Quantum Monte Carlo simulations of disordered Fermi systems

Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite $N$ , beyond the large- $N$ used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the $ω\ln ω$ type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite $N$, beyond the large-$N$ used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the $ω\ln ω$ type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.

arXiv:2410.13858Oct 17, 20241 citation

Superconductor-insulator transition in a disordered electronic system

Nandini Trivedi, Richard T. Scalettar, Mohit Randeria

We study an electronic model of a two-dimensional $s$ -wave superconductor in a random potential using quantum Monte Carlo simulations. The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder. We calculate the temperature-dependent resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)$ for a highly disordered interacting Fermi system. Using this we identify the nonsuperconducting state as an insulator.We study an electronic model of a two-dimensional $s$-wave superconductor in a random potential using quantum Monte Carlo simulations. The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder. We calculate the temperature-dependent resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)$ for a highly disordered interacting Fermi system. Using this we identify the nonsuperconducting state as an insulator.

arXiv:cond-mat/9509029Physical review. B, Condensed matterAug 1, 1996125 citations

Quantum-Monte-Carlo simulations for fermionic systems

I. Morgenstern

The European Physical Journal BJun 1, 198914 citations

Recent developments in quantum Monte Carlo simulations with applications for cold gases

Lode Pollet

This is a review of recent developments in Monte Carlo methods in the field of ultracold gases. For bosonic atoms in an optical lattice we discuss path-integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons and spinful bosonic systems. For repulsive fermionic systems, determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.This is a review of recent developments in Monte Carlo methods in the field of ultracold gases. For bosonic atoms in an optical lattice we discuss path-integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons and spinful bosonic systems. For repulsive fermionic systems, determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.

arXiv:1206.0781Reports on Progress in PhysicsAug 10, 2012152 citations

N

, beyond the large-

N

used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the

ω\ln ω

type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.

We study an electronic model of a two-dimensional

s

-wave superconductor in a random potential using quantum Monte Carlo simulations. The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder. We calculate the temperature-dependent resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)$ for a highly disordered interacting Fermi system. Using this we identify the nonsuperconducting state as an insulator.