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We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established…

Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The…

In this paper we discuss the quantum properties for superposition of squeezed displaced number states against multiphoton Jaynes-Cummings model (JCM). In particular, we investigate atomic inversion, photon-number distribution, purity,…

We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state…

An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…

Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical…

Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg…

We consider a two-dimensional geometrically frustrated integer-spin Heisenberg system that admits an exact ground state. The system corresponds to a decorated square lattice with two coupling constants J1 and J2, and it can be understood as…

We consider the joint inference of regression coefficients and the inverse covariance matrix for covariates in high-dimensional probit regression, where the predictors are both relevant to the binary response and functionally related to one…

- A hamiltonian graph $G$ verifying $e(G)>n(k-1)/2$ %with a vertex of degree greater or equal than $k$ contains any $k$-spider. - If $G$ is a graph with average degree $\bar{d} > k-1$, then every spider of size $k$ is contained in $G$ for…

An A-type coefficient polynomial introduced by Kawauchi recovers the HOMFLY-PT polynomial as a formal power series within skein theory. A notable feature of this construction is that each coefficient defines a link invariant, yielding an…

Finding an exact solution for a realistic interacting quantum many-body problem is often challenging. There are only a few problems where an exact solution can be found, usually in a narrow parameter space. Here, we propose a spin-$1/2$…

The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written…

Classical chimera states are paradigmatic examples of partial synchronization patterns emerging in nonlinear dynamics. These states are characterized by the spatial coexistence of two dramatically different dynamical behaviors, i.e.,…

We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…

We consider a quantum integrable inhomogeneous model based on the Brauer algebra B(1) and discuss the properties of its ground state eigenvector. In particular we derive various sum rules, and show how some of its entries are related to…

We study the spin-1 bilinear-biquadratic model on the complete graph of N sites, i.e., when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be…

We develop an improved variant of $U(1)$-symmetric infinite projected entangled-pair state (iPEPS) ansatz to investigate the ground state phase diagram of the spin-$1/2$ square $J_{1}-J_{2}$ Heisenberg model. In order to improve the…

A new particle - discovered recently with the Atlas and CMS detectors at LHC - has been interpreted as the long sought Higgs-boson. A corresponding scalar field is needed to make the weak interaction gauge invariant and to understand the…