Related papers: Bethe Logarithms for Rydberg States: Numerical Val…
We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models.…
It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…
We explore the validity of the generalized Bekenstein bound, S <= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width a. If boundary…
In this work, we systematically study the $D\bar{D}^*$/$B\bar{B}^*$ and $DD^*$/$\bar{B}\bar{B}^*$ systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation…
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions…
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…
Simple analytic formulae for energy relaxation (ER) in electron-ion systems, with quantum corrections, ion dynamics and RPA-type screening are presented. ER in the presence of bound electrons is examined in view of of recent simulations for…
We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings $S/I$, where $S$ is a polynomial ring and $I\subseteq S$ is an…
We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase…
In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian…
The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is…
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the…
Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum…
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…
The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model,…
Recent measurements of the ionization energies of the Rydberg $^1P$ states of helium for principal quantum number $n = 24$ and higher present a new challenge to theoretical atomic physics. A long-standing obstacle to high precision atomic…
In this communication, we report results of three-dimensional hydrodynamic computations, by using equations of state with a critical end point as suggested by the lattice QCD. Some of the results are an increase of the multiplicity in the…