Related papers: Competing interactions and the Lifshitz-type Nonli…
We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional…
We consider an interacting Lifshitz field with z=3 in a curved spacetime. We analyze the renormalizability of the theory for interactions of the form lambda phi^n, with arbitrary even n. We compute the running of the coupling constants both…
We investigate nonlinear optical analogues of quantum phase transitions within a squeezing-enhanced generalized Lipkin-Meshkov-Glick (LMG) model, focusing on excited-state quantum phase transitions in optical fibers with tetragonal…
Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in…
We study electron correlation effects on quantum criticalities of Lifshitz transitions at zero temperature, using the mean-field theory based on a preexisting symmetry-broken order, in two-dimensional systems. In the presence of…
A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies…
We explore a new approach to boundaries and interfaces in the $O(N)$ model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is $4-\epsilon$, and they explicitly break the $O(N)$…
The linear O($N$) sigma model undergoes a symmetry restoring phase transition at finite temperature. We show that the nonlinear O($N$) sigma model also undergoes a symmetry restoring phase transition; the critical temperatures are the same…
Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard $\phi^4$ model.…
This article studies large $N$ limits of a coupled system of $N$ interacting $\Phi^4$ equations posed over $\mathbb{T}^{d}$ for $d=2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on the dynamics are established, allowing…
The ground state of a one-dimensional spin-1/2 chain with periodical boundary condition in the Heisenberg XY model is investigated. We consider the spatial correlation and concurrence between any nearest-neighbor pair of spins under the…
We study the non-equilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex…
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disordered electron systems. They also occur in dimensionally reduced quantum gravity; recently they have been…
We present a theoretical analysis of the properties of low-dimensional quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model description, we use a spin stiffness analysis, a 1/N expansion, and a renormalization…
Using new as well as known results on dimerized quantum spin chains with frustration, we are able to infer some properties on the low-energy spectrum of the O(3) Nonlinear Sigma Model with a topological theta-term. In particular, for…
The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one and two-point correlation functions for two types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa. In the…
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the…
In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field…
This chapter summarizes the recent progress in the theory and analytical tools of quadratic optomechanical interactions, as one of the prominent domains of contemporary nonlinear quantum optics. Emphasis has been put here first to show what…
We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba SOC $ \alpha=\beta $. It supports collinear spin-bond correlated magnetic Y-x phase, a gapped in-commensurate (IC-) co-planar…