Bin-Bin Mao

University of Hong Kong

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Hong‐Gang Luo

Lanzhou University

Maoxin Liu

Beijing Normal University

Chenjie Wang

University of Chinese Academy of Sciences

Fuzhou Chen

South Dakota State University

Zhe Wang

TU Dortmund University

Wen‐Long You

Nanjing University of Aeronautics and Astronautics

Chen Cheng

Lanzhou University

Zheng Yan

Westlake University

Liangsheng Li

Sun Yat-sen University

Shang-Qiang Ning

University of Hong Kong

Cooperative Institutions

Chinese Academy of Sciences

University of Hong Kong

Fudan University

University of Chinese Academy of Sciences

Lanzhou University

Beijing Computational Science Research Center

State Key Laboratory of Surface Physics

Zhejiang University

Beijing University of Posts and Telecommunications

Peking University

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Probably the simplest and cheapest quantum Monte Carlo method so far for extracting high-precision entanglement entropy and its derivative

arXiv (Cornell University) (2024)

Zhe Wang Zhiyan Wang Yiming Ding Bin-Bin Mao Zheng Yan

Measuring entanglement entropy (EE) to probe the intrinsic physics of quantum many-body systems is an important but challenging topic in condensed matter, high energy and computational physics. Designing quantum Monte Carlo (QMC) algorithm to obtain the R\'enyi EE is a promising solution in large-scale many-body systems. However, to gain high-precision EE, the QMC-based algorithm for EE becomes more and more complex at the designing level. The entangled region needs being changed during the QMC simulation, and the detailed balance condition becomes more complicated. Moreover, the intermediately incremental processes introduced cannot be exploited neither. In this paper, we propose a simple QMC scheme able to extract EE and its derivative with high-precision, which requires neither changing replica manifold during the simulation nor adding extra detailed balance conditions. All the values measured in the incremental process are the EE under physical parameters, which greatly improves the efficiency. It opens an access to numerically probe the novel phases and phase transitions by scanning EE in a wide parameter-region in 2D and higher dimensional systems. The method has low-technical barrier and is natural for parallel computing. Our algorithm makes it no longer a dream to calculate a large amount of high-precision EE values without complicated techniques and huge computational cost.

Derivative (finance)

10.48550/arxiv.2406.05324

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Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer

Physical review. B./Physical review. B (2023)

Siying Wu Xiaoxue Ran Binbin Yin Qifang Li Bin-Bin Mao

By developing a cluster sampling of stochastic series expansion quantum Monte Carlo method, we investigate a spin-$1/2$ model on a bilayer square lattice with intra-layer ferromagnetic (FM) Ising coupling and inter-layer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at $g_c=3.045(2)$ between the FM Ising phase and the dimerized phase is studied via large scale simulations. From the analyzes of critical exponents we show that this phase transition belongs to the (2+1)-dimensional Ising universality class. Besides, the quantum entanglement is strong between the two layers, especially in dimerized phase. The effective Hamiltonian of single layer seems like a transverse field Ising model. However, we found the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.

Hamiltonian (control theory)

Heisenberg model

Quantum phases

10.1103/physrevb.107.155121

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Building 1D lattice models with $G$-graded fusion category

arXiv (Cornell University) (2023)

Shang-Qiang Ning Bin-Bin Mao Chenjie Wang

We construct a family of one-dimensional (1D) quantum lattice models based on $G$-graded unitary fusion category $\mathcal{C}_G$. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category $\mathcal{C}_G$. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the the models to the extent that the low-energy physics has a large likelihood to be gapless.

Anyon

Lattice (music)

Gapless playback

10.48550/arxiv.2301.06416

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Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model

Physical review. A/Physical review, A (2019)

Bin-Bin Mao Liangsheng Li Yimin Wang Wen‐Long You Wei Wu

We present an analytical method for the two-qubit quantum Rabi model. While still operating in the frame of the generalized rotating-wave approximation (GRWA), our method further embraces the idea of introducing variational parameters. The optimal value of the variational parameter is determined by minimizing the energy function of the ground state. Comparing with numerical exact results, we show that our method evidently improves the accuracy of the conventional GRWA in calculating fundamental physical quantities, such as energy spectra, mean photon number, and dynamics. Interestingly, the accuracy of our method allows us to reproduce the asymptotic behavior of mean photon number in large frequency ratio for the ground state and investigate the quasi-periodical structure of the time evolution, which are incapable of being predicted by the GRWA. The applicable parameter ranges cover the ultrastrong coupling regime, which will be helpful to recent experiments.

Variational method

10.1103/physreva.99.033834

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Squeezing based analytical variational method for the biased quantum Rabi model in the ultrastrong coupling regime

Journal of Physics A Mathematical and Theoretical (2019)

Weijie Xie Bin-Bin Mao Guangzhuo Li Weihang Wang Chen Sun

Rabi cycle

10.1088/1751-8121/ab4b7a

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Sampling reduced density matrix to extract fine levels of entanglement spectrum

arXiv (Cornell University) (2023)

Bin-Bin Mao Yiming Ding Zheng Yan

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.

Density matrix

TRACE (psycholinguistics)

Matrix (chemical analysis)

10.48550/arxiv.2310.16709

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Magnetization jump in one dimensional J − Q 2 model with anisotropic exchange

Scientific Reports (2017)

Bin-Bin Mao Chen Cheng Fuzhou Chen Hong‐Gang Luo

We investigate the adiabatic magnetization process of the one-dimensional $J-Q_{2}$ model with XXZ anisotropy $g$ in an external magnetic field $h$ by using density matrix renormalization group (DMRG) method. According to the characteristic of the magnetization curves, we draw a magnetization phase diagram consisting of four phases. For a fixed nonzero pair coupling $Q$, i) when $g<-1$, the ground state is always ferromagnetic in spite of $h$; ii) when $g>-1$ but still small, the whole magnetization curve is continuous and smooth; iii) if further increasing $g$, there is a macroscopic magnetization jump from partially- to fully-polarized state; iv) for a sufficiently large $g$, the magnetization jump is from non- to fully-polarized state. By examining the energy per magnon and the correlation function, we find that the origin of the magnetization jump is the condensation of magnons and the formation of magnetic domains. We also demonstrate that while the experienced states are Heisenberg-like without long-range order, all the \textit{jumped-over} states have antiferromagnetic or N\'eel long-range orders, or their mixing.

Heisenberg model

10.1038/s41598-017-17887-w

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An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Chinese Physics B (2018)

Bin-Bin Mao Maoxin Liu Wei Wu Liangsheng Li Zu‐Jian Ying

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ, which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation (GRWA) in both qualitative and quantitative aspects.

Unitary transformation

Variational method

10.1088/1674-1056/27/5/054219

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Citations (8)

Anomaly and symmetry fractionalization of mirror-symmetric fermionic topological orders

Bulletin of the American Physical Society (2020)

Bin-Bin Mao Chenjie Wang

Fractionalization

Anomaly (physics)

Source

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Mirror anomaly in fermionic topological orders

Physical Review Research (2020)

Bin-Bin Mao Chenjie Wang

The authors derive an expression for the anomaly indicator which is able to detect quantum anomaly associated with the mirror symmetry in general two dimensional fermionic topological orders. Anomalous topological orders can live only on the surface of 3D topological crystalline superconductors, and the authors' derivation establishes a direct correspondence between properties of the bulk and boundary, namely a bulk-boundary correspondence.

Anomaly (physics)

Mirror symmetry

10.1103/physrevresearch.2.023339

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Citations (4)