String tension and robustness of confinement properties of in the Schwinger-Thirring model

Abstract

Confinement properties of the $1+1$ Schwinger model can bestudied by computing the string tension between two charges. It is finite (vanishing) if the fermions are massive (massless) corresponding to the occurrence of confinement (screening). Motivated by the possibility of experimentally simulate the Schwinger model, we investigate here the robustness of its screened and confined phases. Firstly, we analyze the effect of nearest-neighbour density-density interaction terms, which -- in the absence of the gauge fields -- give rise to the Thirring model. The resulting Schwinger-Thirring model is studied, also in presence of a topological $\theta$ term, showing that the massless (massive) model remains screened (confined) and that there is deconfinement only for $\theta =\pm \pi$ in the massive case. Estimates of the parameters of the Schwinger-Thirring model are provided with a discussion of a possible experimental setup for its realization with ultracold atoms. The possibility that the gauge fields live in higher dimensions while the fermions remain in $1+1$ is also considered. One may refer to this model as the Pseudo-Schwinger-Thirring model. It is shown that the screening of external charges occurs for $2+1$ and $3+1$ gauge fields, exactly as it occurs in $1+1$ dimensions, with a radical change of the long distance interaction induced by the gauge fields. The massive (massless) model continues to exhibit confinement (screening), signalling that it is the dimensionality of the matter fields, and not of the gauge fields to determine confinement properties. A computation for the string tension is presented in perturbation theory. Our conclusion is that $1+1$ models exhibiting confinement or screening -- massless or massive, in presence of a topological term or not -- retain their main properties when the Thirring interaction is added or the gauge fields live in higher dimension.

References in corpus (53)

• Cold bosonic atoms in optical lattices
• Bosonization and Strongly Correlated Systems
• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Quantum Inverse Scattering Method and Correlation Functions
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Lattice gauge theories simulations in the quantum information era
• Simulations of non-Abelian gauge theories with optical lattices
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Screening vs. Confinement in 1+1 Dimensions
• Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
• Cold atom simulation of interacting relativistic quantum field theories
• Observation of Feshbach resonances in an ultracold gas of ${}^{52}$Cr
• Quantum simulation of a lattice Schwinger model in a chain of trapped ions
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Scattering in Mixed Dimensions with Ultracold Gases
• Towards Quantum Simulating QCD
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Schwinger pair production with ultracold atoms
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
• Interaction Induced Quantum Valley Hall Effect in Graphene
• Generalized Thirring Models
• Quantum simulation of $(1+1)$-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Massive Schwinger model within mass perturbation theory
• Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
• Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
• On the mass spectrum of the two-dimensional O(3) sigma model with theta term
• Spin g-factor due to electronic interactions in graphene
• Quantum-electrodynamical approach to the exciton spectrum in Transition-Metal Dichalcogenides
• Bosonization and Functional Renormalization Group Approach in the Framework of QED_2
• On the renormalization of the bosonized multi-flavor Schwinger model
• The influence of a weak magnetic field in the Renormalization-Group functions of (2+1)-dimensional Dirac systems
• Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics
• The Luttinger-Schwinger Model
• Causal Theory for the Gauged Thirring Model
• Non-Perturbative Field Theory - From two dimensional conformal field theory to QCD in four dimensions
• Charge screening and confinement in the massive Schwinger model
• The Gauged Thirring Model
• Radiative Corrections for the Gauged Thirring Model in Causal Perturbation Theory
• Conformal QED in two-dimensional topological insulators
• Bosonisation Excercise in Three Dimensions: Gauged Massive Thirring Model
• Gauged Thirring Model in the Heisenberg Picture
• Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions
• Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions
• Restrictions over two-dimensional gauge models with Thirring-like interaction
• Excitonic gap generation in thin-film topological insulators
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch

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• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Quantum simulation of the phase transition of the massive Thirring model
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Dynamical deconfinement transition driven by density of excitations
• Reformulation of gauge theories in terms of gauge invariant fields