Related papers: Dispersion Relations in Two- and Three-Dimensional…
The integrated perturbation theory (iPT) is a set of methods in nonlinear perturbation theory for the structure formation in the Universe. In Papers I and II [arXiv:2210.10435, arXiv:2210.11085], the basic formalism and technical methods of…
Many-body correlations in strongly coupled liquids and plasmas are critical for many applications in nanofluids, biology, and fusion-related plasma physics, but their description in fully heterogeneous environments remains challenging due…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the…
We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks %, i.e. tensor…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…