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Title: Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions

Abstract

Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scale-invariant system? To make our statements precise, here we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

Authors:
 [1];  [1];  [1]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES); Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1566379
Alternate Identifier(s):
OSTI ID: 1435676
Grant/Contract Number:  
AC02-98CH10886; AC0298CH1088
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; phonons; thermal conductivity; energy storage (including batteries and capacitors); superconductivity; defects; spin dynamics

Citation Formats

Phillips, Philip W., Setty, Chandan, and Zhang, Shuyi. Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions. United States: N. p., 2018. Web. doi:10.1103/physrevb.97.195102.
Phillips, Philip W., Setty, Chandan, & Zhang, Shuyi. Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions. United States. doi:10.1103/physrevb.97.195102.
Phillips, Philip W., Setty, Chandan, and Zhang, Shuyi. Wed . "Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions". United States. doi:10.1103/physrevb.97.195102. https://www.osti.gov/servlets/purl/1566379.
@article{osti_1566379,
title = {Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions},
author = {Phillips, Philip W. and Setty, Chandan and Zhang, Shuyi},
abstractNote = {Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scale-invariant system? To make our statements precise, here we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.},
doi = {10.1103/physrevb.97.195102},
journal = {Physical Review B},
number = 19,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

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Works referenced in this record:

A universal scaling relation in high-temperature superconductors
journal, July 2004

  • Homes, C. C.; Dordevic, S. V.; Strongin, M.
  • Nature, Vol. 430, Issue 6999
  • DOI: 10.1038/nature02673

Study on a toy Model of Strongly Correlated Electrons
journal, December 1996

  • Nogueira, Flavio S.; Anda, Enrique V.
  • International Journal of Modern Physics B, Vol. 10, Issue 27
  • DOI: 10.1142/S0217979296002014

Theory of the Luttinger surface in doped Mott insulators
journal, March 2007


What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors
journal, May 2000

  • Abrahams, E.; Varma, C. M.
  • Proceedings of the National Academy of Sciences, Vol. 97, Issue 11
  • DOI: 10.1073/pnas.100118797

Why the temperature is high
journal, July 2004


Infrared conductivity of cuprate metals: Detailed fit using Luttinger-liquid theory
journal, May 1997


Conductivity and diffusion constant in Lifshitz backgrounds
journal, January 2010


Quantum Phase Transitions in the Cuprate Superconductor Bi 2 Sr 2 x La x CuO 6 + δ
journal, June 2004


Quantum critical behaviour in a high-Tc superconductor
journal, September 2003

  • Marel, D. van der; Molegraaf, H. J. A.; Zaanen, J.
  • Nature, Vol. 425, Issue 6955
  • DOI: 10.1038/nature01978

Holographic spectral functions and diffusion constants for fundamental matter
journal, November 2007

  • Myers, Robert C.; Starinets, Andrei O.; Thomson, Rowan M.
  • Journal of High Energy Physics, Vol. 2007, Issue 11
  • DOI: 10.1088/1126-6708/2007/11/091

Analytical shear viscosity in hyperscaling violating black brane
journal, October 2017


Absence of a quantum limit to charge diffusion in bad metals
journal, February 2015


Universal conductivity and central charges
journal, September 2008


Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
journal, August 2016


An Exactly Solvable Fermion Model: Spinons, Holons and a Non-Fermi Liquid Phase
journal, April 1991


Lindhard Dielectric Function in the Relaxation-Time Approximation
journal, March 1970


Holography and hydrodynamics: diffusion on stretched horizons
journal, October 2003


Exactly Solvable Model of Correlated Lattice Electrons in Any Dimensions
journal, June 1992

  • Hatsugai, Yasuhiro; Kohmoto, Mahito
  • Journal of the Physical Society of Japan, Vol. 61, Issue 6
  • DOI: 10.1143/JPSJ.61.2056

Gapless spin-fluid ground state in a random quantum Heisenberg magnet
journal, May 1993


Theory of universal incoherent metallic transport
journal, December 2014


A toy Model of Interlayer pair Hopping
journal, May 1994


Scaling close to a Mott transition in an exactly soluble model
journal, June 1994