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arXiv:1303.7369

Correlation driven Mott-insulator-to-metal transition

Rubem Mondaini, Thereza Paiva

Published Mar 29, 2013• 0 citations
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Abstract

We study transport properties of the half-filled two-dimensional (2D) Hubbard model with spatially varying interactions, where a pattern of interacting and non-interacting sites is formed. We use Determinantal Quantum Monte Carlo method to calculate the double occupation, effective hopping and Drude weight. These data point to two phase transitions, driven by fermionic correlations. The first is the expected metal to a Mott insulating state. The second one, is an exotic transition from a Mott insulating state to a highly anisotropic metal, that takes place at large values of the fermion-fermion interaction. This second transition occurs when the layers formed by the spatially varying interactions decouple due to the suppression of the hopping between interacting and non-interacting sites, leading to fermionic transport along the non-interacting ones.

DOI
10.48550/arxiv.1303.7369

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We study transport properties of the half-filled two-dimensional (2D) Hubbard model with spatially varying interactions, where a pattern of interacting and non-interacting sites is formed. We use Determinantal Quantum Monte Carlo method to calculate the double occupation, effective hopping and Drude weight. These data point to two phase transitions, driven by fermionic correlations. The first is the expected metal to a Mott insulating state. The second one, is an exotic transition from a Mott insulating state to a highly anisotropic metal, that takes place at large values of the fermion-fermion interaction. This second transition occurs when the layers formed by the spatially varying interactions decouple due to the suppression of the hopping between interacting and non-interacting sites, leading to fermionic transport along the non-interacting ones.
We investigate the Mott metal-insulator transition in the asymmetric Hubbard model, which may describe the ground states of fermionic atoms trapped in optical lattices. We use the dynamical mean-field theory and the equation of motion approach to calculate the density of states at the Fermi level and the double occupation for various values of the on-site interaction U and the hopping asymmetry r . The critical interaction is also obtained as a function of the hopping asymmetry. Our results are in good agreement with the ones obtained by using the dynamical mean field theory with the exact diagonalization and the quantum Monte Carlo techniques.
The Quantum Monte-Carlo simulations of the two-dimensional Hubbard model are presented for the half filling. The method based on the direct-space proposed by Suzuki and al., and Hirsch and al. was used. The states generated by this method are basis states in occupation number representation built with Wannier states localised on each site of the square array. The configurations of fermions can be observed on the real 2D array. An antiferromagnetic factor is defined and calculated for each temperature. The curves of energy, specific heat, conducivity and antiferromagnetic factor are presented for different values of the repulsive coulombian on site interaction U. There is a metal-insulator transition at low temperature for small values of U. This transition corresponds with a paramagnetic-ferromagnetic first order transition. Indeed, for these interaction values, the energy curves show a gap which is a characteristic of a first order transition. An hysteresis phenomenon appears on the conductivity curves. There is a behaviour change for U/t=3.5. For the values U>3.5 there is ferromagnetic-paramagnetic change without observable effect on the energy and the specific heat. The metal-insulator transition does not exist any more, the conductivity stays very small. Isotherms of the physical quantities versus U/t show a transition which seems to be the metal-insulator Mott transition. These results allow to draw a phase diagram with two first order transition lines.
We investigate a nonmagnetic metal-insulator transition in the 1/5-depleted square lattice Hubbard model at half filling within the eight-site cellular dynamical mean field theory. We find that a metal-insulator transition without any signatures of a first-order transition, a continuous Mott transition, takes place in a certain range of parameters. The nature of the continuous Mott transition is merely a Lifshitz transition driven by the on-site Coulomb interaction. The renormalized matrix elements of hoppings and the spin-spin correlation functions reveal that the physics of this transition is a strong enhancement of the dimerization due to the nonlocal effects of the electron-electron interaction.
We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.
The ability to cool fermions in optical lattices to ultra cold temperatures has led to an interdisciplinary area of research, that has attracted a lot of attention in recent years. An interesting development in this area is the possibility to realize models for strongly correlated fermions in the laboratory, such as the fermionic Hubbard Model. Determinantal Quantum Monte Carlo simulations have proven to be an important tool in the study of fermionic atoms. Nonetheless, it is important to compare the results and efficiency of different methods. Here comparisons with Numerical Linked Cluster Expansion and Dynamical Mean Field Theory data for double occupation and short range correlations, both relevant to current optical lattice experiments, will be presented and discussed. Another topic relevant in the context of optical lattice experiments is the study of metal insulator transitions. Indeed, the Mott insulating phase has been realized and observed in two-flavor mixtures of fermionic atoms loaded on optical lattices, being characterized both by the double occupation and the compressibility. An interesting point that has been addressed in the literature over the years is whether the same fermion-fermion interaction, responsible for the Mott insulating state, could drive an insulating system metallic. Here we show that, when fermions are loaded in optical lattices with spatially varying interactions a correlation induced Mott insulator to metal transition can take place. The spatial modulation of the interactions was recently demonstrated and opens the possibility for the experimental realization of such exotic phases.
We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the magnetically ordered and superfluid states are not realized, but the metal-insulator transition occurs. This transition is characterized by the Mott and pairing transitions discussed in the conventional repulsive and attractive Hubbard models. In the doped system, commensurability emerges owing to the repulsive interactions and the metal-insulator transition occurs down to quarter-filling.