One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface (FS) underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion $U$ and chemical potential $μ$ , we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the "Luttinger Breaking" (LB) phase, as the Mott insulator is approached. This transition into a non-Fermi liquid phase that violates the Luttinger count, is a continuous phase transition at a critical density in the absence of any other broken symmetry. We obtain the Fermi surface contour from the spectral weight $A_{\vec{k}}(ω=0)$ and from an analysis of the poles and zeros of the retarded Green's function $G_{\vec{k}}^{ret}(E=0)$ , calculated using determinantal quantum Monte Carlo and analytic continuation methods.We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy and angle resolved photoemission spectroscopy.One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface (FS) underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion $U$ and chemical potential $μ$, we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the "Luttinger Breaking" (LB) phase, as the Mott insulator is approached. This transition into a non-Fermi liquid phase that violates the Luttinger count, is a continuous phase transition at a critical density in the absence of any other broken symmetry. We obtain the Fermi surface contour from the spectral weight $A_{\vec{k}}(ω=0)$ and from an analysis of the poles and zeros of the retarded Green's function $G_{\vec{k}}^{ret}(E=0)$, calculated using determinantal quantum Monte Carlo and analytic continuation methods.We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy and angle resolved photoemission spectroscopy.

arXiv:2001.07197Jan 20, 20201 citation

Broken Luttinger theorem in the two-dimensional Fermi-Hubbard model

Ian S. Osborne, Thereza Paiva, Nandini Trivedi

One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion $U$ and chemical potential $\ensuremath{\mu}$, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the ``Luttinger breaking'' phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight ${A}_{\mathbf{k}}(\ensuremath{\omega}=0)$ and from an analysis of the singularities of the Green's function $\mathrm{Re}\phantom{\rule{0.16em}{0ex}}{G}_{\mathbf{k}}(E=0)$ , calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion $U$ and chemical potential $\ensuremath{\mu}$, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the ``Luttinger breaking'' phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight ${A}_{\mathbf{k}}(\ensuremath{\omega}=0)$ and from an analysis of the singularities of the Green's function $\mathrm{Re}\phantom{\rule{0.16em}{0ex}}{G}_{\mathbf{k}}(E=0)$, calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.

Physical review. B./Physical review. BDec 10, 202114 citations

Fermi Surface Restructuring in the Fermi-Hubbard Model

Ian S. Osborne

We take an in depth look into the celebrated Fermi-Hubbard model for strongly interacting fermions, beginning with a two-site exact diagonalization demonstration of the Mott ground state. We continue with measurements of compressibility and susceptibility using Determinantal Quantum Monte Carlo (DQMC) methods on a larger square lattice 6x6 over the parameter space of interaction strength U/t and doping, controlled by the chemical potential, mu/t. We construct the Fermi surface for a 16x16 cluster size using the retarded Green's function and the single particle spectral function (derived from the Green's function using an analytic continuation procedure) and find conclusive evidence of Fermi surface restructuring (FSR) as a result of strong interactions freezing out states from contributing to the Luttinger count, n, at intermediate temperatures, T = t/2. FSR is found for strongly interacting, doped systems for dopings p < 0.2. This phase is dubbed the Luttinger's rule breaking (LB) phase, and we provide a discussion of the consequences of the deviation from Luttinger's theorem. We strongly suggest a topological nature underlying the restructuring of the Fermi surface by eliminating competing ordering in spin or charge channels.We take an in depth look into the celebrated Fermi-Hubbard model for strongly interacting fermions, beginning with a two-site exact diagonalization demonstration of the Mott ground state. We continue with measurements of compressibility and susceptibility using Determinantal Quantum Monte Carlo (DQMC) methods on a larger square lattice 6x6 over the parameter space of interaction strength U/t and doping, controlled by the chemical potential, mu/t. We construct the Fermi surface for a 16x16 cluster size using the retarded Green's function and the single particle spectral function (derived from the Green's function using an analytic continuation procedure) and find conclusive evidence of Fermi surface restructuring (FSR) as a result of strong interactions freezing out states from contributing to the Luttinger count, n, at intermediate temperatures, T = t/2. FSR is found for strongly interacting, doped systems for dopings p < 0.2. This phase is dubbed the Luttinger's rule breaking (LB) phase, and we provide a discussion of the consequences of the deviation from Luttinger's theorem. We strongly suggest a topological nature underlying the restructuring of the Fermi surface by eliminating competing ordering in spin or charge channels.

Apr 16, 20201 citation

The Luttinger Model: Its Role in the RG-Theory of One Dimensional Many Body Fermi Systems

Giovanni Gallavotti

arXiv:cond-mat/0008090Journal of Statistical PhysicsMay 1, 20011 citation

U

and chemical potential

μ

, we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the "Luttinger Breaking" (LB) phase, as the Mott insulator is approached. This transition into a non-Fermi liquid phase that violates the Luttinger count, is a continuous phase transition at a critical density in the absence of any other broken symmetry. We obtain the Fermi surface contour from the spectral weight

A_{\vec{k}}(ω=0)

and from an analysis of the poles and zeros of the retarded Green's function

G_{\vec{k}}^{ret}(E=0)

, calculated using determinantal quantum Monte Carlo and analytic continuation methods.We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy and angle resolved photoemission spectroscopy.

U

and chemical potential $\ensuremath{\mu}$, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the ``Luttinger breaking'' phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight ${A}_{\mathbf{k}}(\ensuremath{\omega}=0)$ and from an analysis of the singularities of the Green's function

\mathrm{Re}\phantom{\rule{0.16em}{0ex}}{G}_{\mathbf{k}}(E=0)

, calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.