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Texts and readings in physical sciences

Quantum Many Particle Physics

Pinaki Majumdar

Published Jan 1, 2001• 47 citations
Publisher

Abstract

This set of lectures focuses on some problems in itinerant Bose and Fermi systems. The first lecture will be an introduction to many-particle physics. In the second we will discuss phase transitions and symmetry breaking and the mean field approach to condensation in Bose systems. In the third we will look at strong interactions in ‘normal’ Fermi systems. The final lecture will be on strong coupling superconductivity which involves both strong interactions and symmetry breaking.

DOI
10.1007/978-93-86279-07-1_2

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•Sep 30, 2013•0 citations
This set of lectures focuses on some problems in itinerant Bose and Fermi systems. The first lecture will be an introduction to many-particle physics. In the second we will discuss phase transitions and symmetry breaking and the mean field approach to condensation in Bose systems. In the third we will look at strong interactions in ‘normal’ Fermi systems. The final lecture will be on strong coupling superconductivity which involves both strong interactions and symmetry breaking.
This chapter discusses phase transitions and symmetry breaking and the mean field approach to condensation in Bose systems and looks at strong interactions in ‘normal’ Fermi systems. ‘Statistical field theory’ encompasses all the applications of quantum field theory to statistical physics. In the context of these notes, it is interpreted as the study of ‘statistical mechanics of quantum many particle systems, employing the methods of field theory’. The identification of the symmetry broken in a phase with long range order allows to construct simple ‘mean field’ theories which provide a qualitative description of the system. Field theoretic methods were those developed by Feynman, Dyson, Schwinger, and others for understanding QED. They were ‘field theoretic’ in that one had to go beyond quantum mechanics, and the Schrodinger equation, to set up a theory. Unlike quantum field theory, there is a Schrodinger equation governing many particle phenomena in condensed matter.
The volume contains the lectures delivered at the XIII Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2008. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographies of relevant subjects in the field of Condensed Matter Physics. Contributions include: Quantum Magnetism in insulators (Single impurities in semiconductors and insulators; One- Two- and Three-dimensional magnets and quantum phase transitions; Undoped and doped Kondo insulators); Novel quantum condensates in excitonic matter (The physical systems: excitonic insulators, the Dicke model, exciton and polariton BEC; Second quantization, coherent states and path integral; exciton and polariton condensates in mean field theory; Open systems and Keldysh formulation; Phase-breaking and open system dynamics); Introduction to unconventional superconductivity (Generalized BCS theory; Phenomenological approach and symmetry aspects; Generalized Ginzburg-Landau theory; Josephson and tunneling effects); Quantum Monte-Carlo simulations (Classical and quantum cluster algorithms; The worm algorithm; Optimized ensembles for classical and quantum Monte-Carlo simulations; Continuous time QMC solvers for quantum impurity problems and DMFT).
The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.
We study quantum phases and transitions in ultra-cold quantum gases, beyond the scope of conventional condensed matter systems. The study focuses on three major thrusts. The first thrust is the study of cold ensembles of bosonic or fermionic atoms in the higher orbital bands of optical lattices. Orbital and topological quantum physics is systematically explored for various lattice geometries, to be outlined below. The second is the low dimensional spin-imbalanced fermions in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We analyze its thermal instability towards Berezinsky-Kosterlitz-Thouless (BKT) phase transitions driven by different topological defects at finite temperature. The third is the theoretical search for a mechanism to achieve a Bose-Einstein crystal phase for bosons in the ground state. A new class of two-body interactions characterized by strong momentum-dependence is found to give rise to such a quantum state. It is different than but related to the long-debated concept of supersolidity. The first thrust forms the main part of the dissertation. Meta-stable phases of high orbital bosons and fermions have been explored for different lattice geometries such as square and bipartite lattices. Exotic Mott and superfluid phases are studied in both one and two dimensions. Quantum and thermal phase transitions, associated with time reversal symmetry breaking and their experimental signatures are discussed. In particular a quantum ``disordered" superfluid phase, beyond the mean field description, is found in one dimension. The challenging problem of probing time reversal symmetry breaking is solved. Besides, a one-dimensional fermionic optical ladder with coupled s- and p-orbitals is shown to mimic spin-orbit interactions and exhibit topological insulator and topological superconducting phases. Charge fractionalization is shown to be realizable in such an sp-orbital ladder.