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## Simulations of strongly-correlated electron systems with coulomb and magnetic interactions in the limit of small movement of carriers

### Szymon Murawski

#### Abstract

Strong electronic correlations, while being a sub-atomic effect, are responsible for plethora of macroscopic properties, of which the most spectacular are superconductivity, magnetic orderings or colossal magnetoresistance. Electronic correlations are a challenge for theoretical description, being the key part of total energy of the system prevents from treating them as perturbation. We are forced to analyze different interactions between particles in many-body problem. This dissertation aims to present the studies on extended Hubbard model with intersite magnetic interactions in atomic limit on two dimensional square lattice. Such a model can be used to describe behavior of magnetic insulators. Omitting the kinetic part of the model Hamiltonian allows the use of classical Monte Carlo simulations, thus making analysis in finite temperatures possible. Simulations were done under grand canonical ensemble, by which critical behawior as a function of electronic concentrations could be obtained, allowing the study of phase separations. Obtained results allowed for construction of phase diagrams as a function of chemical potential as well as electron concentration. System investigated exhibits homogeneous phases: ordered magnetic and unordered. Depending on temperaturę and interaction parameteres transition between phases are either of first or second order. In some range of interaction parameteres only first order transitions exists in the system. Analysis of the hysteresis allowed for the localization of tricritical point, while susceptibility measurements confirmed the existence of phase separation in the system. In presented work a problem of parallel Monte Carlo simulations is also being discussed. Proposed solution relies on distribution of the global lattice among parallel processes, which in turn communicate between themselves using Message-Passing Interface library. This method could be used for models with external fields, where cluster methods like Wolff or Swendsen-Wang could not be used. Implementation of this method using MPI2 standard in C++ was presented. Measurements of execution time of the algorithm allowed for calculating the speedup and efficiency of parallelization for two differents ways of distributing the lattice. Obtained results were confronted with implementation using cooperative means of communication of MPI1 standard. As the model was studied in the limit of infinite repulsive interaction, thus reducing it to simple Ising model, implementation of discussed algorithm for Monte Carlo simulation under grand canonical ensemble was presented, as well as its possible influence on results.
Record ID
UAM5604444cbccf470fa19eb828532e3043
Diploma type
Doctor of Philosophy
Author
Title in Polish
Symulacje układów silnie skorelowanych elektronów z uwzględnieniem oddziaływań kulombowskich i magnetycznych w granicy małej ruchliwości nośników
Title in English
Simulations of strongly-correlated electron systems with coulomb and magnetic interactions in the limit of small movement of carriers
Language
pol (pl) Polish
Certifying Unit
Faculty of Physics (SNŚ/WyF/FoP)
Discipline
physics / (physical sciences domain) / (physical sciences)
Scientific discipline (2.0)
6.6 physical sciences
Status
Finished
Defense Date
27-10-2015
Title date
27-10-2015
Supervisor
Grzegorz Pawłowski Grzegorz Pawłowski,, Wydział Fizyki [nowa struktura organizacyjna] (SNŚ/WyF)Szkoła Nauk Ścisłych [nowa struktura organizacyjna] (SNŚ)
URL
http://hdl.handle.net/10593/13972 Opening in a new tab
Keywords in English
Monte Carlo, electronic correlations, phase transitions, parallel computing
Abstract in English
Strong electronic correlations, while being a sub-atomic effect, are responsible for plethora of macroscopic properties, of which the most spectacular are superconductivity, magnetic orderings or colossal magnetoresistance. Electronic correlations are a challenge for theoretical description, being the key part of total energy of the system prevents from treating them as perturbation. We are forced to analyze different interactions between particles in many-body problem. This dissertation aims to present the studies on extended Hubbard model with intersite magnetic interactions in atomic limit on two dimensional square lattice. Such a model can be used to describe behavior of magnetic insulators. Omitting the kinetic part of the model Hamiltonian allows the use of classical Monte Carlo simulations, thus making analysis in finite temperatures possible. Simulations were done under grand canonical ensemble, by which critical behawior as a function of electronic concentrations could be obtained, allowing the study of phase separations. Obtained results allowed for construction of phase diagrams as a function of chemical potential as well as electron concentration. System investigated exhibits homogeneous phases: ordered magnetic and unordered. Depending on temperaturę and interaction parameteres transition between phases are either of first or second order. In some range of interaction parameteres only first order transitions exists in the system. Analysis of the hysteresis allowed for the localization of tricritical point, while susceptibility measurements confirmed the existence of phase separation in the system. In presented work a problem of parallel Monte Carlo simulations is also being discussed. Proposed solution relies on distribution of the global lattice among parallel processes, which in turn communicate between themselves using Message-Passing Interface library. This method could be used for models with external fields, where cluster methods like Wolff or Swendsen-Wang could not be used. Implementation of this method using MPI2 standard in C++ was presented. Measurements of execution time of the algorithm allowed for calculating the speedup and efficiency of parallelization for two differents ways of distributing the lattice. Obtained results were confronted with implementation using cooperative means of communication of MPI1 standard. As the model was studied in the limit of infinite repulsive interaction, thus reducing it to simple Ising model, implementation of discussed algorithm for Monte Carlo simulation under grand canonical ensemble was presented, as well as its possible influence on results.

Uniform Resource Identifier
https://researchportal.amu.edu.pl/info/phd/UAM5604444cbccf470fa19eb828532e3043/
URN
urn:amu-prod:UAM5604444cbccf470fa19eb828532e3043

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