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Although the entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo (QMC) has achieved huge success in pure ground states of quantum many-body systems, numerical explorations on mixed states remain limited, despite the fact that most real-world systems are non-isolated. Meanwhile, entanglement negativity, as a rarely computable entanglement monotone for mixed states, is significant in characterizing mixed-state entanglement, such as in systems with two disconnected regions, dissipation or at finite temperature. However, efficient numerical approaches are scarce to calculate this quantity in large-scale and high-dimensional systems, especially when we need to access how it varies with certain parameters to study critical behaviors. Within the reweight-annealing frame, we present an accessible and efficient QMC algorithm, which is able to achieve the values as well as tracking the variation of the R\'enyi version of entanglement negativity on some specified parameter path. Our algorithm makes it feasible to directly study the role that entanglement plays at the critical point and in different phases for mixed states in high dimensions numerically. In addition, this method is accessible and easy to parallelize on computers. Through this method, different intrinsic mechanisms in quantum and thermal criticalities with the same universal class have been revealed clearly through the numerical calculations on R\'enyi negativity., Comment: 10 pages, 4 figures

Using entanglement entropy (EE) to probe the intrinsic physics of the novel phases and phase transitions in quantum many-body systems is an important but challenging topic in condensed matter physics. Thanks to our newly developed bipartite-reweight-annealing algorithm, we can systematically study EE behaviors near both first and second-order phase transition points of two-dimensional strongly correlated systems by scanning the EE across a large parameter region, which was super difficult previously due to the huge computation resources demanded. Interestingly, we find that the EE or its derivative diverges at the critical point, which essentially reveals the phase transition involving discrete or continuous symmetry breaking. What's more, we observe that the peak of the EE curve can detect first-order phase transitions at high symmetry breaking points, separating phases with lower symmetry broken. This behavior also applies to the symmetry-enhanced first-order phase transition in the two-dimensional chequerboard $J-Q$ model, where the emergent higher symmetry arises from the related deconfined criticality beyond the Landau-Ginzburg-Wilson paradigm. This work points to new phenomena and mechanisms that can help us better identify different phase transitions and the underlying symmetry breaking., Comment: 10 pages, 7 figures

This study investigates the nature of the $X_0(2900)$ and $\chi_{c0}(3930)$ based on experimental results of the process $B^+$$\to$$D^+ D^- K^+$. We focus on the S-wave $D^{*-}K^{*+}$ and $D_s^+D_s^-$ molecular states, which can be related to the $X_0(2900)$ and $\chi_{c0}(3930)$, respectively. Using effective Lagrangians, we construct the potential kernel of the $D^{*-}K^{*+}$$-$$D^{-}K^{+}$ and $D_s^+D_s^-$$-$$D^+D^-$ interactions with a one-boson-exchange model, and determine the scattering amplitudes and their poles through a quasipotential Bethe-Salpeter equation approach. By incorporating the potential kernel into the three-body decay process $B^+$$\to$$D^+ D^- K^+$, we evaluate the $D^-K^+$ and $D^+D^-$ invariant mass spectra, as well as the Dalitz plot, with Monte Carlo simulation. A satisfactory fit to the $D^-K^+$ and $D^+D^-$ invariant mass spectra is achieved after introducing additional Breit-Wigner resonances, the $X_1(2900)$, $\psi(3770)$, and $\chi_{c2}(3930)$ states. Prominent signals of the $X_0(2900)$ and $\chi_{c0}(3930)$ states appear as peaks in the $D^-K^+$ and $D^+D^-$ invariant mass spectra near 2900 and 3930 MeV, respectively. Clear event concentration of the $X_0(2900)$ and $\chi_0(3930)$ states is evident as strips in the Dalitz plot. The results suggest that both $X_0(2900)$ and $\chi_{c0}(3930)$ can be interpreted as molecular states, with the inclusion of $X_1(2900)$ and $\chi_2(3930)$ necessary to describe structures in the regions near 2900 and 3930 MeV., Comment: 9 pages, 5figures

We propose a quantum Monte Carlo (QMC) scheme able to extract large-scale data of entanglement entropy (EE) and its derivative with high precision and low technical barrier. We avoid directly computing the overlap of two partition functions within different spacetime manifolds and instead obtain them separately via reweight-annealing scheme. The incremental process can be designed along the path of real physical parameters in this frame, and all intermediates are EEs of corresponding parameters, so the algorithm efficiency is improved by more than $10^4$ of times. The calculation of EE becomes much cheaper and simpler. It opens a way to numerically detect the novel phases and phase transitions by scanning EE in a wide parameter-region in two and higher dimensional systems. We then show the feasibility of using EE and its derivative to find phase transition points and to probe novel phases.

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., Comment: 10 pages, 7 figures

Low-lying entanglement spectrum provides the quintessential fingerprint to identify the highly entangled quantum matter with topological and conformal field-theoretical properties. However, when the entangling region acquires long boundary with the environment, such as that between long coupled chains or in two or higher dimensions, there unfortunately exists no universal yet practical method to compute the entanglement spectra with affordable computational cost. Here we propose a new scheme to overcome such difficulty and successfully extract the low-lying fine entanglement spectrum (ES). We trace out the environment via quantum Monte Carlo simulation and diagonalize the reduced density matrix to gain the ES. We demonstrate the strength and reliability of our method through long coupled spin chains and answer its long-standing controversy. Our simulation results, with unprecedentedly large system sizes, establish the practical computation scheme of the entanglement spectrum with a huge freedom degree of environment.

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., Comment: 12 pages, 11 figures

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., Comment: 9 pages, 4 figures

In this work, a study of the $D_s\bar{D}_s$ interaction and its couplings to the channels $D\bar{D}$ and $J/\psi \phi$ is performed in a quasipotential Bethe-Salpeter equation approach. The $D_s^+{D}_s^-$ and $D^+{D}^-$ invariant mass spectra in three-body $B$ decays are investigated in order to understand the origin of $X(3960)$, $\chi_{c0}(3930)$, and $X_0(4140)$ structures reported at LHCb. With the help of effective Lagrangians, the potential kernel can be constructed with meson exchanges, from which the scattering amplitudes can be obtained. By inserting it into the three-body decay processes, the invariant mass spectra can be calculated with an additional Breit-Wigner resonance introduced. The $D_s^+{D}_s^-$ invariant mass spectrum in the decay process $B^+\to D^+_sD^-_sK^+$ is well reproduced, and the $X(3960)$ structure can be explained as a molecular state from the $D_s\bar{D}_s$ interaction. The state also exhibits as a peak in the $D^+{D}^-$ invariant mass spectrum in the decay $B^+\to D^+D^-K^+$, however, it is too narrow to reproduce the experimental structure around 3930~MeV. The dip around 4140~MeV in the $D_s^+{D}_s^-$ invariant mass spectrum can be reproduced by the additional resonance with interference effect. However, a small bump instead of a dip is produced from the $D_s\bar{D}_s-J/\psi \phi$ coupled-channel effect, which suggests that the $X_0(4140)$ cannot be interpreted as the $D_s\bar{D}_s-J/\psi \phi$ coupling in the current model., Comment: 4 figures, to be published in Euro. Phys. J. C

Molecular docking plays a pivotal role in drug discovery and precision medicine, enabling us to understand protein functions and advance novel therapeutics. Here, we introduce a potential alternative solution to this problem, the digitized-counterdiabatic quantum approximate optimization algorithm (DC-QAOA), which utilizes counterdiabatic driving and QAOA on a quantum computer. Our method was applied to analyze diverse biological systems, including the SARS-CoV-2 Mpro complex with PM-2-020B, the DPP-4 complex with piperidine fused imidazopyridine 34, and the HIV-1 gp120 complex with JP-III-048. The DC-QAOA exhibits superior performance, providing more accurate and biologically relevant docking results, especially for larger molecular docking problems. Moreover, QAOA-based algorithms demonstrate enhanced hardware compatibility in the noisy intermediate-scale quantum era, indicating their potential for efficient implementation under practical docking scenarios. Our findings underscore quantum computing's potential in drug discovery and offer valuable insights for optimizing protein-ligand docking processes., Comment: 23 pages, 17 figures, All comments are welcome

With the accumulation of experimental data, more and more exotic hadrons are observed. Among the interpretations of these exotic hadrons, molecular state and compact multiquark are two of the most popular pictures. However, it is still difficult to determine the structure of an exotic hadron. In this work, we propose a possible way to detect the internal structure of an exotic state. When a molecular state composed of two consistent hadrons is attacked by another particle, one of the constituents should be kicked out while another quasifree constituent stays almost unaffected. It is different from a compact multiquark which has no obvious subcluster. In this work, taking the $X(3872)$ as an example, we perform a Dalitz plot analysis of such reaction to find the effect of the different internal structures. Under the assumption of the $X(3872)$ as a molecular state or a compact tetraquark state, with the help of the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are estimated with different total invariant mass of three final particles, and the effect of different binding energies is also discussed. Obvious event concentration can be observed as strips in the Dalitz plot and sharp peaks in the invariant mass spectrum for the $X(3872)$ with a small binding energy under the molecular state picture, while such concentration cannot be observed under the compact tetraquark picture. Such phenomenon can be applied to identify the internal structure of a new hadron state., Comment: 6 pages, 3figures

In this work, we perform a systematical investigation about the possible hidden and doubly heavy molecular states with open and hidden strangeness from interactions of $D^{(*)}{\bar{D}}^{(*)}_{s}$/$B^{(*)}{\bar{B}}^{(*)}_{s}$, ${D}^{(*)}_{s}{\bar{D}}^{(*)}_{s}$/${{B}}^{(*)}_{s}{\bar{B}}^{(*)}_{s}$, ${D}^{(*)}D_{s}^{(*)}$/${B}^{(*)}B_{s}^{(*)}$, and $D_{s}^{(*)}D_{s}^{(*)}$/$B_{s}^{(*)}B_{s}^{(*)}$ in a quasipotential Bethe-Salpeter equation approach. The interactions of the systems considered are described within the one-boson-exchange model, which includes exchanges of light mesons and $J/\psi/\Upsilon$ meson. Possible molecular states are searched for as poles of scattering amplitudes of the interactions considered. The results suggest that recently observed $Z_{cs}(3985)$ can be assigned as a molecular state of $D^*\bar{D}_s+D\bar{D}^*_s$, which is a partner of $Z_c(3900)$ state as a $D\bar{D}^*$ molecular state. The calculation also favors the existence of hidden heavy states $D_s\bar{D}_s/B_s\bar{B}_s$ with spin parity $J^P=0^+$, $D_s\bar{D}^*_s/B_s\bar{B}^*_s$ with $1^{+}$, and $D^*_s\bar{D}^*_s/B^*_s\bar{B}^*_s$ with $0^+$, $1^+$, and $2^+$. In the doubly heavy sector, the bound states can be found from the interactions $(D^*D_s+DD^*_s)/(B^*B_s+BB^*_s)$ with $1^+$, $D_s\bar{D}_s^*/B_s\bar{B}_s^*$ with $1^+$, $D^*D^*_s/B^*B^*_s$ with $1^+$ and $2^+$, and $D^*_sD^*_s/B^*_sB^*_s$ with $1^+$ and $2^+$. Some other interactions are also found attractive, but may be not strong enough to produce a bound state. The results in this work are helpful for understanding the $Z_{cs}(3985)$, and future experimental search for the new molecular states., Comment: 1 figure, 11 pages

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, $l_1$-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods by using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228 (2021)]. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation., Comment: 7 pages, 1 figure

Recent studies reported that adenosine triphosphate (ATP) could inhibit as well as enhance the phase separation in prion-like proteins. The molecular mechanism underlying such a puzzling phenomenon remains elusive. Here, taking the fused in sarcoma (FUS) solution as an example, we comprehensively reveal the underlying mechanism by which ATP regulates phase separation by combining the semiempirical quantum mechanical method, mean-field theory, and molecular simulation. At the microscopic level, ATP acts as a bivalent or trivalent binder; at the macroscopic level, the reentrant phase separation indeed occurs in dilute FUS solutions, resulting from the ATP-concentration--dependent binding ability under different conditions. Importantly, the ATP concentration for dissolving the protein condensates is about 10 mM, agreeing with experimental results. Furthermore, from a dynamic point of view, the effect of ATP on phase separation is also non-monotonic. This work provides a clear physical description of the microscopic interaction and macroscopic phase diagram of the ATP-modulated phase separation., Comment: 24 pages, 5 figures

The outbreak of the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has become a worldwide public health crisis. When the SARS-CoV-2 enters the biological fluids in the human body, different types of biomolecules (in particular proteins) may adsorb on its surface and alter its infection ability. Although great efforts have recently been devoted to the interaction of the specific antibodies with the SARS-CoV-2, it still remains largely unknown how the other serum proteins affect the infection of the SARS-CoV-2. In this work, we systematically investigate the interaction of serum proteins with the SARS-CoV-2 RBD by the molecular docking and the all-atom molecular dynamics simulations. It is found that the non-specific immunoglobulin (Ig) indeed cannot effectively bind to the SARS-CoV-2 RBD while the human serum albumin (HSA) may have some potential of blocking its infection (to ACE2). More importantly, we find that the RBD can cause the significant structural change of the Apolipoprotein E (ApoE), by which SARS-CoV-2 may hijack the metabolic pathway of the ApoE to facilitate its cell entry. The present study enhances the understanding of the role of protein corona in the bio-behaviors of SARS-CoV-2, which may aid the more precise and personalized treatment for COVID-19 infection in the clinic., Comment: 18 pages, 7 figures

The spread of the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has become a global health crisis. The binding affinity of SARS-CoV-2 (in particular the receptor binding domain, RBD) to its receptor angiotensin converting enzyme 2 (ACE2) and the antibodies is of great importance in understanding the infectivity of COVID-19 and evaluating the candidate therapeutic for COVID-19. In this work, we propose a new method based on molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) to accurately calculate the free energy of SARS-CoV-2 RBD binding to ACE2 and antibodies. The calculated binding free energy of SARS-CoV-2 RBD to ACE2 is -13.3 kcal/mol, and that of SARS-CoV RBD to ACE2 is -11.4 kcal/mol, which agrees well with experimental result (-11.3 kcal/mol and -10.1 kcal/mol, respectively). Moreover, we take two recently reported antibodies as the example, and calculate the free energy of antibodies binding to SARS-CoV-2 RBD, which is also consistent with the experimental findings. Further, within the framework of the modified MM/PBSA, we determine the key residues and the main driving forces for the SARS-CoV-2 RBD/CB6 interaction by the computational alanine scanning method. The present study offers a computationally efficient and numerically reliable method to evaluate the free energy of SARS-CoV-2 binding to other proteins, which may stimulate the development of the therapeutics against the COVID-19 disease in real applications., Comment: 18 pages, 5 figures

In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $D^{(*)}\bar{D}^{(*)}/B^{(*)}\bar{B}^{(*)}$ and $D^{(*)}D^{(*)}/\bar{B}^{(*)}\bar{B}^{(*)}$ interactions in the quasipotential Bethe-Salpeter equation (qBSE) approach. With the help of Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the $\pi$, $\eta$, $\rho$, $\omega$ and $\sigma$ exchanges, as well as $J/\psi$ or $\Upsilon$ exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$, and $Z_b(10650)$, can be related to the $D\bar{D}^{*}$, $D^*\bar{D}^{*}$, $B\bar{B}^{*}$, and $B^*\bar{B}^{*}$ interactions with quantum numbers $I^G(J^P)=1^+(1^{+})$, respectively. The $D\bar{D}^{*}$ interaction is also attractive enough to produce a pole with $0^+(0^+)$ which is related to the $X(3872)$. Within the same theoretical frame, the existence of $D\bar{D}$ and $B\bar{B}$ molecular states with $0(0^+)$ are predicted. The possible $D^*\bar{D}^*$ molecular states with $0(0^+, 1^+, 2^+)$ and $1(0^+)$ and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $DD/\bar{B}\bar{B}$ interaction while a bound state is found with $0(1^+)$ from $DD^*/\bar{B}\bar{B}^*$ interaction. The $D^*D^*/\bar{B}^*\bar{B}^*$ interaction produces three molecular states with $0(1^+)$, $0(2^+)$ and $1(2^+)$., Comment: 7 pages

Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for large-scale multipartite systems. Here, we propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements and the upper bound is determined by a single measurement. We verify our theory with a four-qubit optical quantum system.We experimentally implement various multi-qubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherence are efficiently inferred from measuring few observables., Comment: 13 pages, 8 figures. Comments are welcome