## Thesis etd-01152022-190118 |

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Thesis type

Tesi di laurea magistrale

Author

MARGARI, FRANCESCA

URN

etd-01152022-190118

Thesis title

Topological properties of CP^(N-1) models

Department

FISICA

Course of study

FISICA

Supervisors

**relatore**Prof. D'Elia, Massimo

Keywords

- CP^(N-1) models
- lattice QCD
- lattice quantum field theory
- Monte Carlo simulations
- multicanonical algorithm
- QCD
- theta-dependence
- topology

Graduation session start date

07/02/2022

Availability

None

Summary

The two-dimensional CP^(N-1) models have been employed in the literature as a theoretical laboratory for the study of gauge theories.

Our aim is to study the continuum limit of the first coefficient of the θ-expansion of the vacuum energy density, parametrized by the topological susceptibility χ, for N=2 and N=3 by means of lattice Monte Carlo simulations.

Our goal is to clarify by the lattice approach whether or not the topological susceptibility of CP^1 diverges, as one would expect from semi-classical arguments.

To determine the behavior of χ for N=2, we approach the continuum limit keeping the volume fixed in lattice units. If the topological susceptibility is finite the continuum limit tends to zero, since the volume in physical units is vanishing as the lattice spacing a → 0. If there is a divergence the expected continuum limit of the χ is non-zero.

The study of this limit is very difficult with standard algorithms: at small lattice spacing the physical volume is small and topological charge fluctuations become rare.

We implement the multicanonical algorithm and we present a systematic study of its performances. We observe that the multicanonical algorithm allows for better accuracy of the lattice measurement of topological susceptibility.

We are able to measure χ for a Q^2 as low as ~ 10^(-7). Despite the use of multicanonical algorithm, we are not able to discriminate between the convergent/divergent behavior of χ. Our results set possible lines of future investigations.

Our aim is to study the continuum limit of the first coefficient of the θ-expansion of the vacuum energy density, parametrized by the topological susceptibility χ, for N=2 and N=3 by means of lattice Monte Carlo simulations.

Our goal is to clarify by the lattice approach whether or not the topological susceptibility of CP^1 diverges, as one would expect from semi-classical arguments.

To determine the behavior of χ for N=2, we approach the continuum limit keeping the volume fixed in lattice units. If the topological susceptibility is finite the continuum limit tends to zero, since the volume in physical units is vanishing as the lattice spacing a → 0. If there is a divergence the expected continuum limit of the χ is non-zero.

The study of this limit is very difficult with standard algorithms: at small lattice spacing the physical volume is small and topological charge fluctuations become rare.

We implement the multicanonical algorithm and we present a systematic study of its performances. We observe that the multicanonical algorithm allows for better accuracy of the lattice measurement of topological susceptibility.

We are able to measure χ for a Q^2 as low as ~ 10^(-7). Despite the use of multicanonical algorithm, we are not able to discriminate between the convergent/divergent behavior of χ. Our results set possible lines of future investigations.

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