Related papers: Reflection positivity and quantum Griffiths' inequ…
We propose a model describing spin-half quantum particles in curved spacetime in the framework of quantum field theory. Our model is based on embodying Einstein's equivalence principle and general covariance in the definition of…
We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application…
We investigate thermal and nonthermal quantum correlations in the one dimensional spin 1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory such as generalized concurrence, negativity, and various measures of…
In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
We investigate a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to quantum lattice vibration using a quantum Monte Carlo method. We study the ground-state lattice fluctuation where the system shows a characteristic…
We study linear functionals on a Clifford algebra (algebra of Ma- joranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient conditions on the coupling…
We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…
We formulate entropic Leggett-Garg inequalities, which place constraints on the statistical outcomes of temporal correlations of observables. The information theoretic inequalities are satisfied if macrorealism holds. We show that the…
We employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the $U_{q}(\hat{gl_n})$ case. With the help of linear intertwining relations involving the…
We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $\theta \in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a…
In 1989, Elliott Lieb published a Physical Review Letter proving two theorems about the Hubbard model. This paper used the concept of spin-reflection positivity to prove that the ground state of the attractive Hubbard model was always a…
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must…
We construct a $\mathcal{PT}$-symmetric Richardson--Gaudin models for spin-$\tfrac{1}{2}$ systems by deforming the closed integrable Hamiltonian through complex-valued transverse magnetic fields and coupling constants. By defining parity as…
The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using…
We study quantum correlations in an isotropic Ising ring under the effects of a transverse magnetic field. After characterizing the behavior of two-spin quantum correlations, we extend our analysis to global properties of the ring, using a…
The difference in the properties of the spin correlation tensor for factorizable and nonfactorizable two-particle states is analyzed. The inequalities for linear combinations of the components of this tensor are obtained for the case of…
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
We investigate Bell inequalities for neutral kaon systems from Phi resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, that means we also include all decay product states,…
This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods…