arXiv subjects

Venkitesh Ayyar

Publications and source records attributed to Venkitesh Ayyar.

25 records · Page 2Linked to original sources

arXiv2016

Search for a continuum limit of the PMS phase

Previous studies of a simple four-fermion model with staggered fermions in 3D have shown the existence of an exotic quantum critical point, where one may be able to define a continuum limit of the Paramagnetic Strong Phase (or the PMS phase). We believe the existence of the critical point suggests a new mechanism for generating fermion masses. In this work we begin the search for this quantum critical point in 4D by extending the 3D model to 4D. Unlike in 3D, now we do find evidence for an intermediate spontaneously broken phase (FM phase) and are able compute the phase boundaries accurately. In terms of the bare coupling, the width of the intermediate region appears to be quite small.

hep-lat↗

arXiv2016

Fermion masses through four-fermion condensates

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.

hep-lat↗

arXiv2015

Exotic Quantum Critical Points with Staggered Fermions

We study two flavors of massless staggered fermions interacting via an on-site four-fermion inter- action and argue that the model contains an exotic quantum critical point separating the perturba- tive massless phase from a massive fermion phase at strong couplings where the fermion bilinear condensate remains zero. We believe that no spontaneous symmetry breaking occurs at the tran- sition. We have extensive calculations in three Euclidian dimensions that are consistent with the existence of a single second order phase transition separating the two phases. Although mean field theory suggests that this transition will turn first order at sufficiently large number of dimensions, preliminary results suggest that the transition remains second order in four-dimensions.

hep-lat↗

arXiv2015

Origin of fermion masses without spontaneous symmetry breaking

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should be of wide interest.

hep-lat↗

arXiv2014

Fermion mass generation without a condensate

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The symmetry of the model forbids non-zero fermion bilinear order parameters that can generate a fermion mass. At weak couplings, we expect a massless fermion phase. At strong couplings, we can argue for the existence of massive fermions without the formation of any fermion bilinear condensate. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order phase transition between the two phases.

hep-lat↗

arXiv2014

Massive fermions without fermion bilinear condensates

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a $SU(4)$ symmetry which forbids non-zero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remained unclear. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order transition between the two phases suggesting that the exotic lattice phase may have a continuum limit at least in three dimensions. A similar exotic second order critical point was found recently in a bilayer system on a honeycomb lattice.

hep-lat↗

arXiv2012

Approach to equilibrium in the Caldeira-Leggett Model

The Caldeira-Leggett model describes a microscopic quantum system, represented by a harmonic oscillator, in interaction with a heat bath, represented by a large number of harmonic oscillators with a range of frequencies. We consider the case when the system oscillator starts out in the ground state and then thermalizes due to interactions with the heat bath, which is at temperature $θ$. We calculate the position autocorrelation function $ $ of the system oscillator at two different times and study its behaviour in the small and large time limits. Our results show that the system oscillator thermalizes as expected. We also confirm by explicit calculation that the position autocorrelation function exhibits periodicity for imaginary values of the time difference $t'-t = iτ$ at late (real) times $t$.

nucl-th↗