinguish these phase transitions in the realistic simulations limited by the computational resource. In this work, we have fixed this problem by introducing a unified finite-size framework based on the Renyi thermal entropy (RTE) and its derivative (DRTE) to detect and characterize quantum phase transitions. We derive complete scaling theories for the RTE and DRTE at second-order, first-order, and weak first-order transitions, showing that the DRTE naturally isolates the singular part of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at (2+1)-dimensional O($N$) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the $J$--$Q$ models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios.

cond-mat.str-el↗
arXiv2026

Entanglement Rényi Negativity across the Finite-Temperature Transition in the O(3) Universality Class

The fate of quantum entanglement at finite-temperature phase transitions remains an open question, particularly for continuous symmetry breaking where zero-temperature Goldstone modes generate long-range correlations. Using large-scale quantum Monte Carlo simulations, we investigate the third Rényi negativity across the O(3) transition in the three-dimensional Heisenberg antiferromagnet. The first such study for a thermal critical point with continuous symmetry. We uncover two fundamental results. First, the negativity exhibits a pure area law at the critical point, with the subleading constant term vanishing within statistical uncertainty. This demonstrates that thermal fluctuations completely destroy the long-range entanglement present at zero temperature. The divergent classical correlation length leaves no imprint on quantum entanglement itself. Second, despite this absence of singular behavior in the negativity, its temperature derivative follows the exact scaling of the specific heat, yielding critical exponents -α/ν=0.190(1) and 1/ν=1.350(5) in precise agreement with the O(3) universality class. Our work establishes that while quantum entanglement is blind to thermal criticality, its thermodynamic derivatives encode the full universal scaling, revealing an unexpected connection between entanglement and classical phase transitions. Furthermore, this also provides further evidence that Rényi negativity can still effectively shield classical correlations in systems with continuous symmetry.

cond-mat.str-el↗
arXiv2025

Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking

Entanglement plays a key role in quantum physics, but how much information it can extract from many-body systems is still an open question, particularly regarding quantum criticalities and emergent symmetries. In this work, we systematically study the entanglement entropy (EE) and derivative entanglement entropy (DEE) near quantum phase transitions in various quantum many-body systems. A one-parameter scaling relation between the DEE and system size at the critical point has been derived for the first time, which successfully obtains the critical exponent via data collapse. Furthermore, we find that the EE peaks at the (emergent) symmetry enhanced first-order transition, reflecting higher symmetry breaking. This work provides a new paradigm for quantum many-body research from the perspective of EE and DEE.

cond-mat.str-el↗
arXiv2025

Mixed-State Phase Transitions in Measurement-Dressed Imaginary-Time Evolution

Motivated by the ubiquity of decoherence in quantum hardware and the growing role of imaginary-time evolution (ITE) in quantum algorithms, we investigate how many-body correlations generated by imaginary-time filtering are modified by local decoherence. We introduce measurement-dressed imaginary-time evolution (MDITE), which alternates ITE with projective-measurement channels, producing a competition between low-energy filtering and local dephasing. By developing a new efficient quantum Monte Carlo method, we uncover MDITE mixed-state transitions with spontaneous-symmetry-breaking signatures in the driving of 1D transverse-field Ising and 2D columnar dimerized Heisenberg Hamiltonians in the resulting density matrices. In the continuous limit, the Choi-Jamiolkowski mapping yields a tractable equilibrium description with conformal criticality that qualitatively captures the phase transitions. At finite protocol parameters, however, the four-point correlator violates the conformal cross-ratio form and the critical exponents deviate from their continuous-limit values, signaling the loss of conformal symmetry and richer nonequilibrium criticality. Our results establish MDITE as a controlled setting for exploring mixed-state phases and critical phenomena driven by the interplay between imaginary-time filtering and decoherence.

quant-ph↗
arXiv2025

Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study

As a powerful theoretical construct, the entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system. From the EH, one can extract a variety of entanglement quantities, such as entanglement entropies, negativity, and the entanglement spectrum. However, its general analytical form remains largely unknown. While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited, especially when Lorentz invariance is absent. In this work, we propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods to numerically reconstruct the entanglement Hamiltonian in two-dimensional systems and systematically explore its applicability to systems without translational invariance, going beyond the original scope of the primordial Bisognano-Wichmann theorem. Various quantum phases--including gapped and gapless phases, critical points, and phases with either discrete or continuous symmetry breaking--are investigated, demonstrating the versatility of our method in reconstructing entanglement Hamiltonians. Furthermore, we find that when the entanglement boundary of a system is ordinary (i.e., free from surface anomalies), the LBW ansatz provides an accurate approximation well beyond Lorentz-invariant cases. Our work thus establishes a general framework for investigating the analytical structure of entanglement in the complex quantum many-body systems.

cond-mat.str-el↗
arXiv2025

Bell sampling in Quantum Monte Carlo simulations

Quantum Monte Carlo (QMC) methods are essential for the numerical study of large-scale quantum many-body systems, yet their utility has been significantly hampered by the difficulty in computing key quantities such as off-diagonal operators and entanglement. This work introduces Bell-QMC, a novel QMC framework leveraging Bell sampling, a two-copy measurement protocol in the transversal Bell basis. We demonstrate that Bell-QMC enables an efficient and unbiased estimation of both challenging classes of observables, offering a significant advantage over previous QMC approaches. Notably, the entanglement across all system partitions can be computed in a single Bell-QMC simulation. We implement this method within the stochastic series expansion (SSE), where we design an efficient update scheme for sampling the configurations in the Bell basis. We demonstrate our algorithm in the one-dimensional transverse-field Ising model and the two-dimensional $\mathbb{Z}_2$ lattice gauge theory, extracting universal quantum features using only simple diagonal measurements. This work establishes Bell-QMC as a powerful framework that significantly expands the accessible quantum properties in QMC simulations, providing a substantial advantage over conventional QMC.

quant-ph↗
arXiv2025

Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point

We investigate the second-order R\'enyi entanglement entropy at the quantum critical point of a spin-1/2 antiferromagnetic Heisenberg model on a columnar dimerized square lattice. The universal constant $\gamma$ in the area-law scaling $S_{2}(\ell) = \alpha\ell - \gamma$ is found to be sensitive to the entangling surface configurations, with $\gamma_{\text{sp}} > 0$ for strong-bond-cut (special) surfaces and $\gamma_{\text{ord}} < 0$ for weak-bond-cut (ordinary) surfaces, which is attributed to the distinct conformal boundary conditions. Introducing boundary dimerization drives a renormalization group (RG) flow from the special to the ordinary boundary criticality, and the constant $\gamma$ decreases monotonically with increasing dimerization strength, demonstrating irreversible evolution under the boundary RG flow. These results provide numerical evidence for a higher-dimensional analog of the $g$ theorem, and suggest $\gamma$ as a possible characteristic function for boundary RG flow in $(2+1)$-dimensional conformal field theory.

cond-mat.stat-mech↗
arXiv2025

Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography

We study the behavior of magic as a bipartite correlation in the quantum Ising chain across its quantum phase transition, and at finite temperature. In order to quantify the magic of partitions rigorously, we formulate a hybrid scheme that combines stochastic sampling of reduced density matrices via quantum Monte Carlo, with state-of-the-art estimators for the robustness of magic - a {\it bona fide} measure of magic for mixed states. This allows us to compute the mutual robustness of magic for partitions up to 8 sites, embedded into a much larger system. We show how mutual robustness is directly related to critical behaviors: at the critical point, it displays a power law decay as a function of the distance between partitions, whose exponent is related to the partition size. Once finite temperature is included, mutual magic retains its low temperature value up to an effective critical temperature, whose dependence on size is also algebraic. This suggests that magic, differently from entanglement, does not necessarily undergo a sudden death.

quant-ph↗
arXiv2025

Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study

Entanglement entropy has been a powerful tool for analyzing phases and criticality in pure ground states via quantum Monte Carlo (QMC). However, mixed-state entanglement, relevant to systems with dissipation, finite temperature, and disjoint regions, remains less explored due to the lack of efficient numerical methods. In this work, we present a practical and easy-to-implement QMC method within the reweight-annealing framework, enabling efficient computation of the entanglement Rényi negativity (RN) by tracking its variation along given parameter paths. This method is scalable, parallelizable, and well-suited for high-dimensional and large-scale simulations. Applying it to diverse scenarios-including 1D and 2D systems, ground and thermal states, and bipartite and tripartite partitions, not only the information of the underlying conformal field theory is achieved, but the role of entanglement in quantum and thermal phase transitions is revealed.

cond-mat.str-el↗
arXiv2025

Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic

We present a novel quantum Monte Carlo method for evaluating the $α$-stabilizer Rényi entropy (SRE) for any integer $α\ge 2$. By interpreting $α$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral by sampling \emph{reduced Pauli strings} within a \emph{reduced configuration space}, which enables efficient classical computations of $α$-SRE and its derivatives to explore magic in previously inaccessible 2D/higher-dimensional systems. We first isolate the free energy part in $2$-SRE, which is a trivial term. Notably, at quantum critical points in 1D/2D transverse field Ising (TFI) models, we reveal nontrivial singularities associated with the \emph{characteristic function} contribution, directly tied to magic. Their interplay leads to complicated behaviors of $2$-SRE, avoiding extrema at critical points generally. In contrast, analyzing the volume-law correction to SRE reveals a discontinuity tied to criticalities, suggesting that it is more informative than the full-state magic. For conformal critical points, we claim it could reflect nonlocal magic residing in correlations. Finally, we verify that $2$-SRE fails to characterize magic in mixed states (e.g. Gibbs states), yielding nonphysical results. This work provides a powerful tool for exploring the roles of magic in large-scale many-body systems, and reveals intrinsic relation between magic and many-body physics.

quant-ph↗
arXiv2025

Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative

We propose a quantum Monte Carlo scheme capable of extracting large-scale data of Rényi entanglement entropy (EE) with high precision and low technical barrier. Instead of directly computing the ratio of two partition functions within different space-time manifolds, we obtain them separately via a reweight-annealing scheme and connect them from the ratio of a reference point. The incremental process can thus be designed along a path of real physical parameters within this framework, and all intermediates are meaningful EEs corresponding to these parameters. In a single simulation, we can obtain many multiples ($\sim βL^d$, d is the space dimension) of EEs, which has been proven to be powerful for determining phase transition points and critical exponents. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. This formula only requires computing the difference of energies in different space-time manifolds. The calculation of EE and its derivative becomes much cheaper and simpler in our scheme. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases.

cond-mat.str-el↗
arXiv2025

Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian

The reduced density matrix (RDM) plays a key role in quantum entanglement and measurement, as it allows the extraction of almost all physical quantities related to the reduced degrees of freedom. However, restricted by the degrees of freedom in the environment, the total system size is often limited, let alone the subsystem. To address this challenge, we propose a quantum Monte Carlo scheme with a low technical barrier, enabling precise extraction of the RDM. To demonstrate the power of the method, we present the fine levels of the entanglement spectrum (ES), which is the logarithmic eigenvalues of the RDM. We clearly show the ES for a $1$D ladder with a long entangled boundary, and that for the $2$D Heisenberg model with a tower of states. Furthermore, we put forward an efficient way to restore the entanglement Hamiltonian in operator-form from the sampled RDM data. Our simulation results, utilizing unprecedentedly large system sizes, establish a practical computational framework for determining entanglement quantities based on the RDM, such as the ES, particularly in scenarios where the environment has a huge number of degrees of freedom.

quant-ph↗
arXiv2024

Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations

Efficient and accurate algorithm for partition function, free energy and thermal entropy calculations is of great significance in statistical physics and quantum many-body physics. Here we present an unbiased but low-technical-barrier algorithm within the quantum Monte Carlo framework, which has exceptionally high accuracy and no systemic error. Compared with the conventional specific heat integral method and Wang-Landau sampling algorithm, our method can obtain a much more accurate result of the sub-leading coefficient of the entropy. This method can be widely used in both classical and quantum Monte Carlo simulations and is easy to be parallelized on computer.

cond-mat.stat-mech↗
arXiv2024

Exploring the topological sector optimization on quantum computers

Optimization problems are the core challenge in many fields of science and engineering, yet general and effective methods are scarce for searching optimal solutions. Quantum computing has been envisioned to help solve such problems, for example, the quantum annealing (QA) method based on adiabatic evolution has been extensively explored and successfully implemented on quantum simulators such as D-wave's annealers and some Rydberg arrays. In this work, we investigate topological sector optimization (TSO) problem, which attracts particular interests in the quantum many-body physics community. We reveal that the topology induced by frustration in the spin model is an intrinsic obstruction for QA and other traditional methods to approach the ground state. We demonstrate that the optimization difficulties of TSO problem are not restricted to the gaplessness, but are also due to the topological nature which are often ignored for the analysis of optimization problems before. To solve TSO problems, we utilize quantum imaginary time evolution (QITE) with a possible realization on quantum computers, which exploits the property of quantum superposition to explore the full Hilbert space and can thus address optimization problems of topological nature. We report the performance of different quantum optimization algorithms on TSO problems and demonstrate that their capability to address optimization problems are distinct even when considering the quantum computational resources required for practical QITE implementations.

quant-ph↗
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↗