Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IOP Conference Series Materials Science and Engineering

Occupancy Fluctuation Effect on Metal-Insulator Transition in 3D Hubbard Model within Dynamical Mean-Field Theory Framework

M.G.A. Al Anshori, Choirun Nisaa Rangkuti, Muhammad Aziz Majidi

Published Apr 17, 2019• 0 citations
Publisher

Abstract

Dynamical Mean-Field Theory (DMFT) is among the most widely used techniques in computational condensed-matter physics, especially in addressing electron-electron interactions. In this regard, Quantum Monte Carlo may be considered as the most accurate DMFT impurity solver, but it usually requires a high numerical cost. On the contrary, lower numerical-cost technique, such as mean-field theory, often gives inaccurate results due to complete suppression of quantum fluctuations. In this study, we propose a new potentially low numerical-cost impurity solver taking a full account of fluctuation effects. Applying this new algorithm on Hubbard model, we formulate local self-energy that depends on the occupancy fluctuations. These fluctuations act as the semi-classical degree of freedom that needs to be integrated to obtain the averaged fully interacting Green functions. We test our algorithm by addressing temperature dependence of the density of states that reveals metal-insulator transition.

DOI
10.1088/1757-899x/515/1/012078

Related papers

Occupancy Fluctuation Effects on 3D Hubbard Model at Quarter Filling within Dynamical Mean-Field Theory

N. A. Tadjuddin, Choirun Nisaa Rangkuti, Muhammad Aziz Majidi

Research on materials classified into strongly-correlated systems has become a crucial subject due to the strong interactions among the material constituents yielding various exotic physical properties and phenomena. There have been many computational methods developed to address the properties of such systems accurately within the Hubbard model, but most of them require a lot of computational costs to expect good results. In this research, we proposed a new approach within the Dynamical Mean Field Theory (DMFT) framework that requires a simpler and potentially less numerical-cost algorithm. We implemented this algorithm by constructing the local self-energy matrix elements that depend on the occupancy fluctuations. We integrated them over all possible occupancy configurations to obtain the fully interacting Green functions. The resulted Green function matrix was then used to compute the density of states (DOS) and other quantities. We investigated the case of quarter filling. Our computation results showed that pseudogap appeared when the onsite Coulomb repulsion was sufficiently high and tended to diminish as temperature increased. The system preserved its paramagnetic metallic character for all circumstances we studied.

IOP Conference Series Materials Science and Engineering•Apr 17, 2019•0 citations

Single-site and cellular dynamical mean-field theory of the Anderson-Hubbard model

Ara Go, Gun Sang Jeon

We study the Anderson-Hubbard model to examine the interplay between the disordered potential and the Hubbard interactions. We use the dynamical mean-field theory (DMFT) with an exact diagonalization as an impurity solver to effectively deal with the quantum fluctuations due to the local interactions. In order to characterize the paramagnetic metal-insulator transition in disordered systems, we compute the typical local density of states, as well as the arithmetically-averaged local density of states. Our approach is found to reproduce the characteristic features of the metal-insulator transition in infinite dimensions, such as the existence of the disorder-driven metallic phase for moderate values of disorder strength and interactions, as observed in earlier studies. In two dimensions, the system turns out to exhibit more insulating behavior when we increase the cluster size in the cellular DMFT. The metallic phase, which is induced from weak Mott insulators by the introduction of a disordered potential, is not observed in two dimensions.

Journal of the Korean Physical Society•Mar 1, 2013•0 citations

Fast impurity solver based on equations of motion and decoupling

Qingguo Feng, Yu‐Zhong Zhang, Harald O. Jeschke

In this paper a fast impurity solver is proposed for dynamical mean-field theory (DMFT) based on a decoupling of the equations of motion for the impurity Green's function. The resulting integral equations are solved efficiently with a method based on genetic algorithms. The Hubbard and periodic Anderson models are studied with this impurity solver. The method describes the Mott metal-insulator transition and works for a large range of parameters at finite temperature on the real frequency axis. This makes it useful for the exploration of real materials in the framework of local-density $\text{approximation}+\text{DMFT}$.

arXiv:0903.4838•Physical Review B•Jun 8, 2009•19 citations

Two-dimensional disordered Mott metal-insulator transition

Martha Villagrán, Nikolaos Mitsakos, Tsung-Han Lee +3 more

We studied several aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator transition. We investigated this model through statistical dynamical mean-field theory (statDMFT). This theory is a natural extension of dynamical mean-field theory (DMFT), which has been used with relative success in the past several years with the purpose of describing the Mott transition in the clean case. As is the case for the latter theory, statDMFT incorporates the electronic correlation effects only in their local manifestations. Disorder, on the other hand, is treated in such a way as to incorporate Anderson localization effects. With this technique, we analyzed the disordered two-dimensional Mott transition, using the quantum Monte Carlo algorithm to solve the associated single-impurity problems. We found spinodal lines at which the metal and insulator ceased to be metastable. We also studied spatial fluctuations of local quantities, such as self-energy and local Green's function, and showed the appearance of metallic regions within the insulator and vice versa. We carried out an analysis of finite-size effects and showed that, in agreement with the theorems of Imry and Ma [Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975).], the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by means of a mapping to a random classical resistor network and calculated both the average current and its distribution across the metal-insulator transition.

arXiv:1908.04144•Physical review. B./Physical review. B•Jun 2, 2020•19 citations

Non-Equilibrium Dynamical Mean Field Theory with Quantum Monte Carlo

Qiaoyuan Dong

This work is motivated by the fact that the investigation of non-equilibrium phenomena in strongly correlated electron systems has developed into one of the most active and exciting branches of condensed matter physics as it provides rich new insights that could not be obtained from the study of equilibrium situations. However, a theoretical description of those phenomena is missing. Therefore, in this thesis, we develop a numerical method that can be used to study two minimal models -- the Hubbard model and the Anderson impurity model with general parameter range and time dependence. We begin by introducing the theoretical framework and the general features of the Hubbard model. We then describe the dynamical mean field theory (DMFT), which was first invented by Georges in 1992. It provides a feasible way to approach strongly correlated electron systems and reduces the complexity of the calculations via a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. We employ the non-equilibrium extension of DMFT and map the Hubbard model to the single impurity Anderson model (SIAM). Since the fundamental component of the DMFT method is a solver of the single impurity Anderson model, we continue with a description of the formalism to study the real-time dynamics of the impurity model staring at its thermal equilibrium state. We utilize the non-equilibrium strong-coupling perturbation theory and derive semi-analytical approximation methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA). We then use the Quantum Monte-Carlo method (QMC) as a numerically exact method and present proper measurements of local observables, current and Green's functions. We perform simulations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibrium times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. However, this bare QMC solver suffers from a dynamical sign problem for long time propagations. To overcome the limitations of this bare treatment, we introduce the ``Inchworm algorithm'', based on iteratively reusing the information obtained in previous steps to extend the propagation to longer times and stabilize the calculations. We show that this algorithm greatly reduces the required order for each simulation and re-scales the exponential challenge to quadratic in time. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state. We conclude with the applications of the unbiased inchworm impurity solver to DMFT calculations. We employ the methods for a study of the one-band paramagnetic Hubbard model on the Bethe lattice in equilibrium, where the DMFT approximation becomes exact. We begin with a brief introduction of the Mott metal insulator phase diagram. We present the results of both real time Green's functions and spectral functions from our nonequilibrium calculations. We observe the metal-insulator crossover as the on-site interaction is increased and the formation of a quasi-particle peak as the temperature is lowered. We also illustrate the convergence of our algorithms in different aspects.

•Jan 1, 2017•0 citations

Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined G W and dynamical mean field theory

Thomas Ayral, Silke Biermann, Philipp Werner

We describe a recent implementation of the combined $GW$ and dynamical mean field method ($GW$+DMFT) for the two-dimensional Hubbard model with onsite and nearest-neighbor repulsion. We clarify the relation of the $GW$+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free-energy functional of the model. Furthermore, we describe a numerically exact technique for the solution of the $GW$+DMFT equations, namely, the hybridization expansion continuous-time algorithm for impurity models with retarded interactions. We compute the low-temperature phase diagram of the half-filled extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. $GW$+DMFT introduces a nontrivial momentum dependence into the many-body self-energy and polarization. We find that the charge fluctuations included in the present approach have a larger impact on the latter than on the former. Finally, within the $GW$+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency dependence of the local effective interaction. We analyze this dependence and show how it affects the local spectral function.

arXiv:1210.2712•Physical Review B•Mar 29, 2013•168 citations
Dynamical Mean-Field Theory (DMFT) is among the most widely used techniques in computational condensed-matter physics, especially in addressing electron-electron interactions. In this regard, Quantum Monte Carlo may be considered as the most accurate DMFT impurity solver, but it usually requires a high numerical cost. On the contrary, lower numerical-cost technique, such as mean-field theory, often gives inaccurate results due to complete suppression of quantum fluctuations. In this study, we propose a new potentially low numerical-cost impurity solver taking a full account of fluctuation effects. Applying this new algorithm on Hubbard model, we formulate local self-energy that depends on the occupancy fluctuations. These fluctuations act as the semi-classical degree of freedom that needs to be integrated to obtain the averaged fully interacting Green functions. We test our algorithm by addressing temperature dependence of the density of states that reveals metal-insulator transition.
Research on materials classified into strongly-correlated systems has become a crucial subject due to the strong interactions among the material constituents yielding various exotic physical properties and phenomena. There have been many computational methods developed to address the properties of such systems accurately within the Hubbard model, but most of them require a lot of computational costs to expect good results. In this research, we proposed a new approach within the Dynamical Mean Field Theory (DMFT) framework that requires a simpler and potentially less numerical-cost algorithm. We implemented this algorithm by constructing the local self-energy matrix elements that depend on the occupancy fluctuations. We integrated them over all possible occupancy configurations to obtain the fully interacting Green functions. The resulted Green function matrix was then used to compute the density of states (DOS) and other quantities. We investigated the case of quarter filling. Our computation results showed that pseudogap appeared when the onsite Coulomb repulsion was sufficiently high and tended to diminish as temperature increased. The system preserved its paramagnetic metallic character for all circumstances we studied.
We study the Anderson-Hubbard model to examine the interplay between the disordered potential and the Hubbard interactions. We use the dynamical mean-field theory (DMFT) with an exact diagonalization as an impurity solver to effectively deal with the quantum fluctuations due to the local interactions. In order to characterize the paramagnetic metal-insulator transition in disordered systems, we compute the typical local density of states, as well as the arithmetically-averaged local density of states. Our approach is found to reproduce the characteristic features of the metal-insulator transition in infinite dimensions, such as the existence of the disorder-driven metallic phase for moderate values of disorder strength and interactions, as observed in earlier studies. In two dimensions, the system turns out to exhibit more insulating behavior when we increase the cluster size in the cellular DMFT. The metallic phase, which is induced from weak Mott insulators by the introduction of a disordered potential, is not observed in two dimensions.
In this paper a fast impurity solver is proposed for dynamical mean-field theory (DMFT) based on a decoupling of the equations of motion for the impurity Green's function. The resulting integral equations are solved efficiently with a method based on genetic algorithms. The Hubbard and periodic Anderson models are studied with this impurity solver. The method describes the Mott metal-insulator transition and works for a large range of parameters at finite temperature on the real frequency axis. This makes it useful for the exploration of real materials in the framework of local-density approximation+DMFT\text{approximation}+\text{DMFT}approximation+DMFT.
We studied several aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator transition. We investigated this model through statistical dynamical mean-field theory (statDMFT). This theory is a natural extension of dynamical mean-field theory (DMFT), which has been used with relative success in the past several years with the purpose of describing the Mott transition in the clean case. As is the case for the latter theory, statDMFT incorporates the electronic correlation effects only in their local manifestations. Disorder, on the other hand, is treated in such a way as to incorporate Anderson localization effects. With this technique, we analyzed the disordered two-dimensional Mott transition, using the quantum Monte Carlo algorithm to solve the associated single-impurity problems. We found spinodal lines at which the metal and insulator ceased to be metastable. We also studied spatial fluctuations of local quantities, such as self-energy and local Green's function, and showed the appearance of metallic regions within the insulator and vice versa. We carried out an analysis of finite-size effects and showed that, in agreement with the theorems of Imry and Ma [Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975).], the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by means of a mapping to a random classical resistor network and calculated both the average current and its distribution across the metal-insulator transition.
This work is motivated by the fact that the investigation of non-equilibrium phenomena in strongly correlated electron systems has developed into one of the most active and exciting branches of condensed matter physics as it provides rich new insights that could not be obtained from the study of equilibrium situations. However, a theoretical description of those phenomena is missing. Therefore, in this thesis, we develop a numerical method that can be used to study two minimal models -- the Hubbard model and the Anderson impurity model with general parameter range and time dependence. We begin by introducing the theoretical framework and the general features of the Hubbard model. We then describe the dynamical mean field theory (DMFT), which was first invented by Georges in 1992. It provides a feasible way to approach strongly correlated electron systems and reduces the complexity of the calculations via a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. We employ the non-equilibrium extension of DMFT and map the Hubbard model to the single impurity Anderson model (SIAM). Since the fundamental component of the DMFT method is a solver of the single impurity Anderson model, we continue with a description of the formalism to study the real-time dynamics of the impurity model staring at its thermal equilibrium state. We utilize the non-equilibrium strong-coupling perturbation theory and derive semi-analytical approximation methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA). We then use the Quantum Monte-Carlo method (QMC) as a numerically exact method and present proper measurements of local observables, current and Green's functions. We perform simulations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibrium times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. However, this bare QMC solver suffers from a dynamical sign problem for long time propagations. To overcome the limitations of this bare treatment, we introduce the ``Inchworm algorithm'', based on iteratively reusing the information obtained in previous steps to extend the propagation to longer times and stabilize the calculations. We show that this algorithm greatly reduces the required order for each simulation and re-scales the exponential challenge to quadratic in time. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state. We conclude with the applications of the unbiased inchworm impurity solver to DMFT calculations. We employ the methods for a study of the one-band paramagnetic Hubbard model on the Bethe lattice in equilibrium, where the DMFT approximation becomes exact. We begin with a brief introduction of the Mott metal insulator phase diagram. We present the results of both real time Green's functions and spectral functions from our nonequilibrium calculations. We observe the metal-insulator crossover as the on-site interaction is increased and the formation of a quasi-particle peak as the temperature is lowered. We also illustrate the convergence of our algorithms in different aspects.
We describe a recent implementation of the combined GWGWGW and dynamical mean field method (GWGWGW+DMFT) for the two-dimensional Hubbard model with onsite and nearest-neighbor repulsion. We clarify the relation of the GWGWGW+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free-energy functional of the model. Furthermore, we describe a numerically exact technique for the solution of the GWGWGW+DMFT equations, namely, the hybridization expansion continuous-time algorithm for impurity models with retarded interactions. We compute the low-temperature phase diagram of the half-filled extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. GWGWGW+DMFT introduces a nontrivial momentum dependence into the many-body self-energy and polarization. We find that the charge fluctuations included in the present approach have a larger impact on the latter than on the former. Finally, within the GWGWGW+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency dependence of the local effective interaction. We analyze this dependence and show how it affects the local spectral function.