Abstract
We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature. Our results exemplify the possibility to obtain virtually all physical properties of an interacting system from the functional renormalization group.
Highlights
The renormalization-group approach has been used primarily for the study of universal properties of systems near a second-order phase transition [1,2,3,4]
The functional renormalization group (FRG) has been used in many models of quantum and statistical field theory ranging from statistical physics and condensed matter to high-energy physics and quantum gravity [10]
We have shown that the FRG approach is a very powerful method, notably at zero temperature, to determine the physical properties of the massive sine-Gordon model, which is the bosonized version of the massive Schwinger model
Summary
The renormalization-group approach has been used primarily for the study of universal properties of systems near a second-order phase transition [1,2,3,4]. To exemplify the predictive power of the FRG formalism, we determine both universal and nonuniversal properties of the Schwinger model, at zero and finite temperature. The results compare well with numerical studies except for the finite-temperature phase diagram where, contrary to the expectation, we find a region with spontaneous symmetry breaking (SSB) at T > 0. This observation is likely an artifact of the FRG calculation using a truncated derivative expansion, as we will discuss.
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