Data-Driven **Many**-**Body** Models for Molecular Fluids: CO2/H2O Mixtures as a Case Study

**many**-

**body**effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO2–CO2 and CO2–H2O dimers and the energetics of small clusters as well as to correctly reproduce various properties in both... Expand abstract.

**many**-

**body**TTM-nrg and MB-nrg potential energy functions (PEFs), originally introduced for halide ion–water and alkali-metal ion–water interactions, to the modeling of carbon dioxide (CO2) and water (H2O) mixtures as prototypical examples of molecular fluids. Both TTM-nrg and MB-nrg PEFs are derived entirely from electronic structure data obtained at the coupled cluster level of theory and are, by construction, compatible with MB-pol, a

**many**-

**body**PEF that has been shown to accurately reproduce the properties of water. Although both TTM-nrg and MB-nrg PEFs adopt the same functional forms for describing permanent electrostatics, polarization, and dispersion, they differ in the representation of short-range contributions, with the TTM-nrg PEFs relying on conventional Born-Mayer expressions and the MB-nrg PEFs employing multidimensional permutationally invariant polynomials. By providing a physically correct description of

**many**-

**body**effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO2–CO2 and CO2–H2O dimers and the energetics of small clusters as well as to correctly reproduce various properties in both gas and liquid phases. Building upon previous studies of aqueous systems, our analysis provides further evidence for the accuracy and efficiency of the MB-nrg framework in representing molecular interactions in fluid mixtures at different temperature and pressure conditions.

10/10 relevant

chemRxiv

Neural-Network Approach to Dissipative Quantum **Many**-**Body** Dynamics

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**body**quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm for their time evolution and stationary states. Expand abstract.

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**body**systems, becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum

**many**-

**body**systems based on machine learning techniques. We represent the mixed

**many**-

**body**quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.

10/10 relevant

arXiv

Time Global Finite-Energy Weak Solutions to the **Many**-**Body** Maxwell-Pauli Equations

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**body**problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the electrons and their self-generated electromagnetic field is referred to as the

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**body**Maxwell-Pauli equations. Here we construct time global, finite-energy, weak solutions to the

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**body**Maxwell-Pauli equations under the assumption that the fine structure constant $\alpha$ and the atomic numbers are not too large. The particular assumptions on the size of $\alpha$ and the atomic numbers ensure that we have energetic stability of the

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**body**Pauli Hamiltonian, i.e., the ground state energy is finite and uniformly bounded below with lower bound independent of the magnetic field and the positions of the nuclei. This work serves as an initial step towards understanding the connection between the energetic stability of matter and the wellposedness of the corresponding dynamical equations.

10/10 relevant

arXiv

Deep Learning-Enhanced Variational Monte Carlo Method for Quantum
**Many**-**Body** Physics

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**body**systems. However, there have been few systematic studies of exploring quantum

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**body**physics using deep neural networks (DNNs), despite of the tremendous success enjoyed by DNNs in

**many**other areas in recent years. One main challenge of implementing DNN in VMC is the inefficiency of optimizing such networks with large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNN in VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNN show excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum

**many**-

**body**calculations.

10/10 relevant

arXiv

NetKet: A Machine Learning Toolkit for **Many**-**Body** Quantum Systems

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**body**physics. Expand abstract.

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**body**quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wave functions. NetKet provides algorithms for several key tasks in quantum

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**body**physics and quantum technology, namely quantum state tomography, supervised learning from wave-function data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and

**many**-

**body**physics.

10/10 relevant

arXiv

Non-Hermitian **Many**-**Body** Localization

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**body**systems with gain and/or loss that breaks time-reversal symmetry, even though the many-body localization transition still persists. Expand abstract.

**Many**-

**body**localization is shown to suppress imaginary parts of complex eigenenergies for general non-Hermitian Hamiltonians having time-reversal symmetry. We demonstrate that a real-complex transition, which we conjecture occurs upon

**many**-

**body**localization, profoundly affects the dynamical stability of non-Hermitian interacting systems with asymmetric hopping that respect time-reversal symmetry. Moreover, the real-complex transition is shown to be absent in non-Hermitian

**many**-

**body**systems with gain and/or loss that breaks time-reversal symmetry, even though the

**many**-

**body**localization transition still persists.

10/10 relevant

arXiv

Scale Invariant Entanglement Negativity at the **Many**-**Body** Localization
Transition

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**body**localization transition. Expand abstract.

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**body**localization transition remains an open question. An aspect which has been posited in various studies is the emergence of scale invariance around this point, however the direct observation of this phenomenon is still absent. Here we achieve this by studying the logarithmic negativity and mutual information between disjoint blocks of varying size across the

**many**-

**body**localization transition. The two length scales, block sizes and the distance between them, provide a clear quantitative probe of scale invariance across different length scales. We find that at the transition point, the logarithmic negativity obeys a scale invariant exponential decay with respect to the ratio of block separation to size, whereas the mutual information obeys a polynomial decay. The observed scale invariance of the quantum correlations in a microscopic model opens the direction to probe the fractal structure in critical eigenstates using tensor network techniques and provide constraints on the theory of the

**many**-

**body**localization transition.

10/10 relevant

arXiv

Variational autoencoder reconstruction of complex **many**-**body** physics

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**body**systems can be reconstructed by using VAE learning of tomographic data, for different parameters of... Expand abstract.

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**body**quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of

**many**-

**body**state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum

**many**-

**body**systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.

10/10 relevant

arXiv

Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to **many**-**body** localisation

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**body**localized system, also in the presence of dephasing. Expand abstract.

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**body**quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a

**many**-

**body**system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a

**many**-

**body**localized system, also in the presence of dephasing.

10/10 relevant

arXiv

Many-**body** quantum dynamics of an asymmetric bosonic Josephson junction

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**body**position variance. Expand abstract.

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**body**Schr\"odinger equation numerically accurately. We examine how the loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric DW, the two wells are not equivalent anymore -the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right well. We examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the

**many**-

**body**position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well. However, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Overall, the

**many**-

**body**position and momentum variances bear the prominent signatures of the density oscillations of the system in the asymmetric double well as well as a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging

**many**-

**body**position variance.

10/10 relevant

arXiv