arXiv subjects

Bin-Bin Mao

Publications and source records attributed to Bin-Bin Mao.

At least 19 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, Rényi 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

Spontaneous continuous-symmetry breaking and tower of states in a comb chain

Based on the study of a one-dimensional (1D) antiferromagnetic Heisenberg model on a comb lattice, this work identifies an example of spontaneous continuous symmetry breaking in a 1D system with short-range interactions. When a symmetry-preserving relevant perturbation is applied to the system, we find that this model can always be described by the Marshall-Lieb-Mattis (MLM) theorem. The Shen-Qiu-Tian theorem establishes a direct connection between the MLM theorem (in the case of bipartite lattices with unequal numbers of sites in the two sublattices) and the breaking of continuous symmetry. Moreover, although authors of previous studies have suggested that the presence of a tower of states (TOS) serves as an important numerical diagnostic of the tendency of a system toward spontaneous symmetry breaking, these investigations have primarily focused on two-dimensional systems. In 1D systems, however, the presence of long-range order does not automatically imply the emergence of a TOS. Here, we observe the existence of a TOS in a 1D realistic ferrimagnetic lattice system with short-range interactions.

cond-mat.str-el↗

arXiv2026

Generalized Reduced-Density-Matrix Quantum Monte Carlo Gives Access to More

For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of them are insurmountable. In this article, we point out that all the difficulties stem from the starting point of the simulation: calculating a partition function. We introduce a paradigm shift: when we transform the simulated object from a partition function to a generalized reduced density matrix (GRDM), the difficult problem of measurement can be readily solved. By designing the GRDM, both equal-time and nonequal-time off-diagonal observables have been measured easily in QMC with a polynomial computation complexity. As a demonstration, the GRDM enables direct access to nonequal-time correlators for dynamical spectra as well as Rényi-1 correlators that reveal strong-to-weak symmetry breaking in the mixed state, capabilities that lie beyond the reach of prior methods. This establishes a unified framework for holographic characterization within QMC.

cond-mat.str-el↗

arXiv2026

Addressing general measurements in quantum Monte Carlo

Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems, namely the sign problem and general measurement issues, have seriously hampered its scope of application. We propose a universal scheme to tackle the problems of general measurement. The target observables are expressed as the ratio of two types of partition functions $\langle \mathrm{O} \rangle=\bar{Z}/Z$, where $\bar{Z}=\mathrm{tr} (\mathrm{Oe^{-βH}})$ and $Z=\mathrm{tr} (\mathrm{e^{-βH}})$. These two partition functions can be estimated separately within the reweight-annealing frame, and then be connected by an easily solvable reference point. We have successfully applied this scheme to XXZ model and transverse field Ising model, from 1D to 2D systems, from two-body to multi-body correlations and even non-local disorder operators, and from equal-time to imaginary-time correlations. The reweighting path is not limited to physical parameters, but also works for space and time. Essentially, this scheme solves the long-standing problem of calculating the overlap between different distribution functions in mathematical statistics, which can be widely used in statistical problems, such as quantum many-body computation, big data and machine learning.

cond-mat.str-el↗

arXiv2026

Detecting (emergent) continuous symmetry of criticality via subsystem's entanglement spectrum

The (emergent) symmetry of a critical point is one of the most important information to identify the universality class and effective field theory, which is fundamental for various critical theories. However, the underlying symmetry so far can only be conjectured indirectly from the dimension of the order parameters in symmetry-breaking phases, and its correctness requires further verifications to avoid overlooking hidden order parameters, which by itself is also a difficult task. In this work, we propose an unbiased way to numerically identify the underlying (emergent) symmetry of a critical point in quantum many-body systems, without prior knowledge about its low-energy effective field theory. Through calculating the reduced density matrix in a very small subsystem of the total system numerically, the Anderson tower of states in the entanglement spectrum clearly reflects the underlying (emergent) symmetry of the criticality. It is attributed to the fact that the entanglement spectrum can observe the broken symmetry of the entanglement ground-state after cooling from the critical point along an extra temperature axis.

quant-ph↗

arXiv2026

Universal and non-universal contributions of entanglement under different bipartitions

Entanglement entropy (EE) is a fundamental probe of quantum phases and critical phenomena, which was thought to reflect only bulk universality for a long time. Very recently, people realized that the microscopic geometry of the entanglement cut can induce distinct entanglement-edge modes, whose coupling to bulk critical fluctuations may alter the scaling of the EE. However, this perception is very qualitative and lacks quantitative consideration. Here, we investigate this problem through high-precision quantum Monte Carlo simulations combined with the analysis of scaling theory to build a quantitative understanding. By considering three distinct bipartitions corresponding to three surface criticality types, we reveal a striking dependence of the constant term γ on the microscopic cut at the quantum critical point. Notably, cuts that generate extra gapless edge modes yield a sign reversal in γ compared to those producing gapped edges. We explain this behavior via a modified scaling form that incorporates contributions from both bulk and surface critical modes. Furthermore, we demonstrate that the derivative of EE robustly extracts the bulk critical point and exponent ν regardless of the cut geometry, providing a reliable diagnostic of bulk universality in the presence of strong surface effects. Our work for the first time establishes a direct quantitative connection between surface criticality and entanglement scaling, challenging the conventional view that EE solely reflects bulk properties and offering a refined framework for interpreting entanglement in systems with boundary-sensitive criticality.

cond-mat.str-el↗

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

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

High-efficiency quantum Monte Carlo algorithm for extracting entanglement entropy in interacting fermion systems

The entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo has made great achievements in large-scale interacting spin/boson systems. In contrast, the numerical exploration in interacting fermion systems is rare, even though fermion systems attract more attentions in condensed matter. The fundamental restrictions is that the computational cost of fermion quantum Monte Carlo ($\sim βN^3$) is much higher than that of spin/boson ($\sim βN$). Here, $N$ is the total number of sites and $β$ is the inverse temperature or projection length. To tackle this problem, we propose a fermionic quantum Monte Carlo algorithm based on the incremental technique along physical parameters, which greatly improves the efficiency of extracting entanglement entropy. We benchmark the developed algorithm by calculating the scaling behavior of the entanglement entropy in a two-dimensional square lattice Hubbard model. The obtained phase diagram including Fermi surface and Goldstone modes validates the correctness of the algorithm. Remarkably, our method shows the high-efficiency with respect to the existing algorithms, while keeping the high computation precision. We proceed to apply this algorithm to explore the scaling behavior of the entanglement entropy and particularly its derivative at Gross-Neveu criticality. Our results elucidate that such critical behavior can be quantified by the correlation length exponent.

cond-mat.stat-mech↗

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↗

arXiv2025

Identifying two-dimensional topological phase transition by entanglement spectrum : A fermion Monte Carlo study

Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in one-dimension properly, while in higher dimension, it exceeds the capacity of the algorithms. To expand the ability of existing numerical methods, we takes a different approach via quantum Monte Carlo algorithm. By exploiting particle number and spin symmetry, we realize an efficient algorithms to solve the entanglement spectrum in the interacting fermionic system. Taking two-dimensional interacting Su-Schrieffer-Heeger as example, we verify the existence of topological phase transition under different types of many-body interactions. The calculated particle number distribution and wave-function of entanglement Hamiltonian indicate that the two belong distinct types of topological phase transitions.

cond-mat.str-el↗

arXiv2024

Sudden change in entanglement Hamiltonian: Phase diagram of an Ising entanglement Hamiltonian

The form of the entanglement Hamiltonian varies with the parameters of the original system. Whether there is a singularity is the key problem for demonstrating/negating the universality of the relation between the entanglement spectrum and edge energy spectrum. We carefully study the phase diagram of a 1D Ising entanglement Hamiltonian as an example to clarify the long-standing controversy of the general relation between the entanglement Hamiltonian and original Hamiltonian. Interestingly, even if the singularities indeed exist, the Li-Haldane-Poilblanc conjecture, i.e., the general relation between the entanglement spectrum and edge energy spectrum, seemingly still holds.

cond-mat.str-el↗

arXiv2023

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

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.

quant-ph↗

arXiv2023

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

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.

cond-mat.str-el↗

arXiv2021

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries

We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous ten-fold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimension reduction and folding approaches, we re-derive the classification of bulk SPT phases and define a \emph{complete} set of bulk topological invariants for every symmetry group under consideration, and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as \emph{anomaly indicators} for the surface SETs which carry 't Hooft anomalies of the associated symmetries whenever the bulk is topologically non-trivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent.

cond-mat.str-el↗

arXiv2021

Mirror anomaly in fermionic topological orders

We study general 2D fermionic topological orders enriched by the mirror symmetry with $\mathcal{M}^2=1$. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors. Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a $\mathbb{Z}_{16}$ classification. In this work, we derive an explicit expression, namely an \emph{anomaly indicator}, for the $\mathbb{Z}_{16}$ mirror anomaly for general fermionic mirror SETs. This derivation is based on the recently developed folding approach, originally proposed for bosonic topological orders. We generalize it to fermion systems. Through this approach, we establish a direct bulk-boundary correspondence between surface fermionic topological orders and 3D bulk topological crystalline superconductors. In addition, during the derivation, we obtain some general properties of fermionic topological orders as well as a few constraints on properties of fermionic mirror SETs.

cond-mat.str-el↗

arXiv2019

Quantum phase transitions and critical behaviors in the two-mode three-level quantum Rabi model

We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio $η$ of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete $Z_{2}$ symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous $U(1)$ symmetry. For a large enough but finite $η$, the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.

quant-ph↗