Related papers: Field Theoretic Studies of Quantum Spin Systems in…
We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b)…
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and…
This chapter is intended as a brief overview of some of the quantum spin liquid phases with unbroken SU(2) spin symmetry available in one dimension. The main characteristics of these phases are discussed by means of the bosonization…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger…
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…
A spin system on a lattice can usually be modelled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables…
The low energy properties of different one-dimensional fermionic lattice models are investigated using the bosonization technique. We attach much importance to a proper consideration of the Klein factors which are neglected or inaccurately…
We introduce a lattice model of interacting spins and bosons that leads to Luttinger-liquid physics, and allows for quantitative tests of the theory of bosonization by means of trapped-ion or superconducting-circuit experiments. By using a…
The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional…
In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this…
We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test-bed for multi-body dynamics and quantum information processing. This system is a paradigm for a new class of quantum information devices…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
A model with a singular forward scattering amplitude for particles with opposite spins in d spatial dimensions is proposed and solved by using the bosonization transformation. This interacting potential leads to the spin-charge separation.…
The one-dimensional Kondo lattice model is investigated by using bosonization techniques and conformal field theory. In the half-filled band, the charge and spin gaps open for the anti-ferromagnetic Kondo coupling. Away from half-filling,…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…
Microscopic models of quantum antiferromagnets are investigated on the basis of a mapping onto effective low energy hamiltonians. Lattice effects are carefully taken into account and their role is discussed. We show that the presence of an…
One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a…
Low-dimensional quantum spin systems are interacting many body systems for which several rigorous results are known. Powerful techniques like the Bethe Ansatz provide exact knowledge of the ground state energy and low-lying excitation…