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Title: Ladderlike optical conductivity in the spin-fermion model

Abstract

In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show here that the renormalization group flow of the corresponding ladder is towards the $d$-Mott phase, a gapped spin-liquid with short-ranged $d$-wave pairing correlations, and reveals an intermediate $$\mathrm{SO}(5)\times{}\mathrm{SO}(3)$$ symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a nonuniversal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.

Authors:
 [1];  [2];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics & Materials Science Division
  2. Univ. of Amsterdam (Netherlands). Inst. for Theoretical Physics
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of Amsterdam (Netherlands)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Alexander von Humboldt Foundation; European Union (EU)
OSTI Identifier:
1501561
Alternate Identifier(s):
OSTI ID: 1502809; OSTI ID: 1546183
Report Number(s):
BNL-211403-2019-JAAM; BNL-211438-2019-JAAM
Journal ID: ISSN 2469-9950
Grant/Contract Number:  
SC0012704; 745944
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 11; 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; conductivity; 1-dimensional systems; high-temperature superconductors; bosonization; renormalization group

Citation Formats

Classen, Laura, Robinson, Neil J., and Tsvelik, Alexei M. Ladderlike optical conductivity in the spin-fermion model. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.115110.
Classen, Laura, Robinson, Neil J., & Tsvelik, Alexei M. Ladderlike optical conductivity in the spin-fermion model. United States. doi:10.1103/PhysRevB.99.115110.
Classen, Laura, Robinson, Neil J., and Tsvelik, Alexei M. Thu . "Ladderlike optical conductivity in the spin-fermion model". United States. doi:10.1103/PhysRevB.99.115110.
@article{osti_1501561,
title = {Ladderlike optical conductivity in the spin-fermion model},
author = {Classen, Laura and Robinson, Neil J. and Tsvelik, Alexei M.},
abstractNote = {In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show here that the renormalization group flow of the corresponding ladder is towards the $d$-Mott phase, a gapped spin-liquid with short-ranged $d$-wave pairing correlations, and reveals an intermediate $\mathrm{SO}(5)\times{}\mathrm{SO}(3)$ symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a nonuniversal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.},
doi = {10.1103/PhysRevB.99.115110},
journal = {Physical Review B},
number = 11,
volume = 99,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
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Works referenced in this record:

Exact zero-temperature correlation functions for two-leg Hubbard ladders and carbon nanotubes
journal, September 2001


Optical Conductivity of One-Dimensional Mott Insulators
journal, January 2001


Spectroscopic evidence for Fermi liquid-like energy and temperature dependence of the relaxation rate in the pseudogap phase of the cuprates
journal, March 2013

  • Mirzaei, S. I.; Stricker, D.; Hancock, J. N.
  • Proceedings of the National Academy of Sciences, Vol. 110, Issue 15
  • DOI: 10.1073/pnas.1218846110

Renormalized SO(5) Symmetry in Ladders with Next-Nearest-Neighbor Hopping
journal, March 1999


Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods
journal, February 2018

  • James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe
  • Reports on Progress in Physics, Vol. 81, Issue 4
  • DOI: 10.1088/1361-6633/aa91ea

Role of Umklapp processes in the conductivity of doped two-leg ladders
journal, October 2002


Excitation spectrum of doped two-leg ladders: A field theory analysis
journal, July 2005


Anomalous Scaling at the Quantum Critical Point in Itinerant Antiferromagnets
journal, December 2004


Conductivity of a Clean One-Dimensional Wire
journal, July 2000


Band-Structure Effects in Itinerant Antiferromagnetism
journal, November 1970


Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions
journal, April 2017


Theory of the optical conductivity in the cuprate superconductors
journal, November 1997


Quantum critical response at the onset of spin-density-wave order in two-dimensional metals
journal, September 2011


Quantum phase transitions of metals in two spatial dimensions. II. Spin density wave order
journal, August 2010


Spin-Fermion Model near the Quantum Critical Point: One-Loop Renormalization Group Results
journal, June 2000


Finite wave vector pairing in doped two-leg ladders
journal, May 2012


Optical conductivity and resistivity of a hole-doped spin-fermion model for cuprates
journal, December 2002


Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
journal, February 1996


Homogeneous Dynamical Conductivity of Simple Metals
journal, August 1972


SO(5)-symmetric description of the low-energy sector of a ladder system
journal, September 1998


Phenomenology of the normal state in-plane transport properties of high- T c cuprates
journal, February 2008


Gauge theory for the cuprates near optimal doping
journal, February 2019


Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
journal, April 2014

  • Chubukov, Andrey V.; Maslov, Dmitrii L.; Yudson, Vladimir I.
  • Physical Review B, Vol. 89, Issue 15
  • DOI: 10.1103/PhysRevB.89.155126

Spin-gap fixed points in the double-chain problem
journal, July 1994


Heavy Fermions and Quantum Phase Transitions
journal, September 2010


Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis
journal, March 2003


Umklapp scattering as the origin of T -linear resistivity in the normal state of high- T c cuprate superconductors
journal, December 2017


Superconductivity in a spin liquid: A one-dimensional example
journal, June 1996


Weak-coupling phase diagram of the two-chain Hubbard model
journal, May 1996


SO ( 5 ) theory of antiferromagnetism and superconductivity
journal, November 2004

  • Demler, Eugene; Hanke, Werner; Zhang, Shou-Cheng
  • Reviews of Modern Physics, Vol. 76, Issue 3
  • DOI: 10.1103/RevModPhys.76.909

Experiments on ladders reveal a complex interplay between a spin-gapped normal state and superconductivity
journal, November 1999


The pseudogap state in high- superconductors: an infrared study
journal, November 1996


Sign-Problem-Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals
journal, December 2012


Colloquium : Theory of intertwined orders in high temperature superconductors
journal, May 2015

  • Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
  • Reviews of Modern Physics, Vol. 87, Issue 2
  • DOI: 10.1103/RevModPhys.87.457

Heavy-fermion systems
journal, October 1984


Effect of Ni impurities on the optical properties of YBa 2 Cu 3 O 6 + y
journal, October 1999


SO(5) symmetric ladder
journal, July 1998


The pseudogap: friend or foe of high T c ?
journal, December 2005


The pseudogap in high-temperature superconductors: an experimental survey
journal, January 1999


Interplay of magnetism and superconductivity
journal, September 2006


Optical conductivity and kinetic energy of the superconducting state: A cluster dynamical mean field study
journal, January 2007


Spinful fermionic ladders at incommensurate filling: Phase diagram, local perturbations, and ionic potentials
journal, December 2013


Umklapp process and resistivity in one-dimensional fermion systems
journal, August 1991


Ladder physics in the spin fermion model
journal, May 2017


Universality in antiferromagnetic strange metals
journal, April 2016


Quasilocal strange metal
journal, March 2015


Competing Orders in a Nearly Antiferromagnetic Metal
journal, August 2016


Effect of Hund coupling in the one-dimensional SU(4) Hubbard model
journal, April 2004


Optical conductivity of a t J ladder
journal, April 1996


Energy gaps in high-transition-temperature cuprate superconductors
journal, June 2014

  • Hashimoto, Makoto; Vishik, Inna M.; He, Rui-Hua
  • Nature Physics, Vol. 10, Issue 7
  • DOI: 10.1038/nphys3009

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

  • Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
  • Reviews of Modern Physics, Vol. 78, Issue 1
  • DOI: 10.1103/RevModPhys.78.17

Dynamical spin response of doped two-leg Hubbard-like ladders
journal, April 2007


Exact SO(8) symmetry in the weakly-interacting two-leg ladder
journal, July 1998


Emergence of a control parameter for the antiferromagnetic quantum critical metal
journal, June 2017


Pair-density-wave superconducting order in two-leg ladders
journal, January 2012