Related papers: Reflection positivity and quantum Griffiths' inequ…
We present a general framework of Griffiths inequalities for quantum systems. Our approach is based on operator inequalities associated with self-dual cones and provides a consistent viewpoint of the Griffiths inequality. As examples, we…
In the Reflection Positivity theory and its application to statistical mechanical systems, certain matrix inequalities play a central role. The Dyson-Lieb-Simon and Kennedy-Lieb-Shastry-Schupp inequalities constitute prominent examples. In…
We show the positivity or negativity of truncated correlation functions in the quantum XY model with spin 1/2 (at any temperature) and spin 1 (in the ground state). These Griffiths-Ginibre inequalities of the second kind generalise an…
Within the context of piecewise linear manifolds we establish reflection positivity with a Hilbert action given in terms of the Regge curvature and a cosmological term. Using this positivity a Hilbert space for a quantum theory is…
The method of reflection positivity and infrared bounds allows to prove the occurrence of phase transitions in systems with continuous symmetries. We review the method in the context of quantum spin systems.
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
The first and second Griffiths inequalities are proved for some classical O($n$)-invariant spin models (including Euclidean quantum field theories) for any $n$. The proof assumes a certain condition on an integral transform of the measure.…
We prove Griffiths inequalities for the $O(N)$-spin model with inhomogeneous coupling constants and external magnetic field for any $N\geq 2$. This is achieved by using a representation of $O(N)$-spins in terms of random paths that reduces…
In a previous work I constructed R-negative scissors states in the Two-Rotors Model in which the rotors are two-sided classical bodies. Such states have |K| = 1; 0 components and negative space parity. Here I extend this work including…
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…
Reflection positivity (RP) is a property of Gibbs measures exhibited by a class of lattice spin systems that include the Ising, Potts and Heisenberg models. The RP property is useful because of its two basic consequences: infrared bound and…
We develop a novel perspective on reflection positivity (RP) on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes…
Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in…
This paper analyzes Sch\"odinger operators from viewpoint of correlation inequalities. We construct Griffiths inequalities for the ground state expectations by applying operator-theoretic correlation inequalities. As an example of such an…
The characterization of quantum information quantifiers has attracted a considerable attention of the scientific community, since they are a useful tool to verify the presence of quantum correlations in a quantum system. In this context, in…
The quantum complex sine-Gordon model on a half line is studied. The quantum spectrum of boundary bound states using the the semi-classical method of Dashen, Hasslacher and Neveu is obtained. The results are compared and found to agree with…
New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection onto sub-spaces. We illustrate this…
We describe the general structure of unbounded derivations in the quantum cylinder. We prove a noncommutative analog of reflection positivity for Laplace-type operators in a noncommutative cylinder following the ideas of Jaffe and Ritter…
Gauge invariant chiral theories satisfying the reflection positivity is constructed on a lattice. This requires the introduction of "half gauge fields" defined some time ago by Brydges, Fr\"{o}hlich, and Seiler \cite{BFS}. A two-dimensional…
We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove…