相关论文: Some Integrable Quantum Systems on the Lattice

An infinite system of nonlocal, individually confining solitons is considered as a model of high-density nuclear matter. The soliton-lattice problem is discussed in the Wigner-Seitz approximation. The cell size is varied to study the…

Optical lattices are considered loaded by atoms or molecules that can exhibit strong interactions between different lattice sites. The strength of these interactions can be sufficient for generating collective phonon excitations above the…

We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations…

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…

The new examples are found of the constraints which link the 1+2-dimensional and multifield integrable equations and lattices. The vector and matrix generalizations of the Nonlinear Schr\"odinger equation and the Ablowitz-Ladik lattice are…

The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and…

The properties of several phase transitions relevant to the lattice study of Quantum Field Theory are investigated.

This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…

An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl…

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…

We introduce a lattice model for a static and isotropic system of relativistic fermions. An action principle is formulated, which describes a particle-particle interaction of all fermions. The model is designed specifically for a numerical…

In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…

We study the spectral properties of a system of electrons interacting through long-range Coulomb potential on a one-dimensional chain. When the interactions dominate over the electronic bandwidth, the charges arrange in an ordered…

In the present work we demonstrate how to realize 1d-optical closed lattice experimentally, including a {\it tunable} boundary phase-twist. The latter may induce ``persistent currents'', visible by studing the atoms' momentum distribution.…

We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…

In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie-Poisson algebras, and in the…

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…

We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary…

We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…

In the last few years, numerical simulations of QCD on the lattice have reached a new level of accuracy. A wide range of thermodynamic quantities is now available in the continuum limit and for physical quark masses. This allows a…