Related papers: Conformal invariance in the quantum Ising model

We discuss the notion of s-embeddings $\mathcal{S}=\mathcal{S}_\mathcal{X}$ of planar graphs carrying a nearest-neighbor Ising model. The construction of $\mathcal{S}_\mathcal{X}$ is based upon a choice of a global complex-valued solution…

A while ago, Luck (J. Stat. Phys. 72 (1993) 417) investigated the critical behaviour of one-dimensional Ising quantum chains with couplings constants modulated according to general non-periodic sequences. In this short note, we take a…

Kadanoff's "correlations along a line" in the critical two-dimensional Ising model (1969) are reconsidered. They are the analytical aspect of a representation of abelian chiral vertex operators as quadratic polynomials, in the sense of…

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…

Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering…

The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by…

Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension $-1$ exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary…

Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…

Two dimensional quantum gravity coupled to a conformally invariant matter field of central charge c=n/2, is represented, in a discretized version, by n independent Ising spins per cell of the triangulations of a random surface. The matrix…

The next decade will feature an abundance of novel cosmological data, while many fundamental questions about inflation remain. Given this, there is ample need for maximally efficient calculations, especially in non-standard scenarios for…

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…

General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…

A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains -- but with inhomogeneous couplings -- which have the same…

The quantum or quantum field theory concept of a complex wave function is useful for understanding the information transport in classical statistical generalized Ising models. We relate complex conjugation to the discrete transformations…

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because a new formulation can be given to…

In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both…

We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a…

This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…