Related papers: N-site-lattice analogues of $V(x)=i x^3$
The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when \beta t is small, or \beta t^2/U is small; here, \beta is the inverse temperature, U the on-site repulsion…
We study lattice formulations of the two-dimensional N=2 Wess-Zumino model with a cubic superpotential. Discretizations with and without lattice supersymmetries are compared. We observe that the "Nicolai improvement" introduces new problems…
We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the…
The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control…
We investigate tensor network simulations of the two-dimensional Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
Maintaining local interactions in the quantum simulation of gauge field theories relegates most states in the Hilbert space to be unphysical -- theoretically benign, but experimentally difficult to avoid. Reformulations of the gauge fields…
We present a new model describing strongly correlated electrons on a general $d$-dimensional lattice. It differs from the Hubbard model by interactions of nearest neighbours, and it contains the $t$-$J$ model as a special case. The model…
Study of the hadronic matrix elements can provide not only tests of the QCD sector of the Standard Model (in comparing with existing experiments) but also reliable low-energy hadronic quantities applicable to a wide range of…
Discrete multiparametric 1D quantum well with PT-symmetric long-range boundary conditions is proposed and studied. As a nonlocal descendant of the square well families endowed with Dirac (i.e., Hermitian) and with complex Robin (i.e.,…
We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented…
The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual…
By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) \delta^3(r-r') is studied. The relative kinetic…
General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
Since the spatially extended periodic parity-time (PT) symmetric potential can possess certain unique properties compared to a single PT cell (with only a pair of coupled gain-loss components), various schemes have been proposed to realize…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
Non-Hermitian quantum one-parametric $N$ by $N$ matrix Hamiltonians $H^{(N)}(\lambda)$ with real spectra are considered. Their special choice $H^{(N)}(\lambda)=J^{(N)}+\lambda\,V^{(N)}(\lambda)$ is studied at small $\lambda$, with a general…