Search results for "Sigma model"
showing 9 items of 19 documents
Classical and Quantum Nonultralocal Systems on the Lattice
1997
We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.
Anomaly and global inconsistency matching: θ angles, SU(3)/U(1)2 nonlinear sigma model, SU(3) chains, and generalizations
2018
We discuss the SU(3)/[U(1)×U(1)] nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as U(1)×U(1) gauge theories and therefore allow for two topological θ angles. These models provide a field theoretic description of the SU(3) chains. We show that, for particular values of θ angles, a global symmetry group of such systems has a 't Hooft anomaly, which manifests itself as an inability to gauge the global symmetry group. By applying anomaly matching, the ground-state properties can be severely constrained. The anomaly matching is an avatar of the Lieb-Schultz-Mattis (LSM) theorem for the spin chain from which the field theory descends, …
Renormalization group analysis of thermal transport in the disordered Fermi liquid
2014
We present a detailed study of thermal transport in the disordered Fermi liquid with short-range interactions. At temperatures smaller than the impurity scattering rate, i.e., in the diffusive regime, thermal conductivity acquires non-analytic quantum corrections. When these quantum corrections become large at low temperatures, the calculation of thermal conductivity demands a theoretical approach that treats disorder and interactions on an equal footing. In this paper, we develop such an approach by merging Luttinger's idea of using gravitational potentials for the analysis of thermal phenomena with a renormalization group calculation based on the Keldysh nonlinear sigma model. The gravita…
The Nonlinear σ Model
1989
The nonlinear (principal) σ model has been for a long time a theoretical laboratory to test different approaches for quantizing classical field theories. Here we shall discuss as an application of the current algebra representation theory a construction of the quantized σ model.
Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description
2021
We suggest a generalization of the nonlinear σ model for diffusive superconducting systems to account for magnetoelectric effects due to spin-orbit scattering. In the leading orders of spin-orbit strength and gradient expansion, it includes two additional terms responsible for the spin-Hall effect and the spin-current swapping. First, assuming a delta-correlated disorder, we derive the terms from the Keldysh path integral representation of the generating functional. Then we argue phenomenologically that they exhaust all invariants allowed in the effective action to the leading order in the spin-orbit coupling (SOC). Finally, the results are confirmed by a direct derivation of the saddle-poi…
Degrees of freedom and the phase transitions of two-flavor QCD
2008
We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the linear sigma model extended by including a Polyakov loop potential, which is fitted to reproduce the pure gauge theory thermodynamics, and a coupling between the chiral fields and the Polyakov loop. Thus the resulting models have as relevant degrees of freedom the Polyakov loop and chiral fields. By comparing the extended models with the bare chiral models we can conclude that the addition of the Polyakov loop is necessary in order to obtain both qualitative and quantitative agreement with known results at finite temperatures. These results are extended to finite net-quark densities, several thermodynamical quantit…
Effective models of two-flavor QCD: from small towards large $m_q$
2009
We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD. We consider the chiral sector described either using a linear sigma model or a Nambu-Jona-Lasinio model and study how these models, on the mean-field level when coupled with the Polyakov loop, behave as a function of increasing bare quark (or pion) mass. We find qualitatively similar behaviors for the cases of the linear sigma model and the Nambu-Jona-Lasinio model and, by comparing with existing lattice data, show that one cannot conclusively decide which of the two approximate symmetries drives the phase transitions at the physical point.
Dispersion relation bounds forππscattering
2008
Axiomatic principles such as analyticity, unitarity, and crossing symmetry constrain the second derivative of the $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of ${\overline{l}}_{1}$ and ${\overline{l}}_{2}$. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude in the linear sigma model (LSM) using the $\overline{\mathrm{MS}}$ scheme, a result…
The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
2021
The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the $O(3)$ non-linear sigma model in $1+1$ dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in $3+1$ dimensio…