cond-mat.str-el

arXiv:2401.01921v2 Announce Type: replace Abstract: We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.

arXiv:2501.07371v1 Announce Type: cross Abstract: Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations. In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues.

arXiv:2312.13185v2 Announce Type: replace-cross Abstract: Measurement-based quantum computation (MBQC) is a paradigm for quantum computation where computation is driven by local measurements on a suitably entangled resource state. In this work we show that MBQC is related to a model of quantum computation based on Clifford quantum cellular automata (CQCA). Specifically, we show that certain MBQCs can be directly constructed from CQCAs which yields a simple and intuitive circuit model representation of MBQC in terms of quantum computation based on CQCA. We apply this description to construct various MBQC-based Ans\"atze for parameterized quantum circuits, demonstrating that the different Ans\"atze may lead to significantly different performances on different learning tasks. In this way, MBQC yields a family of Hardware-efficient Ans\"atze that may be adapted to specific problem settings and is particularly well suited for architectures with translationally invariant gates such as neutral atoms.

arXiv:2412.16317v1 Announce Type: new Abstract: The Epstein zeta function generalizes the Riemann zeta function to oscillatory lattice sums in higher dimensions. Beyond its numerous applications in pure mathematics, it has recently been identified as a key component in simulating exotic quantum materials. This work establishes the Epstein zeta function as a powerful tool in numerical analysis by rigorously investigating its analytical properties and enabling its efficient computation. Specifically, we derive a compact and computationally efficient representation of the Epstein zeta function and thoroughly examine its analytical properties across all arguments. Furthermore, we introduce a superexponentially convergent algorithm, complete with error bounds, for computing the Epstein zeta function in arbitrary dimensions. We also show that the Epstein zeta function can be decomposed into a power law singularity and an analytic function in the first Brillouin zone. This decomposition facilitates the rapid evaluation of integrals involving the Epstein zeta function and allows for efficient precomputations through interpolation techniques. We present the first high-performance implementation of the Epstein zeta function and its regularisation for arbitrary real arguments in EpsteinLib, a C library with Python and Mathematica bindings, and rigorously benchmark its precision and performance against known formulas, achieving full precision across the entire parameter range. Finally, we apply our library to the computation of quantum dispersion relations of three-dimensional spin materials with long-range interactions and Casimir energies in multidimensional geometries, uncovering higher-order corrections to known asymptotic formulas for the arising forces.