Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRenormalization group analysis of competition between distinct order parameters
191
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We perform a detailed renormalization group analysis to study a (2+1)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort of field theory can describe the competition and coexistence between distinct long-range orders, and therefore plays a vital role in statistical physics and condensed matter physics. We first derive and solve the renormalization group equations of all the relevant physical parameters, and then show that the system does not have any stable fixed point in the lowest energy limit. Interestingly, this conclusion holds in both the ordered and disordered phases, and also at the quantum critical point. Therefore, the originally continuous transitions are unavoidably turned to first-order due to ordering competition. Moreover, we examine the impacts of massless Goldstone boson generated by continuous symmetry breaking on ordering competition, and briefly discuss the physical implications of our results.
rate research
Read More
We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose to use symmetry breaking counterterms for each instability, and employ a self-consistency condition for fixing the counterterms. As a validity check, results are compared to known exact results for the case of one-dimensional systems. We find that whilst one-dimensional peculiarities, in particular algebraically decaying correlation functions, can not be reproduced, the phase boundaries are reproduced accurately, encouraging further explorations for higher-dimensional systems.
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the $varphi^4$ theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
The Holstein Model (HM) describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits, but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature $T_{rm cdw}$ for CDW order, and also uncover several novel features of diagonal long range order in the phase diagram, including a competition between charge patterns at momenta ${bf q}=(pi,pi)$ and ${bf q}=(0,pi)$ which lends insight into the relationship between Fermi surface nesting and the wavevector at which charge order occurs. We also demonstrate SC order at half-filling in situations where nonzero bandwidth sufficiently suppresses $T_{rm cdw}$.
We investigate the infrared properties of SU(N)$_k$ conformal field theory perturbed by its adjoint primary field in 1+1 dimensions. The latter field theory is shown to govern the low-energy properties of various SU(N) spin chain problems. In particular, using a mapping onto k-leg SU(N) spin ladder, a massless renormalization group flow to SU(N)$_1$ criticality is predicted when N and k have no common divisor. The latter result extends the well-known massless flow between SU(2)$_k$ and SU(2)$_1$ Wess-Zumino-Novikov-Witten theories when k is odd in connection to the Haldanes conjecture on SU(2) Heisenberg spin chains. A direct approach is presented in the simplest N=3 and k=2 case to investigate the existence of this massless flow.
We develop a variational scheme called Gutzwiller renormalization group (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method can exploit the low-entanglement property of the ground state in combination with the framework of the Gutzwiller wavefunction, and suggests that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and indicate that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
