493 research outputs found
Theory and applications of lattice fermionic regularisations
SIGLEAvailable from British Library Document Supply Centre- DSC:D76851 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
We discuss designer Hamiltonians---lattice models tailored to be free from
sign problems ("de-signed") when simulated with quantum Monte Carlo methods but
which still host complex many-body states and quantum phase transitions of
interest in condensed matter physics. We focus on quantum spin systems in which
competing interactions lead to non-magnetic ground states. These states and the
associated quantum phase transitions can be studied in great detail, enabling
direct access to universal properties and connections with low-energy effective
quantum field theories. As specific examples, we discuss the transition from a
Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously
symmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. We
also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids
and the XY* transition. We briefly review recent progress on quantum Monte
Carlo algorithms, including ground state projection in the valence-bond basis
and direct computation of the Renyi variants of the entanglement entropy.Comment: 23 pages, 10 figure
Confinement, chiral symmetry, and the lattice
Two crucial properties of QCD, confinement and chiral symmetry breaking,
cannot be understood within the context of conventional Feynman perturbation
theory. Non-perturbative phenomena enter the theory in a fundamental way at
both the classical and quantum level. Over the years a coherent qualitative
picture of the interplay between chiral symmetry, quantum mechanical anomalies,
and the lattice has emerged and is reviewed here.Comment: 126 pages, 36 figures. Revision corrects additional typos and
renumbers equations to be more consistent with the published versio
DECONFINED QUANTUM CRITICALITY IN 2D SU(N) MAGNETS WITH ANISOTROPY
In this thesis I will outline various quantum phase transitions in 2D models of magnets that are amenable to simulation with quantum Monte Carlo techniques. The key player in this work is the theory of deconfined criticality, which generically allows for zero temperature quantum phase transitions between phases that break distinct global symmetries. I will describe models with different symmetries including SU(N), SO(N), and easy-plane SU(N) and I will demonstrate how the presence or absence of continuous transitions in these models fits together with the theory of deconfined criticality
A computational multi-scale approach for brittle materials
Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
Conformal field theories have been long known to describe the fascinating
universal physics of scale invariant critical points. They describe continuous
phase transitions in fluids, magnets, and numerous other materials, while at
the same time sit at the heart of our modern understanding of quantum field
theory. For decades it has been a dream to study these intricate strongly
coupled theories nonperturbatively using symmetries and other consistency
conditions. This idea, called the conformal bootstrap, saw some successes in
two dimensions but it is only in the last ten years that it has been fully
realized in three, four, and other dimensions of interest. This renaissance has
been possible both due to significant analytical progress in understanding how
to set up the bootstrap equations and the development of numerical techniques
for finding or constraining their solutions. These developments have led to a
number of groundbreaking results, including world record determinations of
critical exponents and correlation function coefficients in the Ising and
models in three dimensions. This article will review these exciting
developments for newcomers to the bootstrap, giving an introduction to
conformal field theories and the theory of conformal blocks, describing
numerical techniques for the bootstrap based on convex optimization, and
summarizing in detail their applications to fixed points in three and four
dimensions with no or minimal supersymmetry.Comment: 81 pages, double column, 58 figures; v3: updated references, minor
typos correcte
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Can high energy physics be simulated by low-energy, non-relativistic,
many-body systems, such as ultracold atoms? Such ultracold atomic systems lack
the type of symmetries and dynamical properties of high energy physics models:
in particular, they manifest neither local gauge invariance nor Lorentz
invariance, which are crucial properties of the quantum field theories which
are the building blocks of the standard model of elementary particles.
However, it turns out, surprisingly, that there are ways to configure atomic
system to manifest both local gauge invariance and Lorentz invariance. In
particular, local gauge invariance can arise either as an effective, low
energy, symmetry, or as an "exact" symmetry, following from the conservation
laws in atomic interactions. Hence, one could hope that such quantum simulators
may lead to new type of (table-top) experiments, that shall be used to study
various QCD phenomena, as the confinement of dynamical quarks, phase
transitions, and other effects, which are inaccessible using the currently
known computational methods.
In this report, we review the Hamiltonian formulation of lattice gauge
theories, and then describe our recent progress in constructing quantum
simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1
dimensions using ultracold atoms in optical lattices.Comment: A review; 55 pages, 14 figure
Scattering Processes via Tensor Network Simulations
Scattering processes are a crucial ingredient for the investigation of fundamental interactions. The ever-increasing amount of data produced at particle colliders has fuelled recent progresses in the field of scattering amplitudes computation. To date, on the numerical side, the results achieved are mainly based on Monte-Carlo simulations. In this Thesis the problem is attacked with a different approach: a real-time simulation of the dynamics of a 1+1 dimensional quantum field theory is performed, exploiting the powerful tensor network methods from many-body theory. A matrix product state representation of the asymptotic input states is identified, allowing for the preparation of the initial momentum wave packets. This initial state is then evolved and we aim to compute the S-matrix elements from the knowledge of the final state. We focus on a specific fermionic U(1)-gauge model, developing a set of tools which are relevant for a broader class of 1+1 dimensional quantum field theories with global or local symmetries
Phase transitions in particle physics
Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions
- âŠ