Session N60: Quantum Many-Body Systems and Methods I

Accurate Variational Simulation of Lattice Bosons with Neural Quantum States

In recent years, neural quantum states have emerged as a powerful variational method, consistently demonstrating remarkable accuracy in representing the ground-state wave function of a wide range of non-trivial Hamiltonians. In addition to spin problems, properly tailored networks have demonstrated their effectiveness in addressing problems involving other kinds of degrees of freedom, such as fermionic and continuous-variable systems. In spite of these successes, accurate neural representations of the ground state of lattice bosonic systems have remained elusive. We introduce a Jastrow Ansatz dressed with translationally equivariant many-body features generated by a deep neural network. We show that this variational state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition and probe signatures of many-body processes involved in the depletion of the superfluid condensate that are not described by standard Bogoliubov theory.   

Tensor Network Algorithims for Simulating Many-Body Open Quantum Systems in Two Dimensions

Quantum many-body systems in the presence of drive and dissipation are some of the more difficult problems to solve numerically. Algorithms based on tensor networks have found great success in the context of closed quantum systems, and open systems in one-dimension, however their extension to two-dimensional open quantum systems has only recently come to fruition. In this presentation, a tensor network aglorithm based on the infinite projected entangled pair operator (iPEPO) ansatz detailed in Ref. [1] utilising the matrix-product operator (MPO) appoximation of the dynamical map, rather than Trotter gates, will be discussed. MPOs have the potential to represent long-range interactions and tend to be computationally less expensive. We demonstrate the accuracy of the results by comparing to exact solutions, and demonstrate that the algorithm remains stable when moving away from the exactly solveable regime. This tensor network algorithm can be used to obtain the steady states and transient dynamics of two-dimensional quantum lattice models evolving according to the Lindblad equation

[1]. C. Mc Keever and M. H. Szymańska, Phys. Rev. X 11, 021035 (2021)   

Temperature Optimization for Parallel Tempering in Neural Networks

We benchmark a parallel tempering method for the variational optimization of neural networks to approximate ground states of many-body quantum systems. We study the role played by two parameters in this method that play the role of temperature in the standard parallel tempering approach. The first is the temperature associated with the entropy term added to the local energy samples, which acts to flatten the energy landscape. The second is the temperature in the swap rule used to determine whether or not two neighboring replicas exchange their neural network configurations. We explore the effect of optimizing or fixing these two different temperatures on the performance of the variational algorithm for approximating the ground state of the two-dimensional J1-J2 model.   

Real-Space Renormalization Process using High-Order Tensor Renormalization Group for CFT properties

In the field of tensor networks, the idea of the real-space renormalization group (RG) is used to compute various properties for lattice models at the thermodynamic limit. High Order Tensor Renormalization Group (HOTRG) is such a method that iteratively combines every two lattice sites into one. Short-distance entanglement removal methods such as Graph Independent Local Truncation (GILT) are crucial for those methods to succeed when the system is at a critical point. In this work, we study the numerical results of HOTRG to see if it can be conceptually understood as a real-space renormalization process. Firstly, we confirmed that the fixed point tensor of HOTRG contains information about the corresponding Conformal Field Theory (CFT), which describes the behavior of a critical system. From the fixed point tensor, we can extract CFT data, including conformal dimensions and operator product coefficients. Secondly, we study the behavior of defects under HOTRG. In particular, we found that the point-like defects are smeared if proper short-distance entanglement removal is applied. This is expected since the concept of RG is to remove the short-distance behavior. We also discussed whether HOTRG can effectively compute the N-point function. Our results provide a better understanding of the capacity and limitations of the tenor renormalization group scheme in coarse-graining defect tensors and throw light on a better understanding of the role of entanglement on critical quantum behaviors.   

Using quantum Monte Carlo to study quantum phase transitions

We derive a scheme to estimate fidelity susceptibility in permutation matrix representation quantum Monte Carlo (PMR-QMC) and test it numerically. Fidelity susceptibility is a universal indicator of quantum phase transitions, and hence, our work allows for the study of quantum phases even without knowledge of an underlying order parameter. We remark that previous works have derived similar schemes for imaginary time and stochastic series expansion QMC (Wang et. al. PhysRevX.5.031007). However, PMR-QMC is neither an imaginary time nor stochastic series expansion method, and hence, our scheme does not follow directly from previous work. Instead, PMR-QMC is a sampling scheme over permutations with weights given by divided differences of the Boltzmann exponential. The PMR-QMC has many benefits over imaginary time and stochastic series expansion methods (Lalit et. al. J. Stat. Mech. (2020) 073105]), so our scheme inherits all these benefits over previous approaches.   

Ensemble dynamics of a classical relativistic non-integrable model

We study quench dynamics and relaxation in relativistic field theories models and give evidence that non-

integrable models do not relax to the thermal ensemble. The information content of the equilibrium state that

emerges at large times after a quench is generally expected to be related to the number of extensive (local and

quasi-local) conserved charges of the Hamiltonian describing the dynamics. In integrable models the equilibrium

state is therefore a Generalised Gibbs Ensemble where each extensive charge enters with an independent Lagrange

multiplier. In non-integrable models this ensemble is expected to reduce to the standard Gibbs ensemble since the

Hamiltonian is the only extensive charge. The mechanism that is responsible for the emergence of such equilibrium

states is believed to be the scrambling of initial state information due to the delocalisation induced by the dynamics

and the fact that initial information originating from spatially distant points is incoherent (a property that can be

expressed as correlation clustering in the initial state).   

Towards High-Precision Heterogeneous Catalysis By Quantum Monte Carlo

Our ongoing efforts to improve green energy transformation by catalysis mainly focuses on surface adsorption phenomena. Surfaces of transition metal oxides [see J. Phys. Chem. C 126, 7903 (2022)] are of particular interest where precision of DFT approximations becomes an issue. In related work, the Diffusion Monte Carlo method was shown to accurately capture the electron correlation in extended systems like CO*-Pt(111) with relatively smaller supercells, leading to cost-effective calculations [J. Phys. Chem. A 126, 4636 (2022)].

We deploy QMCPACK [J. Phys.: Condens. Matter 30, 195901 (2018)] on the NERSC Perlmutter machine and discuss the relative performance of the CPU and GPU implementation. We reproduced the CO*-Pt(111) puzzle and tested the size extrapolation scheme. Our main project is to assess the accuracy of the commonly utilized DFT methods for the (110) surface of RuO2, a well-known catalytic system for oxygen evolution reaction. Finally, we will discuss the challenges in the accurate prediction of catalytic properties such as reaction and formation energies, and general surface adsorption phenomena.   

Gauge-invariant neural networks for quantum many-body dynamics

The dynamics of many-body systems is typically accompanied by the growth of entanglement. This imposes limitations on system size and evolution time for many existing numerical methods. On the other hand, neural network wavefunctions have demonstrated the capability to describe some volume law states phases, in principle making them a suitable ansatz for simulating long-time evolution. When dealing with systems (e.g., lattice gauge theories) featuring exact or approximate gauge symmetry, enhancing neural networks with this symmetry can significantly enhance their performance. In this study, we investigate the quench dynamics of a toric code under a perturbed Hamiltonian with gauge symmetry persisting throughout the evolution. We attempt to overcome restrictions in both evolution time and system size by harnessing gauge-invariant neural networks.   

Selected configuration interaction at the exascale within an integral driven framework

Selected Configuration Interaction (sCI) is a multireference many-body method for accurate calculations of properties of ground- and excited-state wavefunctions, achieved by expanding the system's wavefunction within the space of its Slater determinants. While sCI's strength lies in its ability to converge to the full CI limit through iterative refinement to the reference wavefunction, it inherently faces computational challenges, stemming from large active spaces and the sheer volume of required electron repulsion integrals for systems with many active orbitals.

In this presentation, we will discuss ARCHES, our recent implementation of a modern sCI framework suitable for exascale calculations and next generation quantum chemistry and materials science calculations. Our framework is built to flexibly handle both distributed parallelization and computational offloading with GPUs, relying upon an integral-driven approach in which the electron repulsion integrals are distributed across workers. We will discuss our approach for optimizing performance in modern HPC settings across several benchmark studies and showcase capabilities of ARCHES such as the calculation of spectral densities within a Green's function approach.   

Majorana sign problem in determinant quantum Monte Carlo

In determinant quantum Monte Carlo simulations, the trace of the evolution operator, constructed using Fermionic Gaussian operators, serves as a vital sampling weight. The sign of this trace, responsible for the well-known sign problem, has been a subject of extensive research for decades. Tremendous efforts have been made to address sign problems by leveraging symmetries or special mathematical structures. However, in majorana systems lacking these special requirements, determining the sign of the evolution operator constructed by Majorana Gaussian operators has posed a longstanding challenge. Previously, the trace could only be determined with an ambiguous sign. In this study, we successfully resolved this ambiguity and derived a closed-form formula for the trace using Pfaffian techniques, enabling complete trace calculation in polynomial time for the first time. Additionally, we explored the overlap of Hartree-Fock-Bogoliubov states evolved by Majorana Gaussian operators. Our findings represent a significant advancement, shedding light on the development in Majorana quantum Monte Carlo simulations and offering new possibilities for the discovery of new sign problem-free models exhibitting novel quantum phases of matter.   

Study of Hubbard model on triangular lattices using linearly scaling semi-classical methods

While several computational techniques, such as Quantum Monte Carlo (QMC), have achieved remarkable success in investigating strongly correlated lattice models, they often face challenges in obtaining reliable results for systems with itinerant electrons, geometric frustration, or realistic electronic interactions like spin-orbit coupling. Semiclassical methods have been extensively employed to study such systems and have proven to be qualitatively and often quantitatively accurate, especially for weakly correlated materials. Previous studies have demonstrated the effectiveness of combining semi-classical methods and Monte Carlo methods in the Hubbard model on square and cubic lattices, accurately predicting the Neel temperature and aligning with results from Determinant Quantum Monte Carlo (DQMC) calculations.

 

This study aims to assess the efficiency and accuracy of semi-classical methods in frustrated systems, specifically the Hubbard model on a triangular lattice. We utilize the Kernel Polynomial Method (KPM) for efficient Monte Carlo sampling of the auxiliary fields introduced during the Hubbard-Stratonovich transformation of the interaction terms. The KPM approach allows us to bypass the computationally expensive matrix diagonalization, resulting in a computational cost that scales linearly with the system size. This scalability enables us to explore large system sizes, providing valuable insights into the behavior of frustrated systems.   

Optimal model description of proton induced reactions on 232Th for the production of 223Ra and 225Ac up to 200 Mev.

Using the EMPIRE 3.2 code, an optimal model has been adapted to describe the proton interaction on ²³²Th for accelerator-based production of ²²³Ra and ²²⁵Ac which are important alpha emitting medical radioisotopes with viable production in accelerators. A hybrid nuclear level density which combines the nuclear level densities in Empire for the production of ²²⁵Ra, and ²²⁵Ac has been determined. The optimal model shows the important roles of the nuclear level densities and pre-equilibrium contribution to the good description of these interactions from 0 – 200 MeV. The reaction descriptions are found to be sensitive to the Nuclear Level Density description at different energies. It is noted that while no single description of the Nuclear Level Density provides an overall generally good description of the reaction throughout the energy range from threshold to 200 MeV, the energy and spin dependent level density parameter affects the Nuclear Level Density contribution significantly. The excitation functions obtained from this optimal description have been shown to have good agreement up to about 12% standard deviation with available measurements in EXFOR. The result of this work gives an insight into the necessary parameters for the production of ²²³Ra and ²²⁵Ac through ²³²Th.   

Effects of Su-Schrieffer-Heeger coupling in single band Hubbard square lattice

Intertwined spin and charge stripes have been identified as ubiquitous features of the cuprate phase diagram. These stripe correlations have also been observed in several state-of-the-art simulations of the single-band Hubbard model. However, numerous numerical analyses consistently predict the formation of charge order at lower temperatures than the spin order, contrary to the experimental results. This disparity hints at potential oversimplifications in the model. Prior research shows that including phonons via the Holstein mechanism in the hole underdoped and overdoped scenarios can significantly impact the stripe correlations. However, these studies have used phonon frequencies much higher than those in cuprates. Our research examines phonons' effects through the Su-Schrieffer-Heeger (SSH) coupling within the single-band Hubbard model using the Determinant Quantum Monte Carlo using realistic phonon energies. Preliminary results show SDW suppression and CDW stripe enhancement as coupling strength increases, suggesting that coupling to bond-stretching phonons may play an important role in stabilizing the stripe order.   

Parallelization of computations on the bundled matrix product state

Computations for excited states play an outsized role in the determination of electronic structure and properties useful for quantum computers. The algorithms for computing anything beyond the extremal eigensolutions can be very computationally intensive owing to the volume law of entanglement. In this talk, I propose a method to compute excited states on the bundled matrix product state, a concatenation of traditional matrix product states. This method is perfectly general to any algorithm, including those similar to the density matrix renormalization group method, and contains an ideal speedup with increasing computational resources.