Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFunctional renormalization group for frustrated magnets with nondiagonal spin interactions
203
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In the field of quantum magnetism, the advent of numerous spin-orbit assisted Mott insulating compounds, such as the family of Kitaev materials, has led to a growing interest in studying general spin models with non-diagonal interactions that do not retain the SU(2) invariance of the underlying spin degrees of freedom. However, the exchange frustration arising from these non-diagonal and often bond-directional interactions for two- and three-dimensional lattice geometries poses a serious challenge for numerical many-body simulation techniques. In this paper, we present an extended formulation of the pseudo-fermion functional renormalization group that is capable of capturing the physics of frustrated quantum magnets with generic (diagonal and off-diagonal) two-spin interaction terms. Based on a careful symmetry analysis of the underlying flow equations, we reveal that the computational complexity grows only moderately, as compared to models with only diagonal interaction terms. We apply the formalism to a kagome antiferromagnet which is augmented by general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as argued to be present in the spin liquid candidate material herbertsmithite. We calculate the complete ground state phase diagram in the strength of in-plane and out-of-plane DM couplings, and discuss the extended stability of the spin liquid of the unperturbed kagome antiferromagnet in the presence of these couplings.
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.
We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of non-collinear magnetic orders of the $J_1$-$J_2$ Heisenberg model ($mathbf{q}=0$, $sqrt{3}timessqrt{3}$, and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral {it herbertsmithite} which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicates that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for {it herbertsmithite}, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.
A functional renormalization group approach to $d$-dimensional, $N$-component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between $d= 2.8$ and $d=4$ for various values of $N$ focusing on the critical value $N_c(d)$ that, for a given dimension $d$, separates a first order region for $N<N_c(d)$ from a second order region for $N>N_c(d)$. Our approach concludes to the absence of stable fixed point in the physical - $N=2,3$ and $d=3$ - cases, in agreement with $epsilon=4-d$-expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on conformal bootstrap program.
Spontaneous current orders due to odd-parity order parameters attract increasing attention in various strongly correlated metals. Here, we discover a novel spin-fluctuation-driven charge loop current (cLC) mechanism based on the functional renormalization group (fRG) theory. The present mechanism leads to the ferro-cLC order in a simple frustrated chain Hubbard model. The cLC appears between the antiferromagnetic and $d$-wave superconducting ($d$SC) phases. While the microscopic origin of the cLC has a close similarity to that of the $d$SC, the cLC transition temperature $T_{rm cLC}$ can be higher than the $d$SC one for wide parameter range. Furthermore, we reveal that the ferro cLC order is driven by the strong enhancement of the forward scatterings $g_2$ and $g_4$ owing to the two dimensionality based on the $g$-ology language. The present study indicates that the cLC can emerge in metals near the magnetic criticality with geometrical frustration
We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. As a specific example we consider the dynamical mean-field theory (DMFT) solution as reference system, and discuss the relation to the recently introduced DMF$^2$RG and the dual-fermion formalism.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
