arXiv subjects

Gaopei Pan

Publications and source records attributed to Gaopei Pan.

At least 19 recordsLinked to original sources

arXiv2025

Quantum Monte Carlo studies of U(1) lattice gauge models of Kondo breakdown

In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. Motivated by this perspective, we study a minimal compact U(1) lattice gauge model describing a spin chain coupled to two-dimensional Dirac conduction electrons. The spin chain is described by fermionic partons carrying spin and U(1) gauge charge. The heavy-fermion quasiparticle is a bound state of a U(1) matter field carrying unit electric charge and U(1) gauge charge, and the fermionic parton. Using sign-problem-free determinant quantum Monte Carlo simulations, we identify two symmetry-equivalent regimes: a heavy-fermion metal with a sharp composite-fermion resonance and robust low-frequency transport, and a Kondo-breakdown metal with an incoherent resonance and vanishing low-frequency transport. For any finite lattice extent in the direction perpendicular to the chain, the Luttinger volume of the heavy-fermion phase counts both composite and conduction electrons, while in the Kondo-breakdown phase it counts only the conduction electrons. The evolution of the composite-fermion spectrum, dynamical spin structure factor, and optical conductivity provides a nonperturbative demonstration of gauge-mediated Kondo breakdown and establishes transport fingerprints of an orbital-selective Mott transition in the context of U(1) gauge theories of heavy fermions.

cond-mat.str-el↗

arXiv2025

Self-learning Monte Carlo Method: A Review

The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of interacting many-body systems, SLMC significantly improves sampling efficiency by constructing an effective model -- via machine learning methods -- based on configurations generated by conventional Monte Carlo methods and then proposes global updates based on the effective model. This enhancement leads to a substantial reduction in autocorrelation time, especially near the critical region, where traditional methods typically suffer from critical slowing down and increased computation complexity. Moreover, SLMC maintains statistical accuracy by implementing a cumulative update scheme that rigorously satisfies the detailed balance condition. And more recent applications have extended the SLMC to convolutional neural networks with applications not only in condensed matter physics but also high-energy physics, quantum chemistry, and quantum simulations. The generic applicability and high computational efficiency make SLMC a powerful and scalable framework for quantum Monte Carlo simulations of strongly correlated electron systems, extending the reach of numerical investigations beyond the limitations of conventional techniques.

cond-mat.str-el↗

arXiv2025

Local spectroscopy of loop current order with individual magnetic atoms

Hidden ordered states--characterized by order parameters that elude conventional probes--pose a fundamental challenge for their identification in quantum materials. Recent experiments report evidence for time-reversal symmetry breaking orbital magnetic order and anomalous transport signatures in the $2a\times2a$ charge density wave state of the kagome metal CsV$_3$Sb$_5$ at a temperature $T<30\,$K. Theoretical analyses propose that a time-reversal symmetry breaking loop-current order could exist as the ground state of this charge density wave. However, this microscopic interpretation remains debated and experimentally unverified. In this work, we employ individual magnetic atoms as local quantum sensors to examine the quasiparticle excitations of the charge density wave in CsV$_3$Sb$_5$ with the scanning tunneling microscope. Our spectroscopic measurements show that the magnetic moment of Co induces a spatially localized $dI/dV$ peak inside the spectral gap of the charge density wave near the Fermi energy. Conducting temperature-dependent spectroscopy, we find that this spectral feature emerges at $T<30\,$K. By comparing our experimental observations with results of quantum many-body simulations and realistic tight-binding model calculations, we show that this spectroscopic signature can be naturally interpreted as a local flux defect in a loop current ordered state, arising from the Kondo coupling of the magnetic moment of Co with the loop current electrons. The excellent agreement between our experimental and theoretical results suggests the presence of loop-current order in the $2a\times2a$ charge density wave of CsV$_3$Sb$_5$ at $T<30\,$K. Our results provide a microscopic picture to the observation of time-reversal symmetry breaking orbital magnetism and anomalous transport signatures detected in measurements of the macroscopic material properties.

cond-mat.str-el↗

arXiv2024

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 ($\sim \beta N^3$) is much higher than that of spin/boson ($\sim \beta N$). Here, $N$ is the total number of sites and $\beta$ 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↗

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

Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions

Employing large-scale quantum Monte Carlo simulations, we find that in the magnetized interacting Dirac fermion model there emerges a universal collective Larmor-Silin spin wave mode in the transverse dynamical spin susceptibility. Such mode purely originates from the interaction among Dirac fermions and distinguishes itself from the usual particle-hole continuum with finite lifetime and clear dispersion, both at small and large momenta in a large portion of the Brillouin zone. Our unbiased numerical results offer the dynamic signature of this collective excitation in interacting Dirac fermion systems, and provide experimental guidance for inelastic neutron scattering, electron spin resonance, and other spectroscopic approaches in the investigation of such universal collective modes in quantum Moire materials, topological insulators, and quantum spin liquid materials under magnetic field, with quintessential interaction nature beyond the commonly assumed noninteracting Dirac fermion or spinon approximations.

cond-mat.str-el↗

arXiv2023

An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation

Exponential observables, formulated as $\log \langle e^{\hat{X}}\rangle$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement entropy. Given that $e^{X}$ becomes exponentially large (or small) in the thermodynamic limit, accurately computing the expectation value of this exponential quantity presents a significant challenge. In this Letter, we propose a comprehensive algorithm for quantifying these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo (DQMC) method. We have applied this novel algorithm to the 2D half-filled Hubbard model. At the strong coupling limit, our method showcases a significant accuracy improvement compared to conventional methods that are derived from the internal energy. We also illustrate that this novel approach delivers highly efficient and precise measurements of the nth R\'enyi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be easily generalized to other models.

cond-mat.str-el↗

arXiv2023

Disorder Operator and R\'enyi Entanglement Entropy of Symmetric Mass Generation

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and R\'enyi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT.

cond-mat.str-el↗

arXiv2023

Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene

The ground states of twisted bilayer graphene (TBG) at chiral and flat-band limit with integer fillings are known from exact solutions, while their dynamical and thermodynamical properties are revealed by unbiased quantum Monte Carlo (QMC) simulations. However, to elucidate experimental observations of correlated metallic, insulating and superconducting states and their transitions, investigations on realistic, or non-chiral cases are vital. Here we employ momentum-space QMC method to investigate the evolution of correlated states in magic-angle TBG away from chiral limit at charge neutrality with polarized spin/valley, which approximates to an experimental case with filling factor $\nu=-3$. We find that the ground state evolves from quantum anomalous Hall insulator into an intriguing correlated semimetallic state possessing heavy-fermion features as AA hopping strength reaches experimental values. Such a state resembles the recently proposed heavy-fermion representations with localized electrons residing at AA stacking regions and delocalized electrons itinerating via AB/BA stacking regions. The spectral signatures of the localized and itinerant electrons in the heavy-fermion semimetal phase are revealed, with the connection to experimental results being discussed.

cond-mat.str-el↗

arXiv2023

Stable computation of entanglement entropy for 2D interacting fermion systems

There is no doubt that the information hidden in entanglement entropy (EE), for example, the $n$-th order R\'enyi EE, i.e., $S^{A}_n=\frac{1}{1-n}\ln \Tr (\rho_A^n)$ where $\rho_A=\mathrm{Tr}_{\overline{A}}\rho$ is the reduced density matrix, can be used to infer the organizing principle of 2D interacting fermion systems, ranging from spontaneous symmetry breaking phases, quantum critical points to topologically ordered states. It is far from clear, however, whether the EE can actually be obtained with the precision required to observe these fundamental features -- usually in the form of universal finite size scaling behavior. Even for the prototypical 2D interacting fermion model -- the Hubbard model, to all existing numerical algorithms, the computation of the EE has not been succeeded with reliable data that the universal scaling regime can be accessed. Here we explain the reason for these unsuccessful attempts in EE computations in quantum Monte Carlo simulations in the past decades and more importantly, show how to overcome the conceptual and computational barrier with the incremental algorithm, such that the stable computation of the EE in 2D interacting fermion systems can be achieved and universal scaling information can be extracted. Relevance towards the experimental 2D interacting fermion systems is discussed.

cond-mat.str-el↗

arXiv2023

The teaching from entanglement: 2D SU(2) antiferromagnet to valence bond solid deconfined quantum critical points are not conformal

The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of symmetries and their spontaneous breaking -- has been proposed and actively pursued for more than two decades. Various 2D quantum many-body lattice models, both in spin/boson and fermion representations have been tested with the state-of-the-art numerical techniques and field-theoretical analyses, and yet, the conclusion is still controversial. Experimental realizations of DQCP in the quantum magnet SrCu$_2$(BO$_3$)$_2$ and superconducting quantum criticality in 2D material have either shown first order transition or intermediate phase. The tension between the lattice scale details and the requirement from continuum limit, manifested in the form of the inconsistent critical scaling behavior and violations of generic conformal bootstrap bound, has not been resolved. Here we solve these decades-long controversies from the new and fundamental perspective of the quantum entanglement. We develop the incremental algorithm to compute the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data and reveal the universal coefficient of the logarithmic correction therein is negative and at odds with positivity requirement of the conformal field theory. Together with results in other 2D DQCP lattice models (both in fermion and spin systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to valence bond solid DQCPs are not conformal fixed point and naturally explain the experimental difficulties in finding them. This marks the end of the beginning of unambiguous finding of the quantum phase transitions truely beyond the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.

cond-mat.str-el↗

arXiv2023

Defining a universal sign to strictly probe a phase transition

The mystery of the infamous sign problem in quantum Monte Carlo simulations mightily restricts applications of the method in fermionic and frustrated systems. A recent work [Science 375, 418 (2022)] made a remarkable breakthrough in the sign problem by pointing out that the sign can be used to probe phase transition. In this work, we proposed a general argument based on the definition of the sign that is related to the difference in free energy between the original and reference systems to clarify that the sign problem and phase transition cannot always be strictly related. The sign can exactly probe phase transition only if the free energy in the reference system is flat under variable parameters, which is almost impossible to design. Generally speaking, the conclusion that the sign can probe phase transition is survivorship bias without universality. To solve this problem, we define a modified sign that excludes the influence of the reference system, which can probe the phase transition strictly. The work gives an unbiased solution for detecting phase transition by the new modified sign.

cond-mat.stat-mech↗

arXiv2022

Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model

We show that for magic-angle twisted bilayer graphene (TBG) away from charge neutrality, although quantum Monte Carlo (QMC) simulations suffer from the sign problem, the computational complexity is at most polynomial at certain integer fillings. For even integer fillings, this polynomial complexity survives even if an extra inter-valley attractive interaction is introduced, on top of Coulomb repulsions. This observation allows us to simulate magic-angle twisted bilayer graphene and to obtain accurate phase diagram and dynamical properties. At the chiral limit and filling $\nu=1$, the simulations reveal a thermodynamic transition separating metallic state and a $C=1$ correlated Chern insulator -- topological Mott insulator (TMI) -- and the pseudogap spectrum slightly above the transition temperature. The ground state excitation spectra of the TMI exhibit a spin-valley U(4) Goldstone mode and a time reversal restoring excitonic gap smaller than the single particle gap. These results are qualitatively consistent with the recent experimental findings at zero-field and $\nu=1$ filling in $h$-BN nonaligned TBG.

cond-mat.str-el↗

arXiv2022

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance and spectroscopy) of the quantum moir\'e materials such as twisted bilayer graphene and transition metal dichalcogenides. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, there exists a unique thermodynamic characteristic for the correlated flat-band models with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which "quantum teleport" the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and give rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.

cond-mat.str-el↗

arXiv2022

A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems

We summarize the recent developments in the model design and computation for a few representative quantum many-body systems, encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity, SYK non-Fermi-liquid with self-tuned quantum criticality and fluctuation induced superconductivity, and the flat-band quantum Moir\'e lattice models in continuum where the interplay of quantum geometry of flat-band wave function and the long-range Coulomb interactions gives rise to novel insulating phases at integer fillings and superconductivity away from them. Although the narrative choreography seems simple, we show how important the appropriate model design and their tailor-made algorithmic developments -- in other words, the scientific imagination inspired by the corresponding fast experimental developments in the aforementioned systems -- compel us to invent and discover new knowledge and insights in the sport and pastime of quantum many-body research.

cond-mat.str-el↗

arXiv2022

Sign Problem in Quantum Monte Carlo Simulation

Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation techniques, ranging from the world-line and stochastic series expansion Monte Carlo for boson and spin systems to the determinant and momentum-space quantum Monte Carlo for interacting fermions. We point out the basis dependency of the sign problem and summarize the progresses to cure, ease and even make use of the sign problem over the years, such as symmetry analysis of the underlying Hamiltonian, basis optimization in writting down the partition functions and many others. Moreover, we state that although traditional lore saying that in case of sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space, there are recent breakthroughs showing this is not always the case and based on the properties of the partition function for finite size systems, one could distinguish when the average sign has the usual exponential scaling and when it is bestowed with an algebraic scaling at the low temperature limit. Fermionic QMC simulations with such algebraic sign problems have been successfully carried out for extended Hubbard-type and quantum Moir\'e lattice models.

cond-mat.str-el↗

arXiv2021

Fermion sign bounds theory in quantum Monte Carlo simulation

Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of reference system and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling at low temperature limit. We analytically explain such algebraic sign problems found in flat band moir\'e lattice models at low temperature limit. At finite temperature, a domain size argument based on sign bounds also explains the connection between sign behavior and finite temperature phase transition. Sign bounds, as a well-defined observable, may have ability to ease or even make use of the sign problem.

cond-mat.str-el↗

arXiv2021

Superconductivity and bosonic fluid emerging from Moir\'e flat bands

Although evidence of inter-valley attraction-mediated by phonon or topological fluctuations is accumulating, the origin of superconductivity in the flat-band quantum moir\'e materials remains an open question. Here, instead of attempting to pinpoint the origin of the superconductivity, we aim at identifying universal properties of moir\'e flat bands that shall emerge in the presence of inter-valley attractions. We show that by matching the interaction strength of inter-valley attraction with intra-valley repulsion, the flat-band limit becomes exactly solvable. Away from the flat-band limit, the system can be simulated via quantum Monte Carlo (QMC) methods without sign problem for any fillings. Combining analytic solutions with large-scale numerical simulations, we show that upon increasing temperature, the superconducting phase melts into a bosonic fluid of Cooper pairs with large/diverging compressibility. In contrast to flat-band attractive Hubbard models, where similar effects arise only for on-site interactions, our study indicates this physics is a universal property of moir\'e flat bands, regardless of microscopic details such as the range of interactions and/or spin-oribt couplings. At higher temperature, the boson fluid phase gives its way to a pseudo gap phase, where some Cooper pairs are torn apart by thermal fluctuations, resulting in fermion density of states inside the gap. Unlike the superconducting transition temperature, which is very sensitive to doping and twisting angles, the gap and the temperature scale of the boson fluid phase and the pseudo gap phase are found to be nearly independent of doping level and/or flat-band bandwidth. The relevance of these phases with experimental discoveries in the flat band quantum moir\'e materials is discussed.

cond-mat.supr-con↗