Riccardo Rossi
In this note, we present an efficient algorithm to sample directly the self-energy in the framework of the Connected Determinant technique. The introduction of the formalism of many-variable formal power series is essential to the proof, and more generally it is a natural mathematical tool for diagrammatic expansions.
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We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient approach expresses the sum of a factorial number of one-particle-irreducible diagrams as a recursive sum of determinants with exponential complexity. By comparing results for the two-dimensional Hubbard model with those obtained from state-of-the-art diagrammatic Monte Carlo, we show that we can reach higher perturbation orders and greater accuracy for the same co…
Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal quantum Monte Carlo simulation of interacting fermion systems. Guided by a self-learned bosonic effective action, our method uses a cumulative update [arXiv:1611.09364] algorithm to sample auxiliary field configurations quickly and efficiently. We demonstrate that self-learning determinantal Monte Carlo method can reduce the auto-correlation time to as short as o…
Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of non-local interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transi…
Truncated-Determinant Diagrammatic Monte Carlo for Fermions with Contact Interaction
对于某些相互作用费米子模型，蒙特卡罗（MC）模拟中臭名昭著的符号问题的已知解决方案是使用宏观费米子行列式;然而，代价是花费在基本局部更新上的数值努力的宏观尺度。我们发现，{ \it比}的两个宏观决定因素，可以找到任何所需的精度，考虑截断（本地的空间和时间）矩阵。在这方面，相互作用费米子系统的MC变得类似于符号问题的玻色子系统的系统大小无关的更新成本。我们证明了截断行列式方法的实用性，通过模拟有吸引力的哈伯德模型内的MC计划的基础上部分求和费曼图。我们推测，类似的方法可能是有用的，在其他实现的无符号行列式计划。
Quantum Monte Carlo determinantal algorithm without Hubbard-Stratonovich transformation: a general consideration
提出了一种连续时间行列式算法，用于相互作用费米子的量子蒙特卡罗模拟。该方案不调用Hubbard-Stratonovich变换。费米子作用分为两部分。其中一个包含相互作用和某些附加项;另一个是纯高斯的。第一部分被认为是一个扰动。配分函数的级数展开式的项在随机游走过程中产生。分析了算法的符号问题和复杂度。我们认为，该计划应该是有用的，特别是与非本地相互作用的系统。
Electrically controllable magnetic order in the bilayer Hubbard model on honeycomb lattice --- a determinant quantum Monte Carlo study
层状反铁磁自旋密度波（LAF）态是电荷中性Bernal堆叠双层石墨烯的一种可能的基态。本文用量子行列式蒙特卡罗方法研究了电场对蜂窝晶格上双层哈伯德模型中磁序的影响。我们的结果定性地支持了平均场论中的LAF基态。然而，得到的磁矩比平均场论中估计的要小得多。随着电场的增加，磁序参量迅速减小。
We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to connected diagrams, allows us to reach high ($\sim 10$) orders of the weak-coupling expansion for the self-energy of the two-dimensional Hubbard model. Access to high orders reveals a non-trivial analytic structure of the self-energy and enables its controlled reconstruction with arbitrary momentum resolution in the nonperturbative regime of essentially strong co…
Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model
用量子蒙特卡罗方法研究了强关联双层扩展哈伯德模型中激子凝聚的可能性。为了模拟现场排斥U和层间相互作用V，我们引入了一种新的更新方案，扩展了标准的谢尔曼-莫里森更新。我们观察到，符号问题急剧增加，包括层间相互作用V，这禁止在这个阶段一个明确的结论，关于激子凝聚的存在。然而，层间隧穿结果的增强表明，最强的激子凝聚趋势位于10- 20%p/n掺杂附近。磁性和导电性被证明是相对独立的层间相互作用。
The quantum Monte Carlo algorithm is arguably one of the most powerful computational many-body methods, enabling accurate calculation of many properties in interacting quantum systems. In the presence of the so-called sign problem, the algorithm typically relies on trial wave functions to eliminate the exponential decay of signal-to-noise ratio, usually at the expense of a bias in the result. The quality of the trial state therefore is critical for accurate simulations. In this work, benchmark results of the ground state auxiliary-field quantum Monte Carlo method are reported for the Hubbard m…
Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is studied using a three-band tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic …
Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study …
Delay Update in determinant quantum Monte Carlo
本文针对行列式量子蒙特卡洛更新效率瓶颈，提出可处理在位与扩展相互作用的广义延迟更新方案，并验证其显著提升模拟效率、支持更大系统尺寸。
While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence o…
The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, $E_F$, which are still above the SC transition. We find that the SC susceptibility at low $T$ agrees quantitatively with the ME theory up to a dimensionless electron-phonon coupling $λ_0 \approx 0.4$ but deviates dramatically for larger $λ_0$. We find that for large $λ_0$ and small …
Determinant Quantum Monte Carlo Study of the Orbitally Selective Mott Transition
利用行列式量子蒙特卡罗（DQMC）方法研究了二维双带费米子哈伯德模型的电导率、态密度和磁关联。我们发现，轨道选择性莫特过渡（OSMT）发生在更弱的相互作用带可以是金属，尽管完全本地化的强相互作用带。DQMC方法使我们能够测试使用动量独立的自能的有效性，这在以前的OSMT研究中一直是一个中心近似。此外，我们发现，长程反铁磁序（LRAFO）建立在绝缘相，类似于单带，正方形晶格哈伯德哈密顿量。由于绝缘行为的临界相互作用强度远小于巡游轨道的带宽，我们认为LRAFO的发展在转变中起着关键作用。
We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scal…
Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model
我们用行列式量子蒙特卡罗方法对二维Hubbard-Holstein模型进行了数值研究。在这里，我们提出的方法的细节，强调治疗的晶格自由度，然后研究的填充和行为的费米子符号作为模型参数的函数。我们发现一个区域的参数空间与大荷斯坦耦合费米子符号恢复，尽管哈伯德相互作用的大值。这表明，在有限的载流子浓度的相关极化子的研究可能是访问DQMC模拟。然后，我们限制自己的半满模型，并检查反铁磁结构因子的演变，其他指标的反铁磁和电荷密度波顺序，和能量的电子和晶格自由度的函数的电子-声子耦合。从这一点上，我们找到了进一步的证据之间的竞争电荷密度波和反铁磁秩序在半填充。
When performing a Monte Carlo calculation, the running time should in principle be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this work, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space", which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and …
We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two non-orthogonal Slater determinants, and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. The significance of orbital optimization in ex…
We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diag…
Néel temperature and thermodynamics of the half-filled 3D Hubbard model by Diagrammatic Determinant Monte Carlo
利用大规模无偏图行列式蒙特卡罗模拟研究了三维哈伯德模型在半充满状态下接近Néel相变的热力学性质.我们得到了在强关联区的转变温度，以及能量、熵、双占有率和最近邻自旋关联函数的温度依赖性。我们的研究结果提高了以前的无偏研究的准确性，并提出了准确的基准正在进行的努力，以实现反铁磁态的物质与超冷原子在光晶格。
A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
我们提出了一个有效的低秩更新算法，用于更新量子蒙特卡罗（QMC）模拟中使用的试验波函数。该算法基于Slater行列式的低秩更新。特别地，与需要O（N^2）次计算的传统算法相比，该算法在第k步期间的计算复杂度为O（kN），其中N是系统大小。对于单行列式试探波函数，新算法比传统的O（N^2）Sherman-Morrison算法快，最多可达O（N）次更新。对于M+1个行列式的多行列式组态相互作用型试探波函数，新算法的效率明显提高，节省了O（MN^2）的工作量和O（MN^2）的存储量。该算法使更准确和更有效的QMC计算使用组态相互作用型波函数。
A comparative determinant quantum Monte Carlo study of the acoustic and optical variants of the Su-Schrieffer-Heeger model
本研究通过行列式量子蒙特卡洛方法比较一维SSH声学模型与两种光学变体，证明半填充下前两者结果误差范围内一致，键模型因q=0声子模耦合存在定量差异，为类SSH相互作用建模提供参考。
We present a method for computing the full probability distribution function of quadratic observables for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo. Especially, in cold atoms experiments with single site resolution, such full counting statistics can be obtained from repeated projective measurements. We demonstrate, that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find exc…
Determinant Quantum Monte Carlo Study of the Screening of the One Body Potential near a Metal-Insulator Transition
本文用行列式量子MonteCarlo方法研究了具有随机位序的二维哈伯德模型。结果表明，与键无序的情况一样，当系统的排斥力U超过临界值U_c时，系统也会经历从Anderson绝缘相到金属相的转变.然而，似乎没有明显的信号，这种金属-绝缘体过渡的屏蔽网站的能量。我们观察到，当相互作用值达到U_c的两倍时，体系仍保持金属性，而电导率在刚超过U_c的金属相中最大，并随着相关性的增大而减小。
Off-diagonal Wave Function Monte Carlo Studies of Hubbard Model I
本文提出了一种研究哈伯德模型的蒙特卡罗方法，它是量子蒙特卡罗方法和变分蒙特卡罗理论的混合方法。该理论是基于非对角和Gutzwiller型相关因子，考虑到由蒙特卡洛算法。在4x4系统中，我们的方法能够再现通过对角化获得的精确结果。最后给出了二维正方晶格半满带情形的应用。的能量是有利的量子蒙特卡罗数据相比。
Determinant Quantum Monte Carlo Study of the Enhancement of d-wave Pairing by Charge Inhomogeneity
条纹相是铜氧化物超导体的一个已知的实验特征，在二维Hubbard哈密顿量的各种数值处理中也发现了这种条纹相，其中自旋、电荷和配对关联在CuO_2平面内不均匀地变化。在本文中，我们使用行列式量子蒙特卡罗表明，如果条纹密度图案施加在模型上，d波配对顶点显着增强。我们将这种增强归因于当掺杂空穴被限制在条纹中时，由更多的接近半填充区域的出现引起的反铁磁有序的增加。我们还观察到磁序中的π相移。
We present a simple trick that allows to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models. With our approach one achieves superior performance compared to Diagrammatic Monte Carlo, while rendering the algorithmic part dramatically simpler. As we consider the sum of all connected diagrams at once, we allow for cancellations between diagrams with different signs, alleviating the sign problem. Moreover, the complexity of the calculation grows exponentially with the order of the expansion, which should be constrasted with the…
Comment on "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory"
关于投影量子蒙特卡罗方法中Anderson正交性突变重要性的一点评论。
Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
纠缠熵等纠缠度量已经成为研究相互作用量子多体系统基态基本性质的重要工具。对于相互作用的自旋或玻色子自由度系统，最近不仅在它们各自的纠缠熵的解析描述方面，而且在它们的数值分类方面都取得了很大进展。然而，相互作用的费米子自由度系统已被证明更难以控制，特别是关于它们的纠缠特性的数值理解。在这里，我们报告了一个概括的复制品技术的计算Renyi熵的框架的行列式量子蒙特卡罗模拟-选择无偏的，大规模的相互作用的费米子系统的模拟的数值方法。我们证明了这种方法的强度在最近的替代建议的基础上分解自由费米子格林函数通过研究一维哈伯德系统的纠缠熵在零和有限的温度。
Sign-problem-resilient singular-value probe in determinant quantum Monte Carlo
该研究提出利用时空费米子矩阵低能奇异值的相邻间隙比，作为行列式量子蒙特卡洛中抗符号问题的探测工具，成功追踪到两类哈伯德模型中相互作用驱动的相变。
Sampling Electronic Fock States using Determinant Quantum Monte Carlo
本文提出在行列式量子蒙特卡洛中引入福克态更新机制，实现电子福克态高效采样，并通过静态关联与动力学谱学模拟验证了方法的可靠性。
Effects of Strong Interactions in a Half Metallic Magnet: a Determinant Quantum Monte Carlo Study
半金属磁体具有带隙自旋通道和金属通道的能带结构，了解半金属磁体中电子-电子相互作用的影响不仅是一个重要的理论问题，而且对它们的潜在应用具有重要意义。在这里，我们使用决定性量子Monte Carlo研究现场哈伯德相互作用$U$，有限的温度，和外部（塞曼）磁场的双层紧束缚模型，这是一个半金属在没有相互作用的影响，通过计算的频谱密度，电导率，自旋极化载流子，和局部磁性。我们量化的影响$U$的热去极化的程度，并遵循相对带移和监测时，显着的间隙状态出现，其中每一个可以降低HM字符。对于这个模型，塞曼耦合诱导，在固定的粒子数，两个连续的转变：补偿半金属与自旋下降带隙$\rightarrow$金属铁磁体$\rightarrow$饱和铁磁绝缘体。然而，在大多数更相关的参数范围内，半金属性质对$U$相当稳健。
Determinant Quantum Monte Carlo Study of d-wave pairing in the Plaquette Hubbard Hamiltonian
决定子量子蒙特卡罗（DQMC）是用来确定配对和磁响应的哈伯德模型建立了四个网站集群-一个二维正方形晶格组成的元素2x2格元与跳跃$t$和现场排斥$U$耦合格元间跳跃$t' \leq t$。在这种几何结构中的超导性以前已经研究了各种解析和数值方法，不同的结论关于配对相关性和转变温度是否提高近半填充的非均匀跳跃或没有。对于$U/t=4$，DQMC表示配对顶点最吸引的最佳$t'/t \approx 0.4$。最佳$t'/t$随$U/t$增加而增加。然后，我们将我们的结果进行对比，这与一个汉密尔顿模型，而不是涉及一个规则的网站能量的大网站能量限制是三带CuO $_2$模型，我们发现，有不均匀性迅速，单调，抑制配对。
The half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
本文利用行列式量子蒙特卡洛模拟研究半满扩展Hubbard模型，通过引入平均符号作为可观测量，精确确定了正方晶格上反铁磁、电荷有序、超导及相分离等相的基态相边界，并给出了部分有限温度相图。
Stable Determinant Monte Carlo Simulations at Large Inverse Temperature $β$
本文提出通过矩阵分解方法解决大β下DQMC模拟中的精度损失和数值不稳定性问题，实现β>90的稳定模拟，适用于石墨烯结构的室温条件。
Superconductivity near two-dimensional Van Hove singularities: a determinant quantum Monte Carlo study
研究通过确定性量子蒙特卡洛模拟，探讨二维吸引性Hubbard模型在普通和高阶Van Hove奇点附近超导临界温度Tc的变化，发现弱耦合下Tc增强不明显，强耦合下Tc最大值出现在非奇点密度区域。
We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, …
In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To investigate this phenomenon, we study a minimal electronic model of FeSe, with interactions that enhance nematic fluctuations. This model is sign problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We developed a DQMC algorithm with parallel tempering, which proves to be an efficient source of global updates and allows us to access the r…
Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
本文发展并验证新型 meron 团簇算法，在不计算费米子行列式的情况下模拟耦合 $\mathbb{Z}_2$ 与 $U(1)$ 规范场的费米子，并在 $(1+1)$ 维模型中展示低温高斯定律涌现。
Motivated by recent experiments realizing correlated phenomena and superconductivity in 2D van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model, and a partially flat band structure containing a non-dispersing region, with identical total non-interacting bandwidth $W$. For both repulsive and attractive weak interactions …
SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
本文介绍了SmoQyDQMC.jl 2.0版本，该工具支持广义紧束缚哈密顿量及Hubbard和电子-声子相互作用，采用优化的混合蒙特卡洛方法高效采样声子场，适用于低能声子分支模拟。
Monte Carlo simulation method for Laughlin-like states in a disk geometry
我们讨论了另一种精确的蒙特卡罗方法来计算圆盘几何中分数量子霍尔效应的劳克林态的基态能量和相关量。这种替代方法使我们能够获得准确的散装制度（热力学极限）的各种数量的蒙特卡罗模拟与少量的粒子（远小于所需的标准蒙特卡罗方法）的值。
Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
本文首次将子矩阵更新全面引入 DQMC，支持扩展相互作用与零温度模拟，效率提升一个数量级，并据此确定半填充三维 Hubbard 模型的有限温度相图。
Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling
该研究提出DQ²MC量子算法，将DQMC核心的辅助场采样迁移至量子计算机，消除马尔可夫链，电路深度更优，其费米子符号问题成本与量子弱值后选择开销精确对应。
We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by multiboson fields located on the boundaries of the blocks. The resultant multiboson domain-decomposed hybrid Monte Carlo passes extensive numerical tests carried out by measuring standard gluonic observables. The combination of the determinant factorization and of the one of the propagator, that we put forward recently, paves the way for multilevel Monte Carlo integ…
GPU-accelerated Auxiliary-field quantum Monte Carlo with multi-Slater determinant trial states
本文在开源ipie中实现GPU加速的多Slater行列式ph-AFQMC，在过渡金属团簇上取得至少六倍加速，并以超10万个行列式恢复化学精度所需动态关联。
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this compara…
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