aqora

Numerical implementation of ``rigorous renormalization group'' for ground states and low-energy excited states of 1d Hamiltonians

Brenden Roberts, Thomas Vidick, Olexei I. Motrunich

Bulletin of the American Physical SocietyMar 14, 20170 citations

Fixed-Point Few-Body Hamiltonians in Quantum Mechanics

Lauro Tomio, T. Frederico, V. S. Timóteo +1 more

We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in the limit of short-range interactions. In this context, it is revised the formulation of the subtracted scattering equations and fixed-point Hamiltonians applied to few-body systems, in which the original interaction contains point-like singularities, such as Dirac-delta and/or its derivatives. The approach is being illustrated by considering two-nucleons described by singular interactions. This revision also includes an extension of the renormalization formalism to three-body systems, which is followed by an updated discussion on the applications to four particles.We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in the limit of short-range interactions. In this context, it is revised the formulation of the subtracted scattering equations and fixed-point Hamiltonians applied to few-body systems, in which the original interaction contains point-like singularities, such as Dirac-delta and/or its derivatives. The approach is being illustrated by considering two-nucleons described by singular interactions. This revision also includes an extension of the renormalization formalism to three-body systems, which is followed by an updated discussion on the applications to four particles.

arXiv:2111.05954Nov 10, 20210 citations

Adiabatic approximation from a renormalization group inspired method

Carlos Contreras, J. C. Retamal, Lautaro Vergara

We show how a method inspired in renormalization group techniques can be useful for deriving Hamiltonians in the adiabatic approximation in a systematic way.

arXiv:quant-ph/0006074Jun 15, 20001 citation

Renormalization group approach to light-front Hamiltonian(光円錐ハミルトニアンにおけるくりこみ群の方法)

杉原崇憲

物理

Jan 1, 19970 citations

A functional renormalization group study of strongly correlated electron systems

Nahom Yirga

A wide variety of phenomena in condensed matter systems is driven primarily by interactions between electrons in the system. This work is concerned with the application of functional renormalization group (fRG) as a generalized solver for the multi-band Hamiltonians that describe these systems. We consider a decoupled formulation of the fRG equations that is optimized in the frequency and momentum domains and retains the flow of relevant modes in the system. Approximate truncations that extend the scheme to arbitrary multiband systems are addressed. This optimized decoupling is then used to derive the flow equations that describe fluctuations in model Hamiltonians for Cuprate and Pnictide superconductors. We construct a full phase diagram of the systems studied as a function of doping, temperature and coupling. Access to the frequency modes in the system allows us to explore the impact of coupling phonons to these model Hamiltonians. Alterations to the diagram due to electron-phonon coupling is derived. The results of the decoupled formulation is in agreement with results in the literature for many of the models considered. Further the fRG captures the sensitivity of susceptibilities of Cuprate Hamiltonians to band structure, the enhanced role of Hunds coupling in Pnictide systems and the impact of phonons in multiband Hamiltonians.A wide variety of phenomena in condensed matter systems is driven primarily by interactions between electrons in the system. This work is concerned with the application of functional renormalization group (fRG) as a generalized solver for the multi-band Hamiltonians that describe these systems. We consider a decoupled formulation of the fRG equations that is optimized in the frequency and momentum domains and retains the flow of relevant modes in the system. Approximate truncations that extend the scheme to arbitrary multiband systems are addressed. This optimized decoupling is then used to derive the flow equations that describe fluctuations in model Hamiltonians for Cuprate and Pnictide superconductors. We construct a full phase diagram of the systems studied as a function of doping, temperature and coupling. Access to the frequency modes in the system allows us to explore the impact of coupling phonons to these model Hamiltonians. Alterations to the diagram due to electron-phonon coupling is derived. The results of the decoupled formulation is in agreement with results in the literature for many of the models considered. Further the fRG captures the sensitivity of susceptibilities of Cuprate Hamiltonians to band structure, the enhanced role of Hunds coupling in Pnictide systems and the impact of phonons in multiband Hamiltonians.

Jan 1, 20210 citations

WAVE FUNCTIONALS, HAMILTONIANS AND THE RENORMALIZATION GROUP

Djordje Minić, V. P. Nair

We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A general discussion of the canonical structure of the renormalization group equation is also given.

arXiv:hep-th/9406074International Journal of Modern Physics AJun 20, 199613 citations

Hamiltonian Renormalization Groups

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Hamiltonian Renormalization Groups

Abstract

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