A sport and a pastime:Model design and computation in quantum many-body systems

We summarize the recent developments in the model design and computation for a few representative quantum manybody systems,encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity,SYK non-Fermi-liquid with self-tuned quantum criticality and fluctuation induced superconductivity,and the flat-band quantum Moirélattice models in continuum where the interplay of quantum geometry of flat-band wave function and the long-range Coulomb interactions gives rise to novel insulating phases at integer fillings and superconductivity away from them.Although the narrative choreography seems simple,we show how important the appropriate model design and their tailor-made algorithmic developments-in other words,the scientific imagination inspired by the corresponding fast experimental developments in the aforementioned systems-compel us to invent and discover new knowledge and insights in the sport and pastime of quantum many-body research.

Superconductivity near the(2+1)-Dimensional Ferromagnetic Quantum Critical Point

We utilize both analytical and numerical methods to study the superconducting transition temperature Tnear a fermionic quantum critical point(QCP) using a model constructed by Xu et al. [Phys. Rev. X 7, 031059(2017)] as an example. In this model, the bosonic critical fluctuation plays the role of pairing glue for the Cooper pairs, and we use a Bardeen–Cooper–Schrieffer-type mean-field theory to estimate T. We further argue that the Tc computed from the BCS theory approximates a pseudogap temperature TPG, instead of the Berezinskii–Kosterlitz–Thouless transition temperature T, which is confirmed by our determinant quantum Monte Carlo simulation. Moreover, due to the fact that electron density of state starts to deplete at T, the critical scaling of the underlying QCP is also affected below TPG. Thus, when studying the critical behavior of fermionic QCPs, we need to monitor that the temperature is above TPG instead of T. This was often ignored in previous studies.

Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene

We report an implementation of the momentum space quantum Monte Carlo(QMC)method on the interaction model for the twisted bilayer graphene(TBG).The long-range Coulomb repulsion is treated exactly with the flat bands,spin and valley degrees of freedom of electrons taking into account.We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered.By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation,we benchmark the QMC data with the exact band gap obtained at the chiral limit,to reveal the insulating ground states at the charge neutrality point(CNP).Then,with the exact Green's functions from QMC,we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP.Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.

Solving quantum rotor model with different Monte Carlo techniques

We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC),hybrid Monte Carlo(HM),hybrid Monte Carlo with Fourier acceleration(FA)schemes,it is clear that among the five different update schemes,at the quantum critical point,the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error,and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones.These results bestow one with the necessary knowledge of extending the quantum rotor model,which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z_(2)topological order,to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.